From c419978aa7f6f16de6dcd78ea2d8756d855b49b0 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Tue, 2 Jun 2026 14:45:12 +0100 Subject: [PATCH 1/8] Add GPConfig passthrough, export and tests Expose and forward AutoGP GPConfig through the wrapper: export GPConfig from the package and accept a config keyword in make_and_fit_model, passing it into AutoGP.GPModel. The make_and_fit_model docs and examples were updated to document the config argument and to clarify that most options (including n_mcmc/n_hmc) are forwarded as kwargs to AutoGP.fit_smc! rather than being wrapper defaults. The SMC call now forwards kwargs unmodified (so callers must provide n_mcmc/n_hmc), and schedule calculation keeps the previous guard for small datasets. Documentation (.github/copilot-instructions.md) was updated to reflect the new passthrough semantics. Added tests (test/test_gpconfig.jl) to verify GPConfig forwarding, custom kernel/prior propagation, and that omitting required passthrough kwargs (n_mcmc/n_hmc) surfaces an error. --- .github/copilot-instructions.md | 13 ++++---- src/NowcastAutoGP.jl | 3 +- src/make_and_fit_model.jl | 55 ++++++++++++++++++++++++++------- test/test_gpconfig.jl | 43 ++++++++++++++++++++++++++ 4 files changed, 96 insertions(+), 18 deletions(-) create mode 100644 test/test_gpconfig.jl diff --git a/.github/copilot-instructions.md b/.github/copilot-instructions.md index 514329a..b9a379d 100644 --- a/.github/copilot-instructions.md +++ b/.github/copilot-instructions.md @@ -15,7 +15,7 @@ NowcastAutoGP.jl is a **Julia package for forecasting with nowcasting** that com ### Main Pipeline (see `docs/vignettes/tutorial.qmd` for complete example) 1. **Transform Data**: `create_transformed_data(dates, values; transformation)` using `get_transformations()` -2. **Fit Base Model**: `make_and_fit_model(data)` on historical "confirmed" data +2. **Fit Base Model**: `make_and_fit_model(data; n_mcmc=200, n_hmc=50)` on historical "confirmed" data (`n_mcmc`/`n_hmc` are required pass-through kwargs of `AutoGP.fit_smc!`) 3. **Create Nowcasts**: Generate multiple `TData` objects representing uncertain recent data scenarios 4. **Forecast with Uncertainty**: `forecast_with_nowcasts()` temporarily adds each nowcast to model, generates forecasts, then removes it @@ -40,14 +40,15 @@ NowcastAutoGP.jl is a **Julia package for forecasting with nowcasting** that com ```julia # Standard pattern for fitting model = make_and_fit_model(data; - n_particles=8, # SMC particles - smc_data_proportion=0.1, # Data proportion per SMC step - n_mcmc=200, # MCMC structure steps - n_hmc=50 # HMC parameter steps + n_particles=8, # SMC particles (forwarded to AutoGP.GPModel) + smc_data_proportion=0.1, # Data proportion per SMC step (wrapper-only; builds the schedule) + config=GPConfig(), # GP prior; pass a customised GPConfig() to change kernel structure / priors + n_mcmc=200, # forwarded to AutoGP.fit_smc! via kwargs... + n_hmc=50 # forwarded to AutoGP.fit_smc! via kwargs... ) ``` -**Key Implementation Detail**: `effective_proportion = max(smc_data_proportion, 1.0/n_train)` prevents schedule step=0 errors with small datasets. +**Key Implementation Detail**: Only `n_particles`, `smc_data_proportion`, and `config` are named wrapper kwargs; everything else (`n_mcmc`, `n_hmc`, `hmc_config`, `biased`, `shuffle`, `verbose`, …) is passed straight through `kwargs...` to `AutoGP.fit_smc!` rather than re-declared here. `effective_proportion = max(smc_data_proportion, 1.0/n_train)` prevents schedule step=0 errors with small datasets. ## Forecasting with Nowcasts (`src/forecasting.jl`) diff --git a/src/NowcastAutoGP.jl b/src/NowcastAutoGP.jl index 3d758ad..0780eb3 100644 --- a/src/NowcastAutoGP.jl +++ b/src/NowcastAutoGP.jl @@ -6,7 +6,8 @@ using LogExpFunctions: logit, logistic using ProgressMeter: @showprogress, Progress, next! const GPModel = AutoGP.GPModel # re-exporting for convenience -export TData, GPModel +const GPConfig = AutoGP.GP.GPConfig # re-exporting for convenience +export TData, GPModel, GPConfig export create_transformed_data, get_transformations, make_and_fit_model, forecast, forecast_with_nowcasts, create_nowcast_data diff --git a/src/make_and_fit_model.jl b/src/make_and_fit_model.jl index 20285e0..3d3c08a 100644 --- a/src/make_and_fit_model.jl +++ b/src/make_and_fit_model.jl @@ -14,7 +14,7 @@ This is a secondary safety net for data that is flat even after transformation. common case of a pathological Box-Cox λ on otherwise-fittable data is handled earlier, in [`get_transformations`](@ref), by falling back to a log transformation. """ -function _stabilize_for_fit(y::AbstractVector{<:Real}; flat_threshold = 1.0e-3) +function _stabilize_for_fit(y::AbstractVector{<:Real}; flat_threshold) n = length(y) n > 1 || return y scale = abs(sum(y) / n) + 1 @@ -27,34 +27,67 @@ jitter (σ = $σ) so the GP covariance stays positive-definite (issue #51)." end """ - make_and_fit_model(data; n_particles=8, smc_data_proportion=0.1, n_mcmc=200, n_hmc=50, flat_threshold=1.0e-3, kwargs...) + function make_and_fit_model( + data::TData; n_particles, smc_data_proportion, + flat_threshold = 1.0e-3, config = AutoGP.GP.GPConfig(), kwargs... + ) Create and fit a Gaussian Process (GP) model using Sequential Monte Carlo (SMC) sampling. # Arguments - `data`: A data structure containing the dataset (`data.ds`) and the target values (`data.y`). -- `n_particles`: The number of particles to use in the SMC sampling (default: 8). -- `smc_data_proportion`: The proportion of the data to use in each SMC step (default: 0.1). -- `n_mcmc`: The number of MCMC samples (default: 200). -- `n_hmc`: The number of HMC samples (default: 50). +- `n_particles`: The number of particles to use in the SMC sampling. +- `smc_data_proportion`: The proportion of the data to use in each SMC step. - `flat_threshold`: If the (transformed) target's relative range is below this, small Gaussian jitter is added so the GP covariance stays positive-definite (default: 1.0e-3). Series with enough spread are left untouched, preserving existing behaviour. -- `kwargs...`: Additional keyword arguments to pass to the `AutoGP.fit_smc!` function. +- `config`: An `AutoGP.GP.GPConfig` describing the GP prior — kernel-structure distribution + (`node_dist_leaf`/`node_dist_nocp`/`node_dist_cp`) and hyperparameter priors + (`prior[:gamma]`/`prior[:period]`/`prior[:wildcard]`). Defaults to `GPConfig()` (AutoGP defaults), + so existing behaviour is unchanged. Build a customised one with the `GPConfig` keyword + constructor — see Examples. +- `kwargs...`: Additional keyword arguments forwarded to `AutoGP.fit_smc!`. Note that `fit_smc!` + *requires* `n_mcmc` and `n_hmc` (number of MCMC structure steps and HMC parameter steps per SMC + step), so these must be supplied here; other `fit_smc!` options (e.g. `hmc_config`, `biased`, + `shuffle`, `verbose`) may also be passed. # Returns - `model`: The fitted GP model. + +# Examples +```julia +# Default prior: +model = make_and_fit_model(data; n_mcmc = 200, n_hmc = 50) + +# Custom prior — pass a GPConfig. Kernel-structure fields go straight to the constructor, +# e.g. give SquaredExponential (code 3) leaf-kernel prior mass: +config = GPConfig(node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25]) +model = make_and_fit_model(data; config = config, n_mcmc = 200, n_hmc = 50) + +# To tweak a single nested prior entry (e.g. re-centre the periodic component near an annual +# cycle) copy the default prior and update the leaf: +prior = deepcopy(GPConfig().prior) +prior[:period][:mu] = log(1.0) +model = make_and_fit_model(data; config = GPConfig(prior = prior), n_mcmc = 200, n_hmc = 50) +``` + +`@set` from [Accessors.jl](https://github.com/JuliaObjects/Accessors.jl) is a handy alternative +for these copy-and-update edits if you have it in your environment +(`config = @set GPConfig().prior[:period][:mu] = log(1.0)`); it is not a dependency of this package. """ function make_and_fit_model( - data::TData; n_particles = 8, smc_data_proportion = 0.1, - n_mcmc = 200, n_hmc = 50, flat_threshold = 1.0e-3, kwargs... + data::TData; n_particles, smc_data_proportion, + flat_threshold = 1.0e-3, config = AutoGP.GP.GPConfig(), kwargs... ) n_train = length(data.y) y_fit = _stabilize_for_fit(data.y; flat_threshold = flat_threshold) - model = AutoGP.GPModel(data.ds, y_fit; n_particles = n_particles) + model = AutoGP.GPModel( + data.ds, y_fit; n_particles = n_particles, + config = config + ) # Ensure smc_data_proportion results in at least step=1 for the schedule effective_proportion = max(smc_data_proportion, 1.0 / n_train) schedule = AutoGP.Schedule.linear_schedule(n_train, effective_proportion) - AutoGP.fit_smc!(model; schedule = schedule, n_mcmc = n_mcmc, n_hmc = n_hmc, kwargs...) + AutoGP.fit_smc!(model; schedule = schedule, kwargs...) return model end diff --git a/test/test_gpconfig.jl b/test/test_gpconfig.jl new file mode 100644 index 0000000..acd4736 --- /dev/null +++ b/test/test_gpconfig.jl @@ -0,0 +1,43 @@ +@testitem "make_and_fit_model forwards config to GPModel" setup = [ModelFittingData] begin + data = create_transformed_data(dates, values; transformation = identity) + + cfg = GPConfig() + model = make_and_fit_model(data; config = cfg, test_params...) + + @test model isa AutoGP.GPModel + # config is stored by reference on the GPModel, so the exact object should round-trip + @test model.config === cfg +end + +@testitem "make_and_fit_model forwards a customised kernel-structure config" setup = [ModelFittingData] begin + data = create_transformed_data(dates, values; transformation = identity) + + cfg = GPConfig(node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25], changepoints = false) + model = make_and_fit_model(data; config = cfg, test_params...) + + @test model.config.node_dist_leaf == [0.0, 0.25, 0.25, 0.25, 0.25] + @test model.config.changepoints == false +end + +@testitem "make_and_fit_model forwards a custom prior" setup = [ModelFittingData] begin + data = create_transformed_data(dates, values; transformation = identity) + + # copy-and-update a single nested prior entry (the documented dependency-free pattern) + prior = deepcopy(GPConfig().prior) + prior[:period][:mu] = log(1.0) + cfg = GPConfig(prior = prior) + model = make_and_fit_model(data; config = cfg, test_params...) + + @test model.config.prior[:period][:mu] == log(1.0) + # untouched sibling entries keep their defaults + @test model.config.prior[:period][:sigma] == GPConfig().prior[:period][:sigma] + @test model.config.prior[:gamma] == GPConfig().prior[:gamma] +end + +@testitem "make_and_fit_model requires n_mcmc/n_hmc (pure passthrough)" setup = [ModelFittingData] begin + data = create_transformed_data(dates, values; transformation = identity) + + # n_mcmc / n_hmc are now required pass-through kwargs of AutoGP.fit_smc!, + # so omitting them surfaces as an UndefKeywordError rather than a wrapper default. + @test_throws UndefKeywordError make_and_fit_model(data; n_particles = 1) +end From fac5d2476f9b4c5623407941d19abfc9e24e4af9 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Tue, 2 Jun 2026 17:14:02 +0100 Subject: [PATCH 2/8] setting priors vignette first pass --- docs/Project.toml | 1 + docs/make.jl | 1 + docs/make_vignettes.jl | 6 +- docs/src/vignettes/setting-priors-11.png | Bin 0 -> 96847 bytes docs/src/vignettes/setting-priors-19.png | Bin 0 -> 295510 bytes docs/src/vignettes/setting-priors-23.png | Bin 0 -> 49602 bytes docs/src/vignettes/setting-priors.md | 369 +++++++++++++++++++++++ docs/vignettes/setting-priors.jl | 298 ++++++++++++++++++ 8 files changed, 674 insertions(+), 1 deletion(-) create mode 100644 docs/src/vignettes/setting-priors-11.png create mode 100644 docs/src/vignettes/setting-priors-19.png create mode 100644 docs/src/vignettes/setting-priors-23.png create mode 100644 docs/src/vignettes/setting-priors.md create mode 100644 docs/vignettes/setting-priors.jl diff --git a/docs/Project.toml b/docs/Project.toml index ec44a3e..a7dcdfe 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,4 +1,5 @@ [deps] +Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697" AutoGP = "6eb593e7-dfb4-4e48-b98e-d7222cdf0053" CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" diff --git a/docs/make.jl b/docs/make.jl index c5fedf1..1169047 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -7,6 +7,7 @@ pages = [ "Getting Started" => "vignettes/getting-started.md", "Tutorials" => [ "vignettes/use-percentages.md", + "vignettes/setting-priors.md", ], "API Reference" => "api.md", ] diff --git a/docs/make_vignettes.jl b/docs/make_vignettes.jl index 30ceb20..ea39b4e 100644 --- a/docs/make_vignettes.jl +++ b/docs/make_vignettes.jl @@ -1,5 +1,9 @@ using Literate -vignettes_to_make = ["getting-started.jl", "use-percentages.jl"] +vignettes_to_make = [ + # "getting-started.jl", + # 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zh5`T`hUo?;lBt3F^erqbAT+ia6x-UPJOzU@B_eB;_zXrebm-7(L+BYTp0NOz>)Z?C znr|06ii!(SuPVK;TSBH}1V~5+FCaMw%q$?|fnG6j-D*asZq`al2tjx&iRmzYaQNmu6lNK}o? zo8+9r!mYIMRVFZ?KNSf~(wAf-+a*gr6K>x$^!)i@q&N00F0ZP};V%7c1!w@3?00~jA=0L|IO53z!^Vx_ zJ}yR~WdO~T%rbUj4QqcOS8=?o_(1ZNNP*7{rNMr8>~s7%WGEog69;;z=7)k#1urno zwOWIhPF=aS*@iA%I(9T8NHe*J4%yJ@gGX63oSrJ;-IdT6|K^2|%x(ZyUa|kxA&O&K zk!P1c{u77f^S>vp^||x~_%Hq3 bP3`-;G!`t2436V*n~gW0H1?>O)6f3{ICo2w literal 0 HcmV?d00001 diff --git a/docs/src/vignettes/setting-priors.md b/docs/src/vignettes/setting-priors.md new file mode 100644 index 0000000..0f4606a --- /dev/null +++ b/docs/src/vignettes/setting-priors.md @@ -0,0 +1,369 @@ +````julia +using Markdown +```` + +# Setting GP priors with `Accessors.jl` + +*Customising the AutoGP prior for epidemiological seasonality* + +**CDC Center for Forecasting and Outbreak Analytics (CFA/CDC)** + +`make_and_fit_model` accepts a `config` keyword — an `AutoGP.GP.GPConfig` that describes the +Gaussian-process **prior**: the distribution over kernel *structures* +(`node_dist_leaf`/`node_dist_nocp`/`node_dist_cp`) and the priors over kernel *hyperparameters* +(`prior[:gamma]`, `prior[:period]`, `prior[:wildcard]`). The default `GPConfig()` reproduces +AutoGP's out-of-the-box behaviour, but its **period prior** is centred well below an annual cycle, so +a periodic component is unlikely to land on the ~1-year seasonality respiratory diseases actually have. + +`GPConfig` is an immutable struct with a nested `prior` `Dict`, which makes "change just this one +field" awkward to write by hand. [`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s +`@set` macro does exactly that: it returns a *copy* with a single leaf changed and every sibling +preserved. This vignette inspects the default prior, re-centres the period prior with `@set`, and — +following the scoring approach of the [Getting started](getting-started.md) vignette — shows the +re-centred prior gives better forecasts across a few **report dates** spanning one seasonal cycle, +measured by the Continuous Ranked Probability Score (CRPS). + +> `Accessors.jl` is a convenience used here in the docs; it is **not** a dependency of +> `NowcastAutoGP` itself. The same edits can be made by constructing a `GPConfig` directly. + +## Loading dependencies + +````julia +using NowcastAutoGP +using Accessors +using CairoMakie +using Dates, Distributions, Random + +Random.seed!(2026) +CairoMakie.activate!(type = "png") +```` + +## Inspecting the default prior + +`GPConfig()` exposes the prior as plain fields. The leaf-kernel distribution is a probability vector +over the primitive kernels, indexed `Constant=1`, `Linear=2`, `SquaredExponential=3`, +`GammaExponential=4`, `Periodic=5`: + +````julia +default_config = GPConfig() +default_config.node_dist_leaf +```` + +```` +5-element Vector{Float64}: + 0.0 + 0.3333333333333333 + 0.0 + 0.3333333333333333 + 0.3333333333333333 +```` + +The hyperparameter priors live in a nested `Dict`; the period prior is a `LogNormal(μ, σ)` over the +periodic component's period: + +````julia +default_config.prior[:period] +```` + +```` +Dict{Symbol, Float64} with 2 entries: + :mu => -1.5 + :sigma => 1.0 +```` + +AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units — +a fraction of the training window. The default median period is therefore only about a fifth of the +window: + +````julia +exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window +```` + +```` +0.22313016014842982 +```` + +## A seasonal series and a few report dates + +We simulate two years of weekly observations with a clear annual cycle, a gentle upward trend and +observation noise. We then imagine sitting at three **report dates** — weeks 26, 39 and 52 (a half, +three-quarters and a full cycle of history) — and at each one forecast a full year ahead. This +mirrors the [Getting started](getting-started.md) workflow of scoring forecasts across report dates +as data accrue. + +````julia +start_date = Date(2022, 1, 1) +all_dates = collect(start_date:Week(1):(start_date + Week(103))) # 104 weekly points ≈ 2 years +n_all = length(all_dates) +tt = 0:(n_all - 1) +truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.08 .* tt # annual cycle (52 weeks) + trend +observations = truth .+ 2.0 .* randn(n_all) + +report_weeks = [26, 39, 52] +horizon = 52 # forecast one year ahead +report_colours = [:steelblue, :darkorange, :seagreen] + +fig_data = let + fig = Figure(size = (820, 400)) + ax = Axis(fig[1, 1]; xlabel = "week", ylabel = "value", title = "Synthetic weekly series") + lines!(ax, Dates.value.(all_dates), truth; color = :black, label = "signal") + scatter!(ax, Dates.value.(all_dates), observations; color = (:black, 0.3), markersize = 5) + vlines!( + ax, Dates.value.(all_dates[report_weeks]); + color = report_colours, linestyle = :dash, linewidth = 2 + ) + axislegend(ax; position = :lt) + fig +end +```` +![](setting-priors-11.png) + +## Re-centring the period prior with `@set` + +A one-year cycle is 52 weeks. In a window of `w` weeks that is a period of `52 / w` in AutoGP's +normalised time, so we re-centre the period prior's median there by setting `μ = log(52 / w)`, and +tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, for example: + +````julia +example_window = 39 +seasonal_example = @set GPConfig().prior[:period][:mu] = log(52 / example_window) +seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.3 +seasonal_example.prior[:period] +```` + +```` +Dict{Symbol, Float64} with 2 entries: + :mu => 0.287682 + :sigma => 0.3 +```` + +`@set` returns a fresh `GPConfig`; every sibling prior is carried over unchanged — it only touched +`prior[:period]`: + +````julia +seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] +```` + +```` +true +```` + +## Forecasting from each report date + +At each report date we fit two models on the data so far — one with the default prior, one with a +seasonal prior built for that window with `@set` — and forecast a year ahead. Everything except +`config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. Each +fitted model is a particle ensemble, so each forecast is a full predictive *distribution* — exactly +what CRPS scores below. + +````julia +fit_params = (n_particles = 16, smc_data_proportion = 0.1, n_mcmc = 75, n_hmc = 15) +n_draws = 300 + +Random.seed!(2026) +results = map(report_weeks) do w + train_data = create_transformed_data( + all_dates[1:w], observations[1:w]; transformation = identity + ) + horizon_dates = all_dates[(w + 1):(w + horizon)] + horizon_truth = truth[(w + 1):(w + horizon)] + + # a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time + seasonal_config = @set GPConfig().prior[:period][:mu] = log(52 / w) + seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 + + default_model = make_and_fit_model(train_data; config = GPConfig(), fit_params...) + seasonal_model = make_and_fit_model(train_data; config = seasonal_config, fit_params...) + + return (; + report_week = w, horizon_dates, horizon_truth, + default = forecast(default_model, horizon_dates, n_draws), + seasonal = forecast(seasonal_model, horizon_dates, n_draws), + ) +end +```` + +```` +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 + +```` + +The default prior (top) tends to extrapolate short cycles or flat trends, while the seasonal prior +(bottom) carries the annual cycle forward. Once three-quarters of a cycle is in view (weeks 39 and 52) +it stays close to the truth (dashed); from only half a cycle (week 26) the annual assumption is a +large extrapolation and overshoots: + +````julia +fig_forecasts = let + fig = Figure(size = (920, 720)) + panels = ( + (key = :default, row = 1, title = "Default prior"), + (key = :seasonal, row = 2, title = "Seasonal prior (re-centred with @set)"), + ) + for panel in panels + ax = Axis(fig[panel.row, 1]; xlabel = "week", ylabel = "value", title = panel.title) + lines!( + ax, Dates.value.(all_dates), truth; + color = :black, linestyle = :dash, label = "truth" + ) + for (res, colour) in zip(results, report_colours) + fc = getproperty(res, panel.key) + fx = Dates.value.(res.horizon_dates) + lower = [quantile(row, 0.25) for row in eachrow(fc)] + med = [quantile(row, 0.5) for row in eachrow(fc)] + upper = [quantile(row, 0.75) for row in eachrow(fc)] + band!(ax, fx, lower, upper; color = (colour, 0.2)) + lines!(ax, fx, med; color = colour, linewidth = 2.5, label = "from week $(res.report_week)") + end + panel.row == 1 && axislegend(ax; position = :lt, nbanks = 2) + end + fig +end +```` +![](setting-priors-19.png) + +## Scoring with CRPS + +This is a probabilistic model, so we score each predictive *distribution* against the value it should +have predicted using the **Continuous Ranked Probability Score (CRPS)** — the proper scoring rule from +the [Getting started](getting-started.md) vignette (lower is better), reusing the same hand-rolled +estimator: + +```math +\text{CRPS}(X, y) = \mathbb{E}[|X - y|] - \frac{1}{2}\mathbb{E}[|X_1 - X_2|] +``` + +The score is then **averaged over the forecasts** — every week of each report date's one-year-ahead +horizon — which is how a probabilistic forecast is evaluated (no repeated simulations required): + +````julia +# Hand-rolled CRPS estimator (reproduced from the Getting started vignette). +function crps(y::Real, X::Vector{<:Real}) + n = length(X) + + # First term: E|X - y| + term1 = mean(abs.(X .- y)) + + # Second term: E|X_1 - X_2| over all ordered pairs + ordered_pairwise_diffs = [abs(X[i] - X[j]) for i in 1:n for j in (i + 1):n] + term2 = mean(ordered_pairwise_diffs) + + # CRPS = E|X - y| - 0.5 * E|X_1 - X_2| + return term1 - 0.5 * term2 +end + +# mean CRPS over a forecast horizon for a (dates × draws) forecast matrix +mean_crps(truth, fc) = mean(crps(y, collect(X)) for (y, X) in zip(truth, eachrow(fc))) + +crps_by_date = map(results) do res + (; + report_week = res.report_week, + default = mean_crps(res.horizon_truth, res.default), + seasonal = mean_crps(res.horizon_truth, res.seasonal), + ) +end +```` + +```` +3-element Vector{@NamedTuple{report_week::Int64, default::Float64, seasonal::Float64}}: + (report_week = 26, default = 8.145047072851177, seasonal = 9.299402943763948) + (report_week = 39, default = 7.139662993075851, seasonal = 4.4957906600468425) + (report_week = 52, default = 5.006893616792975, seasonal = 3.268268898264733) +```` + +The seasonal prior is clearly better once enough of the cycle is in view — a much lower CRPS at weeks +39 and 52. At week 26, with only half a cycle observed, the annual assumption overshoots and scores a +little worse: a useful reminder that a prior is an assumption, most valuable when the data can support +it: + +````julia +fig_scores = let + n = length(crps_by_date) + defaults = [row.default for row in crps_by_date] + seasonals = [row.seasonal for row in crps_by_date] + + fig = Figure(size = (640, 400)) + ax = Axis( + fig[1, 1]; + xticks = (1:n, ["week $(row.report_week)" for row in crps_by_date]), + ylabel = "mean CRPS (lower is better)", + title = "Forecast skill by report date" + ) + barplot!( + ax, repeat(1:n, 2), vcat(defaults, seasonals); + dodge = vcat(fill(1, n), fill(2, n)), + color = vcat(fill(:tomato, n), fill(:steelblue, n)) + ) + Legend( + fig[1, 2], + [PolyElement(color = :tomato), PolyElement(color = :steelblue)], + ["default", "seasonal"] + ) + fig +end +```` +![](setting-priors-23.png) + +Averaged over the three report dates the seasonal prior still comes out ahead overall: + +````julia +overall_crps = (; + default = mean(row.default for row in crps_by_date), + seasonal = mean(row.seasonal for row in crps_by_date), +) +```` + +```` +(default = 6.7638678942400015, seasonal = 5.687820834025175) +```` + +## Enabling `SquaredExponential` structure + +The leaf-kernel distribution is editable the same way. The default gives `SquaredExponential` +(index 3) **zero** prior mass; `@set` can spread mass evenly over `Linear`, `SquaredExponential`, +`GammaExponential` and `Periodic` (the vector must sum to 1): + +````julia +se_config = @set GPConfig().node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25] +se_config.node_dist_leaf +```` + +```` +5-element Vector{Float64}: + 0.0 + 0.25 + 0.25 + 0.25 + 0.25 +```` + +`se_config` can be passed to `make_and_fit_model(...; config = se_config)` exactly like the seasonal +one, and edits compose — chain further `@set` calls (or use `@reset`) to adjust the period prior *and* +the kernel distribution together. + +## Summary + +- `make_and_fit_model(...; config = ...)` forwards any `AutoGP.GP.GPConfig` to the model, so the full + AutoGP prior is available without re-declaring it in `NowcastAutoGP`. +- `Accessors.@set` is a clean way to change one prior entry while preserving the rest, including deep + edits into the nested `prior` `Dict`. +- Re-centring `prior[:period]` on the seasonality you expect improves forecasts once enough of the + cycle is in view — here, a lower mean CRPS over the report dates, with clear gains by weeks 39 and + 52. Like any prior it is an assumption: from only half a cycle it can overshoot, so score it (with + CRPS, averaged over the forecasts) rather than assuming it always helps. + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl new file mode 100644 index 0000000..7bf4410 --- /dev/null +++ b/docs/vignettes/setting-priors.jl @@ -0,0 +1,298 @@ +using Markdown +md""" +# Setting GP priors with `Accessors.jl` + +*Customising the AutoGP prior for epidemiological seasonality* + +**CDC Center for Forecasting and Outbreak Analytics (CFA/CDC)** + +`make_and_fit_model` accepts a `config` keyword — an `AutoGP.GP.GPConfig` that describes the +Gaussian-process **prior**: the distribution over kernel *structures* +(`node_dist_leaf`/`node_dist_nocp`/`node_dist_cp`) and the priors over kernel *hyperparameters* +(`prior[:gamma]`, `prior[:period]`, `prior[:wildcard]`). The default `GPConfig()` reproduces +AutoGP's out-of-the-box behaviour, but its **period prior** is centred well below an annual cycle, so +a periodic component is unlikely to land on the ~1-year seasonality respiratory diseases actually have. + +`GPConfig` is an immutable struct with a nested `prior` `Dict`, which makes "change just this one +field" awkward to write by hand. [`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s +`@set` macro does exactly that: it returns a *copy* with a single leaf changed and every sibling +preserved. This vignette inspects the default prior, re-centres the period prior with `@set`, and — +following the scoring approach of the [Getting started](getting-started.md) vignette — shows the +re-centred prior gives better forecasts across a few **report dates** spanning one seasonal cycle, +measured by the Continuous Ranked Probability Score (CRPS). + +> `Accessors.jl` is a convenience used here in the docs; it is **not** a dependency of +> `NowcastAutoGP` itself. The same edits can be made by constructing a `GPConfig` directly. + +## Loading dependencies +""" + +using NowcastAutoGP +using Accessors +using CairoMakie +using Dates, Distributions, Random + +Random.seed!(2026) +CairoMakie.activate!(type = "png") +nothing #hide + +md""" +## Inspecting the default prior + +`GPConfig()` exposes the prior as plain fields. The leaf-kernel distribution is a probability vector +over the primitive kernels, indexed `Constant=1`, `Linear=2`, `SquaredExponential=3`, +`GammaExponential=4`, `Periodic=5`: +""" + +default_config = GPConfig() +default_config.node_dist_leaf + +md""" +The hyperparameter priors live in a nested `Dict`; the period prior is a `LogNormal(μ, σ)` over the +periodic component's period: +""" + +default_config.prior[:period] + +md""" +AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units — +a fraction of the training window. The default median period is therefore only about a fifth of the +window: +""" + +exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window + +md""" +## A seasonal series and a few report dates + +We simulate two years of weekly observations with a clear annual cycle, a gentle upward trend and +observation noise. We then imagine sitting at three **report dates** — weeks 26, 39 and 52 (a half, +three-quarters and a full cycle of history) — and at each one forecast a full year ahead. This +mirrors the [Getting started](getting-started.md) workflow of scoring forecasts across report dates +as data accrue. +""" + +start_date = Date(2022, 1, 1) +all_dates = collect(start_date:Week(1):(start_date + Week(103))) # 104 weekly points ≈ 2 years +n_all = length(all_dates) +tt = 0:(n_all - 1) +truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.08 .* tt # annual cycle (52 weeks) + trend +observations = truth .+ 2.0 .* randn(n_all) + +report_weeks = [26, 39, 52] +horizon = 52 # forecast one year ahead +report_colours = [:steelblue, :darkorange, :seagreen] +nothing #hide + +fig_data = let + fig = Figure(size = (820, 400)) + ax = Axis(fig[1, 1]; xlabel = "week", ylabel = "value", title = "Synthetic weekly series") + lines!(ax, Dates.value.(all_dates), truth; color = :black, label = "signal") + scatter!(ax, Dates.value.(all_dates), observations; color = (:black, 0.3), markersize = 5) + vlines!( + ax, Dates.value.(all_dates[report_weeks]); + color = report_colours, linestyle = :dash, linewidth = 2 + ) + axislegend(ax; position = :lt) + fig +end + +md""" +## Re-centring the period prior with `@set` + +A one-year cycle is 52 weeks. In a window of `w` weeks that is a period of `52 / w` in AutoGP's +normalised time, so we re-centre the period prior's median there by setting `μ = log(52 / w)`, and +tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, for example: +""" + +example_window = 39 +seasonal_example = @set GPConfig().prior[:period][:mu] = log(52 / example_window) +seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.3 +seasonal_example.prior[:period] + +md""" +`@set` returns a fresh `GPConfig`; every sibling prior is carried over unchanged — it only touched +`prior[:period]`: +""" + +seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] + +md""" +## Forecasting from each report date + +At each report date we fit two models on the data so far — one with the default prior, one with a +seasonal prior built for that window with `@set` — and forecast a year ahead. Everything except +`config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. Each +fitted model is a particle ensemble, so each forecast is a full predictive *distribution* — exactly +what CRPS scores below. +""" + +fit_params = (n_particles = 16, smc_data_proportion = 0.1, n_mcmc = 75, n_hmc = 15) +n_draws = 300 + +Random.seed!(2026) +results = map(report_weeks) do w + train_data = create_transformed_data( + all_dates[1:w], observations[1:w]; transformation = identity + ) + horizon_dates = all_dates[(w + 1):(w + horizon)] + horizon_truth = truth[(w + 1):(w + horizon)] + + ## a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time + seasonal_config = @set GPConfig().prior[:period][:mu] = log(52 / w) + seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 + + default_model = make_and_fit_model(train_data; config = GPConfig(), fit_params...) + seasonal_model = make_and_fit_model(train_data; config = seasonal_config, fit_params...) + + return (; + report_week = w, horizon_dates, horizon_truth, + default = forecast(default_model, horizon_dates, n_draws), + seasonal = forecast(seasonal_model, horizon_dates, n_draws), + ) +end +nothing #hide + +md""" +The default prior (top) tends to extrapolate short cycles or flat trends, while the seasonal prior +(bottom) carries the annual cycle forward. Once three-quarters of a cycle is in view (weeks 39 and 52) +it stays close to the truth (dashed); from only half a cycle (week 26) the annual assumption is a +large extrapolation and overshoots: +""" + +fig_forecasts = let + fig = Figure(size = (920, 720)) + panels = ( + (key = :default, row = 1, title = "Default prior"), + (key = :seasonal, row = 2, title = "Seasonal prior (re-centred with @set)"), + ) + for panel in panels + ax = Axis(fig[panel.row, 1]; xlabel = "week", ylabel = "value", title = panel.title) + lines!( + ax, Dates.value.(all_dates), truth; + color = :black, linestyle = :dash, label = "truth" + ) + for (res, colour) in zip(results, report_colours) + fc = getproperty(res, panel.key) + fx = Dates.value.(res.horizon_dates) + lower = [quantile(row, 0.25) for row in eachrow(fc)] + med = [quantile(row, 0.5) for row in eachrow(fc)] + upper = [quantile(row, 0.75) for row in eachrow(fc)] + band!(ax, fx, lower, upper; color = (colour, 0.2)) + lines!(ax, fx, med; color = colour, linewidth = 2.5, label = "from week $(res.report_week)") + end + panel.row == 1 && axislegend(ax; position = :lt, nbanks = 2) + end + fig +end + +md""" +## Scoring with CRPS + +This is a probabilistic model, so we score each predictive *distribution* against the value it should +have predicted using the **Continuous Ranked Probability Score (CRPS)** — the proper scoring rule from +the [Getting started](getting-started.md) vignette (lower is better), reusing the same hand-rolled +estimator: + +```math +\text{CRPS}(X, y) = \mathbb{E}[|X - y|] - \frac{1}{2}\mathbb{E}[|X_1 - X_2|] +``` + +The score is then **averaged over the forecasts** — every week of each report date's one-year-ahead +horizon — which is how a probabilistic forecast is evaluated (no repeated simulations required): +""" + +## Hand-rolled CRPS estimator (reproduced from the Getting started vignette). +function crps(y::Real, X::Vector{<:Real}) + n = length(X) + + ## First term: E|X - y| + term1 = mean(abs.(X .- y)) + + ## Second term: E|X_1 - X_2| over all ordered pairs + ordered_pairwise_diffs = [abs(X[i] - X[j]) for i in 1:n for j in (i + 1):n] + term2 = mean(ordered_pairwise_diffs) + + ## CRPS = E|X - y| - 0.5 * E|X_1 - X_2| + return term1 - 0.5 * term2 +end + +## mean CRPS over a forecast horizon for a (dates × draws) forecast matrix +mean_crps(truth, fc) = mean(crps(y, collect(X)) for (y, X) in zip(truth, eachrow(fc))) + +crps_by_date = map(results) do res + (; + report_week = res.report_week, + default = mean_crps(res.horizon_truth, res.default), + seasonal = mean_crps(res.horizon_truth, res.seasonal), + ) +end + +md""" +The seasonal prior is clearly better once enough of the cycle is in view — a much lower CRPS at weeks +39 and 52. At week 26, with only half a cycle observed, the annual assumption overshoots and scores a +little worse: a useful reminder that a prior is an assumption, most valuable when the data can support +it: +""" + +fig_scores = let + n = length(crps_by_date) + defaults = [row.default for row in crps_by_date] + seasonals = [row.seasonal for row in crps_by_date] + + fig = Figure(size = (640, 400)) + ax = Axis( + fig[1, 1]; + xticks = (1:n, ["week $(row.report_week)" for row in crps_by_date]), + ylabel = "mean CRPS (lower is better)", + title = "Forecast skill by report date" + ) + barplot!( + ax, repeat(1:n, 2), vcat(defaults, seasonals); + dodge = vcat(fill(1, n), fill(2, n)), + color = vcat(fill(:tomato, n), fill(:steelblue, n)) + ) + Legend( + fig[1, 2], + [PolyElement(color = :tomato), PolyElement(color = :steelblue)], + ["default", "seasonal"] + ) + fig +end + +md""" +Averaged over the three report dates the seasonal prior still comes out ahead overall: +""" + +overall_crps = (; + default = mean(row.default for row in crps_by_date), + seasonal = mean(row.seasonal for row in crps_by_date), +) + +md""" +## Enabling `SquaredExponential` structure + +The leaf-kernel distribution is editable the same way. The default gives `SquaredExponential` +(index 3) **zero** prior mass; `@set` can spread mass evenly over `Linear`, `SquaredExponential`, +`GammaExponential` and `Periodic` (the vector must sum to 1): +""" + +se_config = @set GPConfig().node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25] +se_config.node_dist_leaf + +md""" +`se_config` can be passed to `make_and_fit_model(...; config = se_config)` exactly like the seasonal +one, and edits compose — chain further `@set` calls (or use `@reset`) to adjust the period prior *and* +the kernel distribution together. + +## Summary + +- `make_and_fit_model(...; config = ...)` forwards any `AutoGP.GP.GPConfig` to the model, so the full + AutoGP prior is available without re-declaring it in `NowcastAutoGP`. +- `Accessors.@set` is a clean way to change one prior entry while preserving the rest, including deep + edits into the nested `prior` `Dict`. +- Re-centring `prior[:period]` on the seasonality you expect improves forecasts once enough of the + cycle is in view — here, a lower mean CRPS over the report dates, with clear gains by weeks 39 and + 52. Like any prior it is an assumption: from only half a cycle it can overshoot, so score it (with + CRPS, averaged over the forecasts) rather than assuming it always helps. +""" From 7ef8c2c572e793707246720ffa5bdb2b8aa900ef Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Wed, 3 Jun 2026 15:12:44 +0100 Subject: [PATCH 3/8] new setting_priors.jl --- docs/src/vignettes/setting-priors-11.png | Bin 96847 -> 114671 bytes docs/src/vignettes/setting-priors-19.png | Bin 295510 -> 268289 bytes docs/src/vignettes/setting-priors-23.png | Bin 49602 -> 46836 bytes docs/src/vignettes/setting-priors.md | 27 +++--- docs/vignettes/setting-priors.jl | 117 ++++++++++++++++++----- 5 files changed, 106 insertions(+), 38 deletions(-) diff --git a/docs/src/vignettes/setting-priors-11.png b/docs/src/vignettes/setting-priors-11.png index aa851357376a5d1be7047266a67304458e5db2de..0ada6d1ccffb5d31b69d88fec0ba183f71dbea24 100644 GIT binary patch literal 114671 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zh5`T`hUo?;lBt3F^erqbAT+ia6x-UPJOzU@B_eB;_zXrebm-7(L+BYTp0NOz>)Z?C znr|06ii!(SuPVK;TSBH}1V~5+FCaMw%q$?|fnG6j-D*asZq`al2tjx&iRmzYaQNmu6lNK}o? zo8+9r!mYIMRVFZ?KNSf~(wAf-+a*gr6K>x$^!)i@q&N00F0ZP};V%7c1!w@3?00~jA=0L|IO53z!^Vx_ zJ}yR~WdO~T%rbUj4QqcOS8=?o_(1ZNNP*7{rNMr8>~s7%WGEog69;;z=7)k#1urno zwOWIhPF=aS*@iA%I(9T8NHe*J4%yJ@gGX63oSrJ;-IdT6|K^2|%x(ZyUa|kxA&O&K zk!P1c{u77f^S>vp^||x~_%Hq3 bP3`-;G!`t2436V*n~gW0H1?>O)6f3{ICo2w diff --git a/docs/src/vignettes/setting-priors.md b/docs/src/vignettes/setting-priors.md index 0f4606a..03f97b2 100644 --- a/docs/src/vignettes/setting-priors.md +++ b/docs/src/vignettes/setting-priors.md @@ -93,13 +93,13 @@ as data accrue. ````julia start_date = Date(2022, 1, 1) -all_dates = collect(start_date:Week(1):(start_date + Week(103))) # 104 weekly points ≈ 2 years +all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) # 104 weekly points ≈ 2 years n_all = length(all_dates) tt = 0:(n_all - 1) -truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.08 .* tt # annual cycle (52 weeks) + trend +truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.2 .* tt # annual cycle (52 weeks) + trend observations = truth .+ 2.0 .* randn(n_all) -report_weeks = [26, 39, 52] +report_weeks = 52 .+ [0, 26, 39] horizon = 52 # forecast one year ahead report_colours = [:steelblue, :darkorange, :seagreen] @@ -126,15 +126,15 @@ tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, ````julia example_window = 39 -seasonal_example = @set GPConfig().prior[:period][:mu] = log(52 / example_window) -seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.3 +seasonal_example = @set GPConfig().prior[:period][:mu] = -log(3.0) +seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.1 seasonal_example.prior[:period] ```` ```` Dict{Symbol, Float64} with 2 entries: - :mu => 0.287682 - :sigma => 0.3 + :mu => -1.09861 + :sigma => 0.1 ```` `@set` returns a fresh `GPConfig`; every sibling prior is carried over unchanged — it only touched @@ -169,8 +169,9 @@ results = map(report_weeks) do w horizon_truth = truth[(w + 1):(w + horizon)] # a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time - seasonal_config = @set GPConfig().prior[:period][:mu] = log(52 / w) - seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 + window_length = Dates.value(all_dates[w] - all_dates[1]) + seasonal_config = @set GPConfig().prior[:period][:mu] = log(365 / window_length) + seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.2 default_model = make_and_fit_model(train_data; config = GPConfig(), fit_params...) seasonal_model = make_and_fit_model(train_data; config = seasonal_config, fit_params...) @@ -277,9 +278,9 @@ end ```` 3-element Vector{@NamedTuple{report_week::Int64, default::Float64, seasonal::Float64}}: - (report_week = 26, default = 8.145047072851177, seasonal = 9.299402943763948) - (report_week = 39, default = 7.139662993075851, seasonal = 4.4957906600468425) - (report_week = 52, default = 5.006893616792975, seasonal = 3.268268898264733) + (report_week = 52, default = 5.8769579095053945, seasonal = 8.818111041709123) + (report_week = 78, default = 11.780098525126478, seasonal = 8.530316456971692) + (report_week = 91, default = 0.6746733104098456, seasonal = 0.8066853953563354) ```` The seasonal prior is clearly better once enough of the cycle is in view — a much lower CRPS at weeks @@ -325,7 +326,7 @@ overall_crps = (; ```` ```` -(default = 6.7638678942400015, seasonal = 5.687820834025175) +(default = 6.110576581680572, seasonal = 6.051704298012383) ```` ## Enabling `SquaredExponential` structure diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl index 7bf4410..f64fdce 100644 --- a/docs/vignettes/setting-priors.jl +++ b/docs/vignettes/setting-priors.jl @@ -1,3 +1,8 @@ +using Pkg +Pkg.activate(joinpath(@__DIR__, "..")) +Pkg.instantiate() + + using Markdown md""" # Setting GP priors with `Accessors.jl` @@ -32,7 +37,7 @@ using Accessors using CairoMakie using Dates, Distributions, Random -Random.seed!(2026) +Random.seed!(1234) CairoMakie.activate!(type = "png") nothing #hide @@ -65,7 +70,7 @@ exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window md""" ## A seasonal series and a few report dates -We simulate two years of weekly observations with a clear annual cycle, a gentle upward trend and +We simulate three years of weekly observations with a clear annual cycle, a gentle upward trend and observation noise. We then imagine sitting at three **report dates** — weeks 26, 39 and 52 (a half, three-quarters and a full cycle of history) — and at each one forecast a full year ahead. This mirrors the [Getting started](getting-started.md) workflow of scoring forecasts across report dates @@ -73,22 +78,35 @@ as data accrue. """ start_date = Date(2022, 1, 1) -all_dates = collect(start_date:Week(1):(start_date + Week(103))) # 104 weekly points ≈ 2 years +all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) # 156 weekly points ≈ 3 years n_all = length(all_dates) tt = 0:(n_all - 1) -truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.08 .* tt # annual cycle (52 weeks) + trend -observations = truth .+ 2.0 .* randn(n_all) +log_truth = log(50.0) .+ 1.0 .* sin.(2π .* tt ./ 52) .+ 0.02 .* tt # annual cycle (52 weeks) + trend +truth = exp.(log_truth) +observations = exp.(log_truth .+ 0.15 .* randn(n_all)) -report_weeks = [26, 39, 52] + +report_weeks = 51 .+ [0, 26, 52] horizon = 52 # forecast one year ahead report_colours = [:steelblue, :darkorange, :seagreen] -nothing #hide fig_data = let fig = Figure(size = (820, 400)) - ax = Axis(fig[1, 1]; xlabel = "week", ylabel = "value", title = "Synthetic weekly series") - lines!(ax, Dates.value.(all_dates), truth; color = :black, label = "signal") - scatter!(ax, Dates.value.(all_dates), observations; color = (:black, 0.3), markersize = 5) + ax = Axis( + fig[1, 1]; + xlabel = "week", + ylabel = "value", + title = "Synthetic weekly series", + ) + lines!( + ax, Dates.value.(all_dates), truth; + color = (:black, 0.5), label = "expected", + linestyle = :dash, linewidth = 2 + ) + scatter!( + ax, Dates.value.(all_dates), observations; + color = (:black, 0.8), markersize = 5, label = "observed" + ) vlines!( ax, Dates.value.(all_dates[report_weeks]); color = report_colours, linestyle = :dash, linewidth = 2 @@ -106,8 +124,8 @@ tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, """ example_window = 39 -seasonal_example = @set GPConfig().prior[:period][:mu] = log(52 / example_window) -seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.3 +seasonal_example = @set GPConfig().prior[:period][:mu] = -log(3.0) +seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.1 seasonal_example.prior[:period] md""" @@ -127,28 +145,66 @@ fitted model is a particle ensemble, so each forecast is a full predictive *dist what CRPS scores below. """ -fit_params = (n_particles = 16, smc_data_proportion = 0.1, n_mcmc = 75, n_hmc = 15) +fit_params = (n_particles = 16, smc_data_proportion = 0.05, n_mcmc = 200, n_hmc = 25) n_draws = 300 Random.seed!(2026) results = map(report_weeks) do w + horizon_dates = all_dates[(w + 1):(w + horizon)] + horizon_truth = observations[(w + 1):(w + horizon)] + + transformation, inv_transformation = get_transformations("positive", observations[1:w]) train_data = create_transformed_data( - all_dates[1:w], observations[1:w]; transformation = identity + all_dates[1:w], observations[1:w]; transformation ) - horizon_dates = all_dates[(w + 1):(w + horizon)] - horizon_truth = truth[(w + 1):(w + horizon)] ## a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time - seasonal_config = @set GPConfig().prior[:period][:mu] = log(52 / w) + window_length = Dates.value(all_dates[w] - all_dates[1]) + seasonal_config = @set GPConfig().prior[:period][:mu] = log(365 / window_length) seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 + seasonal_config_lin_period_prior = @set seasonal_config.node_dist_leaf = [0.0, 0.5, 0., 0., 0.5] + default_config_lin_period_prior = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0., 0., 0.5] - default_model = make_and_fit_model(train_data; config = GPConfig(), fit_params...) - seasonal_model = make_and_fit_model(train_data; config = seasonal_config, fit_params...) + n_particles = Threads.nthreads() # use all available threads for SMC sampling + default_model = make_and_fit_model( + train_data; + n_particles, config = GPConfig(), fit_params... + ) + seasonal_model = make_and_fit_model( + train_data; + n_particles, config = seasonal_config, fit_params... + ) + seasonal_config_lin_period_model = make_and_fit_model( + train_data; + n_particles, config = seasonal_config_lin_period_prior, fit_params... + ) + default_config_lin_period_model = make_and_fit_model( + train_data; + n_particles, config = default_config_lin_period_prior, fit_params... + ) return (; report_week = w, horizon_dates, horizon_truth, - default = forecast(default_model, horizon_dates, n_draws), - seasonal = forecast(seasonal_model, horizon_dates, n_draws), + default = forecast( + default_model, horizon_dates, n_draws; + inv_transformation + ), + seasonal = forecast( + seasonal_model, horizon_dates, n_draws; + inv_transformation + ), + seasonal_config_lin_period = forecast( + seasonal_config_lin_period_model, horizon_dates, n_draws; + inv_transformation + ), + default_config_lin_period = forecast( + default_config_lin_period_model, horizon_dates, n_draws; + inv_transformation + ), + default_model = default_model, + seasonal_model = seasonal_model, + seasonal_config_lin_period_model = seasonal_config_lin_period_model, + default_config_lin_period_model = default_config_lin_period_model, ) end nothing #hide @@ -164,13 +220,15 @@ fig_forecasts = let fig = Figure(size = (920, 720)) panels = ( (key = :default, row = 1, title = "Default prior"), - (key = :seasonal, row = 2, title = "Seasonal prior (re-centred with @set)"), + (key = :default_config_lin_period, row = 2, title = "Default prior with linear/periodic GP structure"), + (key = :seasonal, row = 3, title = "Seasonal prior"), + (key = :seasonal_config_lin_period, row = 4, title = "Seasonal prior with linear/periodic GP structure"), ) for panel in panels ax = Axis(fig[panel.row, 1]; xlabel = "week", ylabel = "value", title = panel.title) - lines!( - ax, Dates.value.(all_dates), truth; - color = :black, linestyle = :dash, label = "truth" + scatter!( + ax, Dates.value.(all_dates), observations; + color = :black, label = "observations" ) for (res, colour) in zip(results, report_colours) fc = getproperty(res, panel.key) @@ -296,3 +354,12 @@ the kernel distribution together. 52. Like any prior it is an assumption: from only half a cycle it can overshoot, so score it (with CRPS, averaged over the forecasts) rather than assuming it always helps. """ + +import NowcastAutoGP.AutoGP as AGP + +weights = AGP.particle_weights(results[end].default_model) +kernels = AGP.covariance_kernels(results[end].default_model) +for (i, (k, w)) in enumerate(zip(kernels, weights)) + println("Model $(i), Weight $(w)") + Base.display(k) +end \ No newline at end of file From 81c95f30cc592f77c303ebc8d6383bdc7ab24302 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Wed, 3 Jun 2026 21:14:27 +0100 Subject: [PATCH 4/8] Update setting-priors.jl --- docs/vignettes/setting-priors.jl | 139 ++++++++++++++++++++----------- 1 file changed, 92 insertions(+), 47 deletions(-) diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl index f64fdce..8c15311 100644 --- a/docs/vignettes/setting-priors.jl +++ b/docs/vignettes/setting-priors.jl @@ -70,11 +70,11 @@ exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window md""" ## A seasonal series and a few report dates -We simulate three years of weekly observations with a clear annual cycle, a gentle upward trend and -observation noise. We then imagine sitting at three **report dates** — weeks 26, 39 and 52 (a half, -three-quarters and a full cycle of history) — and at each one forecast a full year ahead. This -mirrors the [Getting started](getting-started.md) workflow of scoring forecasts across report dates -as data accrue. +We simulate three years of weekly observations on a **log scale** — a clear annual cycle and a gentle +upward trend, with multiplicative (log-normal) observation noise. We then imagine sitting at three +**report dates** — at roughly one, one-and-a-half and two years of history — and at each one forecast a +full year ahead. This mirrors the [Getting started](getting-started.md) workflow of scoring forecasts +across report dates as data accrue. """ start_date = Date(2022, 1, 1) @@ -118,12 +118,13 @@ end md""" ## Re-centring the period prior with `@set` -A one-year cycle is 52 weeks. In a window of `w` weeks that is a period of `52 / w` in AutoGP's -normalised time, so we re-centre the period prior's median there by setting `μ = log(52 / w)`, and -tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, for example: +AutoGP works in *normalised* time: it rescales the training window to `[0, 1]`, so a `Periodic` +kernel's period is expressed as a **fraction of the window**, and `prior[:period]` is a +`LogNormal(μ, σ)` over that fraction (its median is `exp(μ)`). Re-centring the prior is then just a +matter of `@set`-ting a new `μ` — here, a median period of a third of the window, held tightly with a +small `σ`: """ -example_window = 39 seasonal_example = @set GPConfig().prior[:period][:mu] = -log(3.0) seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.1 seasonal_example.prior[:period] @@ -145,8 +146,14 @@ fitted model is a particle ensemble, so each forecast is a full predictive *dist what CRPS scores below. """ -fit_params = (n_particles = 16, smc_data_proportion = 0.05, n_mcmc = 200, n_hmc = 25) -n_draws = 300 +n_particles = 32 +fit_params = ( + smc_data_proportion = 0.005, + n_mcmc = 200, + n_hmc = 25, + adaptive_rejuvenation = true, +) +n_draws = 1000 Random.seed!(2026) results = map(report_weeks) do w @@ -158,14 +165,14 @@ results = map(report_weeks) do w all_dates[1:w], observations[1:w]; transformation ) - ## a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time + ## a seasonal prior for *this* window: an annual cycle is 365 days and the window spans + ## `window_length` days, so in normalised units the period is 365/window_length → μ = log(365/window_length) window_length = Dates.value(all_dates[w] - all_dates[1]) seasonal_config = @set GPConfig().prior[:period][:mu] = log(365 / window_length) seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 - seasonal_config_lin_period_prior = @set seasonal_config.node_dist_leaf = [0.0, 0.5, 0., 0., 0.5] - default_config_lin_period_prior = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0., 0., 0.5] + seasonal_config_lin_period_prior = @set seasonal_config.node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] + default_config_lin_period_prior = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] - n_particles = Threads.nthreads() # use all available threads for SMC sampling default_model = make_and_fit_model( train_data; n_particles, config = GPConfig(), fit_params... @@ -210,10 +217,9 @@ end nothing #hide md""" -The default prior (top) tends to extrapolate short cycles or flat trends, while the seasonal prior -(bottom) carries the annual cycle forward. Once three-quarters of a cycle is in view (weeks 39 and 52) -it stays close to the truth (dashed); from only half a cycle (week 26) the annual assumption is a -large extrapolation and overshoots: +We forecast a year ahead from each report date under all four priors (one row each). The strong +seasonal prior (rows 3–4) is what carries the annual cycle forward and stays close to the data; +restricting the leaf kernels to Linear + Periodic (rows 2 and 4) makes little difference on its own: """ fig_forecasts = let @@ -256,8 +262,6 @@ estimator: \text{CRPS}(X, y) = \mathbb{E}[|X - y|] - \frac{1}{2}\mathbb{E}[|X_1 - X_2|] ``` -The score is then **averaged over the forecasts** — every week of each report date's one-year-ahead -horizon — which is how a probabilistic forecast is evaluated (no repeated simulations required): """ ## Hand-rolled CRPS estimator (reproduced from the Getting started vignette). @@ -282,49 +286,65 @@ crps_by_date = map(results) do res (; report_week = res.report_week, default = mean_crps(res.horizon_truth, res.default), + default_lin_period = mean_crps(res.horizon_truth, res.default_config_lin_period), seasonal = mean_crps(res.horizon_truth, res.seasonal), + seasonal_lin_period = mean_crps(res.horizon_truth, res.seasonal_config_lin_period), ) end md""" -The seasonal prior is clearly better once enough of the cycle is in view — a much lower CRPS at weeks -39 and 52. At week 26, with only half a cycle observed, the annual assumption overshoots and scores a -little worse: a useful reminder that a prior is an assumption, most valuable when the data can support -it: +Scoring confirms the visual read. The strong seasonal prior gives a markedly lower CRPS, while +restricting the leaf kernels to Linear + Periodic barely moves the score — on its own it is not +particularly beneficial. It is the period *hyperparameter* prior, not the kernel menu, doing the work: """ fig_scores = let + ## one dodged bar per approach, grouped by report date + approaches = [ + (key = :default, label = "default", colour = :tomato), + (key = :default_lin_period, label = "default, lin+periodic leaves", colour = :goldenrod), + (key = :seasonal, label = "seasonal", colour = :steelblue), + (key = :seasonal_lin_period, label = "seasonal, lin+periodic leaves", colour = :seagreen), + ] n = length(crps_by_date) - defaults = [row.default for row in crps_by_date] - seasonals = [row.seasonal for row in crps_by_date] - fig = Figure(size = (640, 400)) + xs = Int[] + heights = Float64[] + dodge = Int[] + colours = Symbol[] + for (j, approach) in enumerate(approaches), (i, row) in enumerate(crps_by_date) + push!(xs, i) + push!(heights, getproperty(row, approach.key)) + push!(dodge, j) + push!(colours, approach.colour) + end + + fig = Figure(size = (820, 430)) ax = Axis( fig[1, 1]; xticks = (1:n, ["week $(row.report_week)" for row in crps_by_date]), ylabel = "mean CRPS (lower is better)", - title = "Forecast skill by report date" - ) - barplot!( - ax, repeat(1:n, 2), vcat(defaults, seasonals); - dodge = vcat(fill(1, n), fill(2, n)), - color = vcat(fill(:tomato, n), fill(:steelblue, n)) + title = "Forecast skill by report date and prior" ) + barplot!(ax, xs, heights; dodge = dodge, color = colours) Legend( fig[1, 2], - [PolyElement(color = :tomato), PolyElement(color = :steelblue)], - ["default", "seasonal"] + [PolyElement(color = a.colour) for a in approaches], + [a.label for a in approaches] ) fig end md""" -Averaged over the three report dates the seasonal prior still comes out ahead overall: +Averaged over the report dates the strong seasonal prior is the clear winner; the leaf-kernel +restriction barely changes the score, with or without it: """ overall_crps = (; default = mean(row.default for row in crps_by_date), + default_lin_period = mean(row.default_lin_period for row in crps_by_date), seasonal = mean(row.seasonal for row in crps_by_date), + seasonal_lin_period = mean(row.seasonal_lin_period for row in crps_by_date), ) md""" @@ -349,17 +369,42 @@ the kernel distribution together. AutoGP prior is available without re-declaring it in `NowcastAutoGP`. - `Accessors.@set` is a clean way to change one prior entry while preserving the rest, including deep edits into the nested `prior` `Dict`. -- Re-centring `prior[:period]` on the seasonality you expect improves forecasts once enough of the - cycle is in view — here, a lower mean CRPS over the report dates, with clear gains by weeks 39 and - 52. Like any prior it is an assumption: from only half a cycle it can overshoot, so score it (with - CRPS, averaged over the forecasts) rather than assuming it always helps. +- Re-centring the period *hyperparameter* prior (`prior[:period]`) on the seasonality you expect can + substantially improve forecasts — here the strong seasonal prior gives the lowest mean CRPS across + the report dates. +- Editing the *structural* prior (`node_dist_leaf`) to allow only Linear + Periodic leaves made little + difference on its own: the period prior, not the kernel menu, drove the gains. As always, score + competing priors with CRPS (averaged over the forecasts) rather than assuming an edit will help. +""" + +md""" +## Appendix: the discovered kernel structures + +Each fitted model is a *weighted ensemble* of SMC particles, and every particle is a complete GP with +its own covariance-kernel structure. AutoGP exposes them directly: `particle_weights` gives each +particle's posterior weight and `covariance_kernels` its discovered kernel. Reading these out shows +which structures the search actually settled on under a given prior — a concrete look at what the prior +did. Here is the ensemble from the default-prior fit at the final report date, ordered by weight: """ import NowcastAutoGP.AutoGP as AGP -weights = AGP.particle_weights(results[end].default_model) -kernels = AGP.covariance_kernels(results[end].default_model) -for (i, (k, w)) in enumerate(zip(kernels, weights)) - println("Model $(i), Weight $(w)") - Base.display(k) -end \ No newline at end of file +function show_discovered_kernels(model) + weights = AGP.particle_weights(model) + kernels = AGP.covariance_kernels(model) + ## list particles from highest to lowest posterior weight + for i in sortperm(weights; rev = true) + println("posterior weight = ", round(weights[i]; digits = 3)) + display(kernels[i]) + end + return nothing +end + +show_discovered_kernels(results[end].default_model) + +md""" +Running the same readout on the strong-seasonal-prior fit lets us compare how re-centring the period +prior reshaped the structures the search selected: +""" + +show_discovered_kernels(results[end].seasonal_model) From 3e386deeaebb5021c2ea24e0a2354a2eb869d563 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Thu, 4 Jun 2026 09:25:00 +0100 Subject: [PATCH 5/8] Revise setting-priors vignette and figures Rewrite and modernize the setting-priors vignette and its script --- docs/src/vignettes/setting-priors-11.png | Bin 114671 -> 91317 bytes docs/src/vignettes/setting-priors-19.png | Bin 268289 -> 0 bytes docs/src/vignettes/setting-priors-21.png | Bin 0 -> 377087 bytes docs/src/vignettes/setting-priors-23.png | Bin 46836 -> 0 bytes docs/src/vignettes/setting-priors-25.png | Bin 0 -> 74170 bytes docs/src/vignettes/setting-priors.md | 422 ++++++++++++++++------- docs/vignettes/setting-priors.jl | 223 ++++++------ 7 files changed, 402 insertions(+), 243 deletions(-) delete mode 100644 docs/src/vignettes/setting-priors-19.png create mode 100644 docs/src/vignettes/setting-priors-21.png delete mode 100644 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+8,26 @@ using Markdown **CDC Center for Forecasting and Outbreak Analytics (CFA/CDC)** -`make_and_fit_model` accepts a `config` keyword — an `AutoGP.GP.GPConfig` that describes the -Gaussian-process **prior**: the distribution over kernel *structures* -(`node_dist_leaf`/`node_dist_nocp`/`node_dist_cp`) and the priors over kernel *hyperparameters* -(`prior[:gamma]`, `prior[:period]`, `prior[:wildcard]`). The default `GPConfig()` reproduces -AutoGP's out-of-the-box behaviour, but its **period prior** is centred well below an annual cycle, so -a periodic component is unlikely to land on the ~1-year seasonality respiratory diseases actually have. - -`GPConfig` is an immutable struct with a nested `prior` `Dict`, which makes "change just this one -field" awkward to write by hand. [`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s -`@set` macro does exactly that: it returns a *copy* with a single leaf changed and every sibling -preserved. This vignette inspects the default prior, re-centres the period prior with `@set`, and — -following the scoring approach of the [Getting started](getting-started.md) vignette — shows the -re-centred prior gives better forecasts across a few **report dates** spanning one seasonal cycle, -measured by the Continuous Ranked Probability Score (CRPS). +`make_and_fit_model` accepts a configuration object of type `AutoGP.GP.GPConfig` using the `config` +keyword. +The configuration object describes priors over the Gaussian Process's kernel structure and +hyperparameters. +In this vignette we show how to edit the default `GPConfig()` to give a strong prior +when we expect a certain seasonal cycle, and how that improves forecasts. + +In this vignette we are interested in two different priors. +First, the underlying `AutoGP` kernel structure can be represented as a tree with primitive kernels at the leaves, and the internal nodes describing the combinations +`Plus`, `Times` and `ChangePoint`, c.f. [AutoGP.jl documentation](https://probsys.github.io/AutoGP.jl/stable/api.html). +We can use the configuration to set the prior probability for each of the primitive kernels to be a leaf in the structure. +Second, we can set three hyperparameter priors for the `gamma` lengthscale exponent for `GammaExponential` primitive, +`period` period for `Periodic` primitive and `wildcard` for all other hyperparameters. + +We will show how to edit the period prior, and likelihood of `Periodic` primitive kernels in the tree kernel structure, to give a +a strong seasonal prior, and how that improves forecasts. We score forecasts following the scoring approach of the [Getting started](getting-started.md) vignette. + +`GPConfig` is an immutable struct which makes "change just this one field" awkward to write by hand. +[`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s `@set` macro does exactly that: it +returns a *copy* with the chosen field(s) changed and all the others preserved. > `Accessors.jl` is a convenience used here in the docs; it is **not** a dependency of > `NowcastAutoGP` itself. The same edits can be made by constructing a `GPConfig` directly. @@ -29,16 +35,49 @@ measured by the Continuous Ranked Probability Score (CRPS). ## Loading dependencies ````julia +import NowcastAutoGP.AutoGP as AGP using NowcastAutoGP using Accessors using CairoMakie using Dates, Distributions, Random -Random.seed!(2026) +Random.seed!(1234) CairoMakie.activate!(type = "png") ```` -## Inspecting the default prior +```` +Precompiling packages... + 1501.6 ms ✓ StatsBase + 684.1 ms ✓ PDMats → StatsBaseExt + 1898.5 ms ✓ BoxCox + 2650.7 ms ✓ Distributions + 987.2 ms ✓ Distributions → DistributionsTestExt + 1376.8 ms ✓ Distributions → DistributionsChainRulesCoreExt + 10716.0 ms ✓ AutoGP + 3231.0 ms ✓ NowcastAutoGP + 8 dependencies successfully precompiled in 19 seconds. 134 already precompiled. +Precompiling packages... + 827.8 ms ✓ StructArrays + 875.8 ms ✓ KernelDensity + 688.1 ms ✓ StructArrays → StructArraysAdaptExt + 814.3 ms ✓ StructArrays → StructArraysSparseArraysExt + 796.5 ms ✓ StructArrays → StructArraysStaticArraysExt + 252.2 ms ✓ StructArrays → StructArraysLinearAlgebraExt + 2742.5 ms ✓ MathTeXEngine + 11083.1 ms ✓ TiffImages + 72556.2 ms ✓ Makie + 25854.3 ms ✓ CairoMakie + 10 dependencies successfully precompiled in 110 seconds. 259 already precompiled. +Precompiling packages... + 599.0 ms ✓ Accessors → StructArraysExt + 1 dependency successfully precompiled in 1 seconds. 20 already precompiled. +Precompiling packages... + 9142.4 ms ✓ BoxCox → BoxCoxMakieExt + 1 dependency successfully precompiled in 10 seconds. 266 already precompiled. + +```` + +## Inspecting the default priors `GPConfig()` exposes the prior as plain fields. The leaf-kernel distribution is a probability vector over the primitive kernels, indexed `Constant=1`, `Linear=2`, `SquaredExponential=3`, @@ -58,6 +97,12 @@ default_config.node_dist_leaf 0.3333333333333333 ```` +So by default, the `SquaredExponential` primitive (index 3) has **zero** prior mass, and is treated as superceded by +the `GammaExponential` (index 4), which recovers it as a special case when the `gamma` lengthscale exponent is exactly 2. +The `Linear` (index 2) and `Periodic` (index 5) primitives have equal prior mass with the `GammaExponential` (index 4), +and the `Constant` (index 1) has zero mass. +Therefore, the default prior is agnostic between `Linear`, `GammaExponential` and `Periodic` primitives. + The hyperparameter priors live in a nested `Dict`; the period prior is a `LogNormal(μ, σ)` over the periodic component's period: @@ -71,9 +116,8 @@ Dict{Symbol, Float64} with 2 entries: :sigma => 1.0 ```` -AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units — -a fraction of the training window. The default median period is therefore only about a fifth of the -window: +AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units as a fraction of the training window. +The default median period is therefore only about a fifth of the window: ````julia exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window @@ -83,33 +127,53 @@ exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window 0.22313016014842982 ```` -## A seasonal series and a few report dates +## Example: A seasonal series and a few report dates + +In this example, we imagine having a new data stream for a pathogen, which _a priori_ we know has a strong +annual cycle. +We will make year long forecasts from three different report dates as data accrue: at one, one-and-a-half and two years of history. +We will show how to build a strong seasonal prior into the model in two ways: + +1. Re-centring the period prior on an annual cycle for that window. +2. Restricting the leaf-kernel distribution to only allow Linear + Periodic kernels. -We simulate two years of weekly observations with a clear annual cycle, a gentle upward trend and -observation noise. We then imagine sitting at three **report dates** — weeks 26, 39 and 52 (a half, -three-quarters and a full cycle of history) — and at each one forecast a full year ahead. This -mirrors the [Getting started](getting-started.md) workflow of scoring forecasts across report dates -as data accrue. +To demonstate, we simulate three years of synthetic weekly observations using a simple log-linear model +with annual sinusoidal variation around a linear trend with multiplicative noise. ````julia start_date = Date(2022, 1, 1) -all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) # 104 weekly points ≈ 2 years +all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) n_all = length(all_dates) tt = 0:(n_all - 1) -truth = 50.0 .+ 20.0 .* sin.(2π .* tt ./ 52) .+ 0.2 .* tt # annual cycle (52 weeks) + trend -observations = truth .+ 2.0 .* randn(n_all) +log_truth = log(50.0) .+ 1.0 .* sin.(2π .* tt ./ 52) .+ 0.02 .* tt +truth = exp.(log_truth) +observations = exp.(log_truth .+ 0.15 .* randn(n_all)) -report_weeks = 52 .+ [0, 26, 39] +# The report dates are at weeks 51, 77 and 103 (1 year, 1.5 years and 2 years in). +report_weeks = 51 .+ [0, 26, 52] horizon = 52 # forecast one year ahead report_colours = [:steelblue, :darkorange, :seagreen] fig_data = let fig = Figure(size = (820, 400)) - ax = Axis(fig[1, 1]; xlabel = "week", ylabel = "value", title = "Synthetic weekly series") - lines!(ax, Dates.value.(all_dates), truth; color = :black, label = "signal") - scatter!(ax, Dates.value.(all_dates), observations; color = (:black, 0.3), markersize = 5) + ax = Axis( + fig[1, 1]; + xlabel = "week", + ylabel = "value", + title = "Synthetic weekly series", + ) + tvals = Dates.value.(all_dates .- first(all_dates)) / 7 + lines!( + ax, tvals, truth; + color = (:black, 0.5), label = "expected", + linestyle = :dash, linewidth = 2 + ) + scatter!( + ax, tvals, observations; + color = (:black, 0.8), markersize = 5, label = "observed" + ) vlines!( - ax, Dates.value.(all_dates[report_weeks]); + ax, Dates.value.(all_dates[report_weeks] .- first(all_dates)) ./ 7; color = report_colours, linestyle = :dash, linewidth = 2 ) axislegend(ax; position = :lt) @@ -118,14 +182,17 @@ end ```` ![](setting-priors-11.png) -## Re-centring the period prior with `@set` +### Choosing priors + +#### Re-centring the period prior with `@set` -A one-year cycle is 52 weeks. In a window of `w` weeks that is a period of `52 / w` in AutoGP's -normalised time, so we re-centre the period prior's median there by setting `μ = log(52 / w)`, and -tighten `σ` to concentrate mass around the annual cycle. For a 39-week window, for example: +AutoGP works in *normalised* time: it rescales the training window to `[0, 1]`, so a `Periodic` +kernel's period is expressed as a **fraction of the window**, and `prior[:period]` is a +`LogNormal(μ, σ)` over that fraction. +We can re-centre the prior using`@set` to give a new `μ` — here, held tightly with a small `σ`. +For example, for a three year window of data an annual cycle is 1/3 of the window, so `μ = log(1/3)`: ````julia -example_window = 39 seasonal_example = @set GPConfig().prior[:period][:mu] = -log(3.0) seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.1 seasonal_example.prior[:period] @@ -137,8 +204,8 @@ Dict{Symbol, Float64} with 2 entries: :sigma => 0.1 ```` -`@set` returns a fresh `GPConfig`; every sibling prior is carried over unchanged — it only touched -`prior[:period]`: +`@set` returns a fresh `GPConfig`; every other prior, and other fields, are carried over unchanged. +`@set` only touched `prior[:period]`: ````julia seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] @@ -148,43 +215,125 @@ seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] true ```` -## Forecasting from each report date +#### Alterating the leaf-kernel distribution -At each report date we fit two models on the data so far — one with the default prior, one with a -seasonal prior built for that window with `@set` — and forecast a year ahead. Everything except -`config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. Each -fitted model is a particle ensemble, so each forecast is a full predictive *distribution* — exactly -what CRPS scores below. +The leaf-kernel distribution is a simple probability vector over the primitive kernels. +We can use `@set` to change it, for example to specialise on only Linear + Periodic kernels (indices 2 and 5): ````julia -fit_params = (n_particles = 16, smc_data_proportion = 0.1, n_mcmc = 75, n_hmc = 15) -n_draws = 300 +config_lin_period = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] +```` + +```` +AutoGP.GP.GPConfig + Constant: Int64 1 + Linear: Int64 2 + SquaredExponential: Int64 3 + GammaExponential: Int64 4 + Periodic: Int64 5 + Plus: Int64 6 + Times: Int64 7 + ChangePoint: Int64 8 + index_to_node: Dict{Integer, Type{<:AutoGP.GP.Node}} + node_dist_leaf: Array{Float64}((5,)) [0.0, 0.5, 0.0, 0.0, 0.5] + node_dist_nocp: Array{Float64}((7,)) [0.0, 0.21428571428571427, 0.0, 0.21428571428571427, 0.21428571428571427, 0.17857142857142858, 0.17857142857142858] + node_dist_cp: Array{Float64}((8,)) [0.0, 0.21428571428571427, 0.0, 0.21428571428571427, 0.21428571428571427, 0.14285714285714285, 0.14285714285714285, 0.07142857142857142] + max_branch: Int64 2 + max_depth: Int64 -1 + changepoints: Bool true + noise: Nothing nothing + prior: Dict{Any, Any} + +```` + +### Forecasting from each report date + +At each report date we fit four models on the data so far that only differ in their priors: + +- Default prior (the default `GPConfig()`) +- Default hyperpriors, but only `Linear` + `Periodic` primitive leaf-kernels allowed, prior on other kernels set to zero. +- Seasonal hyperprior, fairly tight around an annual cycle, but the default primitive leaf-kernel distribution. +- Seasonal hyperprior, _and_ only `Linear` + `Periodic` primitive leaf-kernels allowed, prior on other kernels set to zero. + +Everything except `config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. +We also set `adaptive_rejuvenation = true` to use the classic SMC resample-then-move adaptive rejuvenation scheme; +that is we make MCMC moves only when the effective sample size (ESS) of the particle ensemble drops below the default threshold of 50% of the particle number. +Each fitted model is a particle ensemble over GP tree-kernels, so each forecast is a full predictive *distribution*. + +````julia +n_particles = 32 +fit_params = ( + smc_data_proportion = 0.005, + n_mcmc = 200, + n_hmc = 50, + adaptive_rejuvenation = true, +) +n_draws = 2000 -Random.seed!(2026) results = map(report_weeks) do w + horizon_dates = all_dates[(w + 1):(w + horizon)] + horizon_truth = observations[(w + 1):(w + horizon)] + + transformation, inv_transformation = get_transformations("positive", observations[1:w]) train_data = create_transformed_data( - all_dates[1:w], observations[1:w]; transformation = identity + all_dates[1:w], observations[1:w]; transformation ) - horizon_dates = all_dates[(w + 1):(w + horizon)] - horizon_truth = truth[(w + 1):(w + horizon)] - # a seasonal prior for *this* window — an annual cycle is log(52/w) in normalised time + # a seasonal prior for *this* window: an annual cycle is 365 days and the window spans + # `window_length` days, so in normalised units the period is 365/window_length → μ = log(365/window_length) window_length = Dates.value(all_dates[w] - all_dates[1]) seasonal_config = @set GPConfig().prior[:period][:mu] = log(365 / window_length) - seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.2 + seasonal_config = @set seasonal_config.prior[:period][:sigma] = 0.3 + seasonal_config_lin_period_prior = @set seasonal_config.node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] + default_config_lin_period_prior = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] - default_model = make_and_fit_model(train_data; config = GPConfig(), fit_params...) - seasonal_model = make_and_fit_model(train_data; config = seasonal_config, fit_params...) + default_model = make_and_fit_model( + train_data; + n_particles, config = GPConfig(), fit_params... + ) + seasonal_model = make_and_fit_model( + train_data; + n_particles, config = seasonal_config, fit_params... + ) + seasonal_config_lin_period_model = make_and_fit_model( + train_data; + n_particles, config = seasonal_config_lin_period_prior, fit_params... + ) + default_config_lin_period_model = make_and_fit_model( + train_data; + n_particles, config = default_config_lin_period_prior, fit_params... + ) return (; - report_week = w, horizon_dates, horizon_truth, - default = forecast(default_model, horizon_dates, n_draws), - seasonal = forecast(seasonal_model, horizon_dates, n_draws), + report_week = w, + horizon_dates, + horizon_truth, + default = forecast( + default_model, horizon_dates, n_draws; + inv_transformation + ), + seasonal = forecast( + seasonal_model, horizon_dates, n_draws; + inv_transformation + ), + seasonal_config_lin_period = forecast( + seasonal_config_lin_period_model, horizon_dates, n_draws; + inv_transformation + ), + default_config_lin_period = forecast( + default_config_lin_period_model, horizon_dates, n_draws; + inv_transformation + ), + default_model = default_model, + seasonal_model = seasonal_model, + seasonal_config_lin_period_model = seasonal_config_lin_period_model, + default_config_lin_period_model = default_config_lin_period_model, ) end ```` ```` +[ Info: Using positive transformation with offset = 0.0 ┌ Warning: Using more particles than available threads. └ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 ┌ Warning: Using more particles than available threads. @@ -193,6 +342,20 @@ end └ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 ┌ Warning: Using more particles than available threads. └ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +[ Info: Using positive transformation with offset = 0.0 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +[ Info: Using positive transformation with offset = 0.0 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 +┌ Warning: Using more particles than available threads. +└ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 ┌ Warning: Using more particles than available threads. └ @ AutoGP ~/.julia/packages/AutoGP/SVRPE/src/api.jl:226 ┌ Warning: Using more particles than available threads. @@ -200,31 +363,38 @@ end ```` -The default prior (top) tends to extrapolate short cycles or flat trends, while the seasonal prior -(bottom) carries the annual cycle forward. Once three-quarters of a cycle is in view (weeks 39 and 52) -it stays close to the truth (dashed); from only half a cycle (week 26) the annual assumption is a -large extrapolation and overshoots: +We forecast a year ahead from each report date under all four priors (one row each). ````julia fig_forecasts = let fig = Figure(size = (920, 720)) panels = ( (key = :default, row = 1, title = "Default prior"), - (key = :seasonal, row = 2, title = "Seasonal prior (re-centred with @set)"), + (key = :default_config_lin_period, row = 2, title = "Default prior with linear/periodic GP structure"), + (key = :seasonal, row = 3, title = "Seasonal prior"), + (key = :seasonal_config_lin_period, row = 4, title = "Seasonal prior with linear/periodic GP structure"), ) + tvals = Dates.value.(all_dates .- first(all_dates)) / 7 for panel in panels - ax = Axis(fig[panel.row, 1]; xlabel = "week", ylabel = "value", title = panel.title) - lines!( - ax, Dates.value.(all_dates), truth; - color = :black, linestyle = :dash, label = "truth" + ax = Axis( + fig[panel.row, 1]; + xlabel = "week", ylabel = "value", title = panel.title, + yscale = log10, + ) + scatter!( + ax, tvals, observations; + color = :black, label = "observations" ) for (res, colour) in zip(results, report_colours) fc = getproperty(res, panel.key) - fx = Dates.value.(res.horizon_dates) - lower = [quantile(row, 0.25) for row in eachrow(fc)] + fx = Dates.value.(res.horizon_dates .- first(all_dates)) / 7 # convert to weeks for x-axis + lower_025 = [quantile(row, 0.025) for row in eachrow(fc)] + lower_25 = [quantile(row, 0.25) for row in eachrow(fc)] med = [quantile(row, 0.5) for row in eachrow(fc)] - upper = [quantile(row, 0.75) for row in eachrow(fc)] - band!(ax, fx, lower, upper; color = (colour, 0.2)) + upper_75 = [quantile(row, 0.75) for row in eachrow(fc)] + upper_975 = [quantile(row, 0.975) for row in eachrow(fc)] + band!(ax, fx, lower_025, upper_975; color = (colour, 0.2)) + band!(ax, fx, lower_25, upper_75; color = (colour, 0.4)) lines!(ax, fx, med; color = colour, linewidth = 2.5, label = "from week $(res.report_week)") end panel.row == 1 && axislegend(ax; position = :lt, nbanks = 2) @@ -232,12 +402,17 @@ fig_forecasts = let fig end ```` -![](setting-priors-19.png) +![](setting-priors-21.png) + +We see that incorporating our prior knowledge of seasonality substantially improves forecasts. +However, this improvement is not uniform; at the first report date, when only one year of data is available, there is insufficient information to learn the secular trend underneath the seasonal variation. +By one and a half years, the change in compared to the previous season is clearer, and the strong seasonal prior allows the model to extrapolate that pattern forward. +This is especially pronounced when we restrict the leaf-kernel distribution to only allow `Linear` + `Periodic` primitives. +Later on, the model has locked onto a combination of kernels that captures the trend and seasonality, so the restriction to `Linear` + `Periodic` leaves makes less difference. -## Scoring with CRPS +### Scoring with CRPS -This is a probabilistic model, so we score each predictive *distribution* against the value it should -have predicted using the **Continuous Ranked Probability Score (CRPS)** — the proper scoring rule from +We score each forecast against out-of-sample observations using the **Continuous Ranked Probability Score (CRPS)** a proper scoring rule from the [Getting started](getting-started.md) vignette (lower is better), reusing the same hand-rolled estimator: @@ -245,9 +420,6 @@ estimator: \text{CRPS}(X, y) = \mathbb{E}[|X - y|] - \frac{1}{2}\mathbb{E}[|X_1 - X_2|] ``` -The score is then **averaged over the forecasts** — every week of each report date's one-year-ahead -horizon — which is how a probabilistic forecast is evaluated (no repeated simulations required): - ````julia # Hand-rolled CRPS estimator (reproduced from the Getting started vignette). function crps(y::Real, X::Vector{<:Real}) @@ -271,98 +443,90 @@ crps_by_date = map(results) do res (; report_week = res.report_week, default = mean_crps(res.horizon_truth, res.default), + default_lin_period = mean_crps(res.horizon_truth, res.default_config_lin_period), seasonal = mean_crps(res.horizon_truth, res.seasonal), + seasonal_lin_period = mean_crps(res.horizon_truth, res.seasonal_config_lin_period), ) end ```` ```` -3-element Vector{@NamedTuple{report_week::Int64, default::Float64, seasonal::Float64}}: - (report_week = 52, default = 5.8769579095053945, seasonal = 8.818111041709123) - (report_week = 78, default = 11.780098525126478, seasonal = 8.530316456971692) - (report_week = 91, default = 0.6746733104098456, seasonal = 0.8066853953563354) +3-element Vector{@NamedTuple{report_week::Int64, default::Float64, default_lin_period::Float64, seasonal::Float64, seasonal_lin_period::Float64}}: + (report_week = 51, default = 150.96006350854293, default_lin_period = 145.27157670070207, seasonal = 148.997823973993, seasonal_lin_period = 136.28855586242133) + (report_week = 77, default = 373.30063983623944, default_lin_period = 316.81415453481105, seasonal = 113.39882438274986, seasonal_lin_period = 80.6348313345601) + (report_week = 103, default = 373.15777527071725, default_lin_period = 67.68526919040802, seasonal = 73.13602965490337, seasonal_lin_period = 69.887260753688) ```` -The seasonal prior is clearly better once enough of the cycle is in view — a much lower CRPS at weeks -39 and 52. At week 26, with only half a cycle observed, the annual assumption overshoots and scores a -little worse: a useful reminder that a prior is an assumption, most valuable when the data can support -it: +Scoring confirms the visual impression. +The strong seasonal prior gives a markedly lower CRPS, after there is available contrast between the seasons to allow the secular trend to be learned. ````julia fig_scores = let + # one dodged bar per approach, grouped by report date + approaches = [ + (key = :default, label = "default", colour = :tomato), + (key = :default_lin_period, label = "default, lin+periodic leaves", colour = :goldenrod), + (key = :seasonal, label = "seasonal", colour = :steelblue), + (key = :seasonal_lin_period, label = "seasonal, lin+periodic leaves", colour = :seagreen), + ] n = length(crps_by_date) - defaults = [row.default for row in crps_by_date] - seasonals = [row.seasonal for row in crps_by_date] - fig = Figure(size = (640, 400)) + xs = Int[] + heights = Float64[] + dodge = Int[] + colours = Symbol[] + for (j, approach) in enumerate(approaches), (i, row) in enumerate(crps_by_date) + push!(xs, i) + push!(heights, getproperty(row, approach.key)) + push!(dodge, j) + push!(colours, approach.colour) + end + + fig = Figure(size = (820, 430)) ax = Axis( fig[1, 1]; xticks = (1:n, ["week $(row.report_week)" for row in crps_by_date]), ylabel = "mean CRPS (lower is better)", - title = "Forecast skill by report date" - ) - barplot!( - ax, repeat(1:n, 2), vcat(defaults, seasonals); - dodge = vcat(fill(1, n), fill(2, n)), - color = vcat(fill(:tomato, n), fill(:steelblue, n)) + title = "Forecast skill by report date and prior" ) + barplot!(ax, xs, heights; dodge = dodge, color = colours) Legend( fig[1, 2], - [PolyElement(color = :tomato), PolyElement(color = :steelblue)], - ["default", "seasonal"] + [PolyElement(color = a.colour) for a in approaches], + [a.label for a in approaches] ) fig end ```` -![](setting-priors-23.png) +![](setting-priors-25.png) -Averaged over the three report dates the seasonal prior still comes out ahead overall: +Averaged over the report dates the strong seasonal prior is the clear winner; the leaf-kernel +restriction barely changes the score, with or without it: ````julia overall_crps = (; default = mean(row.default for row in crps_by_date), + default_lin_period = mean(row.default_lin_period for row in crps_by_date), seasonal = mean(row.seasonal for row in crps_by_date), + seasonal_lin_period = mean(row.seasonal_lin_period for row in crps_by_date), ) ```` ```` -(default = 6.110576581680572, seasonal = 6.051704298012383) -```` - -## Enabling `SquaredExponential` structure - -The leaf-kernel distribution is editable the same way. The default gives `SquaredExponential` -(index 3) **zero** prior mass; `@set` can spread mass evenly over `Linear`, `SquaredExponential`, -`GammaExponential` and `Periodic` (the vector must sum to 1): - -````julia -se_config = @set GPConfig().node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25] -se_config.node_dist_leaf -```` - -```` -5-element Vector{Float64}: - 0.0 - 0.25 - 0.25 - 0.25 - 0.25 +(default = 299.13949287183317, default_lin_period = 176.59033347530703, seasonal = 111.84422600388207, seasonal_lin_period = 95.60354931688981) ```` -`se_config` can be passed to `make_and_fit_model(...; config = se_config)` exactly like the seasonal -one, and edits compose — chain further `@set` calls (or use `@reset`) to adjust the period prior *and* -the kernel distribution together. - ## Summary - `make_and_fit_model(...; config = ...)` forwards any `AutoGP.GP.GPConfig` to the model, so the full AutoGP prior is available without re-declaring it in `NowcastAutoGP`. - `Accessors.@set` is a clean way to change one prior entry while preserving the rest, including deep edits into the nested `prior` `Dict`. -- Re-centring `prior[:period]` on the seasonality you expect improves forecasts once enough of the - cycle is in view — here, a lower mean CRPS over the report dates, with clear gains by weeks 39 and - 52. Like any prior it is an assumption: from only half a cycle it can overshoot, so score it (with - CRPS, averaged over the forecasts) rather than assuming it always helps. +- Re-centring the period *hyperparameter* prior (`prior[:period]`) on the seasonality you expect can + substantially improve forecasts — here the strong seasonal prior gives the lowest mean CRPS across + the report dates. +- Editing the *structural* prior (`node_dist_leaf`) to allow only Linear + Periodic leaves also improves forecasts. +- However, note that strong priors can be a double-edged sword: they can help when data are scarce, but if they are too tight or the wrong shape they can be a problem. --- diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl index 8c15311..87ab0eb 100644 --- a/docs/vignettes/setting-priors.jl +++ b/docs/vignettes/setting-priors.jl @@ -1,8 +1,3 @@ -using Pkg -Pkg.activate(joinpath(@__DIR__, "..")) -Pkg.instantiate() - - using Markdown md""" # Setting GP priors with `Accessors.jl` @@ -11,20 +6,26 @@ md""" **CDC Center for Forecasting and Outbreak Analytics (CFA/CDC)** -`make_and_fit_model` accepts a `config` keyword — an `AutoGP.GP.GPConfig` that describes the -Gaussian-process **prior**: the distribution over kernel *structures* -(`node_dist_leaf`/`node_dist_nocp`/`node_dist_cp`) and the priors over kernel *hyperparameters* -(`prior[:gamma]`, `prior[:period]`, `prior[:wildcard]`). The default `GPConfig()` reproduces -AutoGP's out-of-the-box behaviour, but its **period prior** is centred well below an annual cycle, so -a periodic component is unlikely to land on the ~1-year seasonality respiratory diseases actually have. - -`GPConfig` is an immutable struct with a nested `prior` `Dict`, which makes "change just this one -field" awkward to write by hand. [`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s -`@set` macro does exactly that: it returns a *copy* with a single leaf changed and every sibling -preserved. This vignette inspects the default prior, re-centres the period prior with `@set`, and — -following the scoring approach of the [Getting started](getting-started.md) vignette — shows the -re-centred prior gives better forecasts across a few **report dates** spanning one seasonal cycle, -measured by the Continuous Ranked Probability Score (CRPS). +`make_and_fit_model` accepts a configuration object of type `AutoGP.GP.GPConfig` using the `config` +keyword. +The configuration object describes priors over the Gaussian Process's kernel structure and +hyperparameters. +In this vignette we show how to edit the default `GPConfig()` to give a strong prior +when we expect a certain seasonal cycle, and how that improves forecasts. + +In this vignette we are interested in two different priors. +First, the underlying `AutoGP` kernel structure can be represented as a tree with primitive kernels at the leaves, and the internal nodes describing the combinations +`Plus`, `Times` and `ChangePoint`, c.f. [AutoGP.jl documentation](https://probsys.github.io/AutoGP.jl/stable/api.html). +We can use the configuration to set the prior probability for each of the primitive kernels to be a leaf in the structure. +Second, we can set three hyperparameter priors for the `gamma` lengthscale exponent for `GammaExponential` primitive, +`period` period for `Periodic` primitive and `wildcard` for all other hyperparameters. + +We will show how to edit the period prior, and likelihood of `Periodic` primitive kernels in the tree kernel structure, to give a +a strong seasonal prior, and how that improves forecasts. We score forecasts following the scoring approach of the [Getting started](getting-started.md) vignette. + +`GPConfig` is an immutable struct which makes "change just this one field" awkward to write by hand. +[`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s `@set` macro does exactly that: it +returns a *copy* with the chosen field(s) changed and all the others preserved. > `Accessors.jl` is a convenience used here in the docs; it is **not** a dependency of > `NowcastAutoGP` itself. The same edits can be made by constructing a `GPConfig` directly. @@ -32,6 +33,7 @@ measured by the Continuous Ranked Probability Score (CRPS). ## Loading dependencies """ +import NowcastAutoGP.AutoGP as AGP using NowcastAutoGP using Accessors using CairoMakie @@ -42,7 +44,7 @@ CairoMakie.activate!(type = "png") nothing #hide md""" -## Inspecting the default prior +## Inspecting the default priors `GPConfig()` exposes the prior as plain fields. The leaf-kernel distribution is a probability vector over the primitive kernels, indexed `Constant=1`, `Linear=2`, `SquaredExponential=3`, @@ -53,6 +55,12 @@ default_config = GPConfig() default_config.node_dist_leaf md""" +So by default, the `SquaredExponential` primitive (index 3) has **zero** prior mass, and is treated as superceded by +the `GammaExponential` (index 4), which recovers it as a special case when the `gamma` lengthscale exponent is exactly 2. +The `Linear` (index 2) and `Periodic` (index 5) primitives have equal prior mass with the `GammaExponential` (index 4), +and the `Constant` (index 1) has zero mass. +Therefore, the default prior is agnostic between `Linear`, `GammaExponential` and `Periodic` primitives. + The hyperparameter priors live in a nested `Dict`; the period prior is a `LogNormal(μ, σ)` over the periodic component's period: """ @@ -60,32 +68,36 @@ periodic component's period: default_config.prior[:period] md""" -AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units — -a fraction of the training window. The default median period is therefore only about a fifth of the -window: +AutoGP rescales the input time axis to `[0, 1]` internally, so this period is in *normalised* units as a fraction of the training window. +The default median period is therefore only about a fifth of the window: """ exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window md""" -## A seasonal series and a few report dates +## Example: A seasonal series and a few report dates + +In this example, we imagine having a new data stream for a pathogen, which _a priori_ we know has a strong +annual cycle. +We will make year long forecasts from three different report dates as data accrue: at one, one-and-a-half and two years of history. +We will show how to build a strong seasonal prior into the model in two ways: -We simulate three years of weekly observations on a **log scale** — a clear annual cycle and a gentle -upward trend, with multiplicative (log-normal) observation noise. We then imagine sitting at three -**report dates** — at roughly one, one-and-a-half and two years of history — and at each one forecast a -full year ahead. This mirrors the [Getting started](getting-started.md) workflow of scoring forecasts -across report dates as data accrue. +1. Re-centring the period prior on an annual cycle for that window. +2. Restricting the leaf-kernel distribution to only allow Linear + Periodic kernels. + +To demonstate, we simulate three years of synthetic weekly observations using a simple log-linear model +with annual sinusoidal variation around a linear trend with multiplicative noise. """ start_date = Date(2022, 1, 1) -all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) # 156 weekly points ≈ 3 years +all_dates = collect(start_date:Week(1):(start_date + Week(52 * 3))) n_all = length(all_dates) tt = 0:(n_all - 1) -log_truth = log(50.0) .+ 1.0 .* sin.(2π .* tt ./ 52) .+ 0.02 .* tt # annual cycle (52 weeks) + trend +log_truth = log(50.0) .+ 1.0 .* sin.(2π .* tt ./ 52) .+ 0.02 .* tt truth = exp.(log_truth) observations = exp.(log_truth .+ 0.15 .* randn(n_all)) - +## The report dates are at weeks 51, 77 and 103 (1 year, 1.5 years and 2 years in). report_weeks = 51 .+ [0, 26, 52] horizon = 52 # forecast one year ahead report_colours = [:steelblue, :darkorange, :seagreen] @@ -98,17 +110,18 @@ fig_data = let ylabel = "value", title = "Synthetic weekly series", ) + tvals = Dates.value.(all_dates .- first(all_dates)) / 7 lines!( - ax, Dates.value.(all_dates), truth; + ax, tvals, truth; color = (:black, 0.5), label = "expected", linestyle = :dash, linewidth = 2 ) scatter!( - ax, Dates.value.(all_dates), observations; + ax, tvals, observations; color = (:black, 0.8), markersize = 5, label = "observed" ) vlines!( - ax, Dates.value.(all_dates[report_weeks]); + ax, Dates.value.(all_dates[report_weeks] .- first(all_dates)) ./ 7; color = report_colours, linestyle = :dash, linewidth = 2 ) axislegend(ax; position = :lt) @@ -116,13 +129,15 @@ fig_data = let end md""" -## Re-centring the period prior with `@set` +### Choosing priors + +#### Re-centring the period prior with `@set` AutoGP works in *normalised* time: it rescales the training window to `[0, 1]`, so a `Periodic` kernel's period is expressed as a **fraction of the window**, and `prior[:period]` is a -`LogNormal(μ, σ)` over that fraction (its median is `exp(μ)`). Re-centring the prior is then just a -matter of `@set`-ting a new `μ` — here, a median period of a third of the window, held tightly with a -small `σ`: +`LogNormal(μ, σ)` over that fraction. +We can re-centre the prior using`@set` to give a new `μ` — here, held tightly with a small `σ`. +For example, for a three year window of data an annual cycle is 1/3 of the window, so `μ = log(1/3)`: """ seasonal_example = @set GPConfig().prior[:period][:mu] = -log(3.0) @@ -130,32 +145,46 @@ seasonal_example = @set seasonal_example.prior[:period][:sigma] = 0.1 seasonal_example.prior[:period] md""" -`@set` returns a fresh `GPConfig`; every sibling prior is carried over unchanged — it only touched -`prior[:period]`: +`@set` returns a fresh `GPConfig`; every other prior, and other fields, are carried over unchanged. +`@set` only touched `prior[:period]`: """ seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] md""" -## Forecasting from each report date +#### Alterating the leaf-kernel distribution -At each report date we fit two models on the data so far — one with the default prior, one with a -seasonal prior built for that window with `@set` — and forecast a year ahead. Everything except -`config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. Each -fitted model is a particle ensemble, so each forecast is a full predictive *distribution* — exactly -what CRPS scores below. +The leaf-kernel distribution is a simple probability vector over the primitive kernels. +We can use `@set` to change it, for example to specialise on only Linear + Periodic kernels (indices 2 and 5): +""" + +config_lin_period = @set GPConfig().node_dist_leaf = [0.0, 0.5, 0.0, 0.0, 0.5] + +md""" +### Forecasting from each report date + +At each report date we fit four models on the data so far that only differ in their priors: + +- Default prior (the default `GPConfig()`) +- Default hyperpriors, but only `Linear` + `Periodic` primitive leaf-kernels allowed, prior on other kernels set to zero. +- Seasonal hyperprior, fairly tight around an annual cycle, but the default primitive leaf-kernel distribution. +- Seasonal hyperprior, _and_ only `Linear` + `Periodic` primitive leaf-kernels allowed, prior on other kernels set to zero. + +Everything except `config` is identical; the `n_mcmc`/`n_hmc` controls pass straight through to `AutoGP.fit_smc!`. +We also set `adaptive_rejuvenation = true` to use the classic SMC resample-then-move adaptive rejuvenation scheme; +that is we make MCMC moves only when the effective sample size (ESS) of the particle ensemble drops below the default threshold of 50% of the particle number. +Each fitted model is a particle ensemble over GP tree-kernels, so each forecast is a full predictive *distribution*. """ n_particles = 32 fit_params = ( smc_data_proportion = 0.005, n_mcmc = 200, - n_hmc = 25, + n_hmc = 50, adaptive_rejuvenation = true, ) -n_draws = 1000 +n_draws = 2000 -Random.seed!(2026) results = map(report_weeks) do w horizon_dates = all_dates[(w + 1):(w + horizon)] horizon_truth = observations[(w + 1):(w + horizon)] @@ -191,7 +220,9 @@ results = map(report_weeks) do w ) return (; - report_week = w, horizon_dates, horizon_truth, + report_week = w, + horizon_dates, + horizon_truth, default = forecast( default_model, horizon_dates, n_draws; inv_transformation @@ -217,9 +248,7 @@ end nothing #hide md""" -We forecast a year ahead from each report date under all four priors (one row each). The strong -seasonal prior (rows 3–4) is what carries the annual cycle forward and stays close to the data; -restricting the leaf kernels to Linear + Periodic (rows 2 and 4) makes little difference on its own: +We forecast a year ahead from each report date under all four priors (one row each). """ fig_forecasts = let @@ -230,19 +259,27 @@ fig_forecasts = let (key = :seasonal, row = 3, title = "Seasonal prior"), (key = :seasonal_config_lin_period, row = 4, title = "Seasonal prior with linear/periodic GP structure"), ) + tvals = Dates.value.(all_dates .- first(all_dates)) / 7 for panel in panels - ax = Axis(fig[panel.row, 1]; xlabel = "week", ylabel = "value", title = panel.title) + ax = Axis( + fig[panel.row, 1]; + xlabel = "week", ylabel = "value", title = panel.title, + yscale = log10, + ) scatter!( - ax, Dates.value.(all_dates), observations; + ax, tvals, observations; color = :black, label = "observations" ) for (res, colour) in zip(results, report_colours) fc = getproperty(res, panel.key) - fx = Dates.value.(res.horizon_dates) - lower = [quantile(row, 0.25) for row in eachrow(fc)] + fx = Dates.value.(res.horizon_dates .- first(all_dates)) / 7 # convert to weeks for x-axis + lower_025 = [quantile(row, 0.025) for row in eachrow(fc)] + lower_25 = [quantile(row, 0.25) for row in eachrow(fc)] med = [quantile(row, 0.5) for row in eachrow(fc)] - upper = [quantile(row, 0.75) for row in eachrow(fc)] - band!(ax, fx, lower, upper; color = (colour, 0.2)) + upper_75 = [quantile(row, 0.75) for row in eachrow(fc)] + upper_975 = [quantile(row, 0.975) for row in eachrow(fc)] + band!(ax, fx, lower_025, upper_975; color = (colour, 0.2)) + band!(ax, fx, lower_25, upper_75; color = (colour, 0.4)) lines!(ax, fx, med; color = colour, linewidth = 2.5, label = "from week $(res.report_week)") end panel.row == 1 && axislegend(ax; position = :lt, nbanks = 2) @@ -251,10 +288,15 @@ fig_forecasts = let end md""" -## Scoring with CRPS +We see that incorporating our prior knowledge of seasonality substantially improves forecasts. +However, this improvement is not uniform; at the first report date, when only one year of data is available, there is insufficient information to learn the secular trend underneath the seasonal variation. +By one and a half years, the change in compared to the previous season is clearer, and the strong seasonal prior allows the model to extrapolate that pattern forward. +This is especially pronounced when we restrict the leaf-kernel distribution to only allow `Linear` + `Periodic` primitives. +Later on, the model has locked onto a combination of kernels that captures the trend and seasonality, so the restriction to `Linear` + `Periodic` leaves makes less difference. -This is a probabilistic model, so we score each predictive *distribution* against the value it should -have predicted using the **Continuous Ranked Probability Score (CRPS)** — the proper scoring rule from +### Scoring with CRPS + +We score each forecast against out-of-sample observations using the **Continuous Ranked Probability Score (CRPS)** a proper scoring rule from the [Getting started](getting-started.md) vignette (lower is better), reusing the same hand-rolled estimator: @@ -293,9 +335,8 @@ crps_by_date = map(results) do res end md""" -Scoring confirms the visual read. The strong seasonal prior gives a markedly lower CRPS, while -restricting the leaf kernels to Linear + Periodic barely moves the score — on its own it is not -particularly beneficial. It is the period *hyperparameter* prior, not the kernel menu, doing the work: +Scoring confirms the visual impression. +The strong seasonal prior gives a markedly lower CRPS, after there is available contrast between the seasons to allow the secular trend to be learned. """ fig_scores = let @@ -348,21 +389,6 @@ overall_crps = (; ) md""" -## Enabling `SquaredExponential` structure - -The leaf-kernel distribution is editable the same way. The default gives `SquaredExponential` -(index 3) **zero** prior mass; `@set` can spread mass evenly over `Linear`, `SquaredExponential`, -`GammaExponential` and `Periodic` (the vector must sum to 1): -""" - -se_config = @set GPConfig().node_dist_leaf = [0.0, 0.25, 0.25, 0.25, 0.25] -se_config.node_dist_leaf - -md""" -`se_config` can be passed to `make_and_fit_model(...; config = se_config)` exactly like the seasonal -one, and edits compose — chain further `@set` calls (or use `@reset`) to adjust the period prior *and* -the kernel distribution together. - ## Summary - `make_and_fit_model(...; config = ...)` forwards any `AutoGP.GP.GPConfig` to the model, so the full @@ -372,39 +398,8 @@ the kernel distribution together. - Re-centring the period *hyperparameter* prior (`prior[:period]`) on the seasonality you expect can substantially improve forecasts — here the strong seasonal prior gives the lowest mean CRPS across the report dates. -- Editing the *structural* prior (`node_dist_leaf`) to allow only Linear + Periodic leaves made little - difference on its own: the period prior, not the kernel menu, drove the gains. As always, score - competing priors with CRPS (averaged over the forecasts) rather than assuming an edit will help. +- Editing the *structural* prior (`node_dist_leaf`) to allow only Linear + Periodic leaves also improves forecasts. +- However, note that strong priors can be a double-edged sword: they can help when data are scarce, but if they are too tight or the wrong shape they can be a problem. """ -md""" -## Appendix: the discovered kernel structures - -Each fitted model is a *weighted ensemble* of SMC particles, and every particle is a complete GP with -its own covariance-kernel structure. AutoGP exposes them directly: `particle_weights` gives each -particle's posterior weight and `covariance_kernels` its discovered kernel. Reading these out shows -which structures the search actually settled on under a given prior — a concrete look at what the prior -did. Here is the ensemble from the default-prior fit at the final report date, ordered by weight: -""" - -import NowcastAutoGP.AutoGP as AGP - -function show_discovered_kernels(model) - weights = AGP.particle_weights(model) - kernels = AGP.covariance_kernels(model) - ## list particles from highest to lowest posterior weight - for i in sortperm(weights; rev = true) - println("posterior weight = ", round(weights[i]; digits = 3)) - display(kernels[i]) - end - return nothing -end - -show_discovered_kernels(results[end].default_model) - -md""" -Running the same readout on the strong-seasonal-prior fit lets us compare how re-centring the period -prior reshaped the structures the search selected: -""" -show_discovered_kernels(results[end].seasonal_model) From a969d57a5ff1862220a02f67ed9b082216e6d243 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Thu, 4 Jun 2026 09:31:08 +0100 Subject: [PATCH 6/8] reformat --- docs/src/vignettes/setting-priors.md | 1 - docs/vignettes/setting-priors.jl | 10 ++++------ 2 files changed, 4 insertions(+), 7 deletions(-) diff --git a/docs/src/vignettes/setting-priors.md b/docs/src/vignettes/setting-priors.md index 578e31e..15a7ede 100644 --- a/docs/src/vignettes/setting-priors.md +++ b/docs/src/vignettes/setting-priors.md @@ -531,4 +531,3 @@ overall_crps = (; --- *This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* - diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl index 87ab0eb..5ee7dff 100644 --- a/docs/vignettes/setting-priors.jl +++ b/docs/vignettes/setting-priors.jl @@ -17,7 +17,7 @@ In this vignette we are interested in two different priors. First, the underlying `AutoGP` kernel structure can be represented as a tree with primitive kernels at the leaves, and the internal nodes describing the combinations `Plus`, `Times` and `ChangePoint`, c.f. [AutoGP.jl documentation](https://probsys.github.io/AutoGP.jl/stable/api.html). We can use the configuration to set the prior probability for each of the primitive kernels to be a leaf in the structure. -Second, we can set three hyperparameter priors for the `gamma` lengthscale exponent for `GammaExponential` primitive, +Second, we can set three hyperparameter priors for the `gamma` lengthscale exponent for `GammaExponential` primitive, `period` period for `Periodic` primitive and `wildcard` for all other hyperparameters. We will show how to edit the period prior, and likelihood of `Periodic` primitive kernels in the tree kernel structure, to give a @@ -25,7 +25,7 @@ a strong seasonal prior, and how that improves forecasts. We score forecasts fol `GPConfig` is an immutable struct which makes "change just this one field" awkward to write by hand. [`Accessors.jl`](https://github.com/JuliaObjects/Accessors.jl)'s `@set` macro does exactly that: it -returns a *copy* with the chosen field(s) changed and all the others preserved. +returns a *copy* with the chosen field(s) changed and all the others preserved. > `Accessors.jl` is a convenience used here in the docs; it is **not** a dependency of > `NowcastAutoGP` itself. The same edits can be made by constructing a `GPConfig` directly. @@ -77,7 +77,7 @@ exp(default_config.prior[:period][:mu]) # ≈ 0.22 of the window md""" ## Example: A seasonal series and a few report dates -In this example, we imagine having a new data stream for a pathogen, which _a priori_ we know has a strong +In this example, we imagine having a new data stream for a pathogen, which _a priori_ we know has a strong annual cycle. We will make year long forecasts from three different report dates as data accrue: at one, one-and-a-half and two years of history. We will show how to build a strong seasonal prior into the model in two ways: @@ -121,7 +121,7 @@ fig_data = let color = (:black, 0.8), markersize = 5, label = "observed" ) vlines!( - ax, Dates.value.(all_dates[report_weeks] .- first(all_dates)) ./ 7; + ax, Dates.value.(all_dates[report_weeks] .- first(all_dates)) ./ 7; color = report_colours, linestyle = :dash, linewidth = 2 ) axislegend(ax; position = :lt) @@ -401,5 +401,3 @@ md""" - Editing the *structural* prior (`node_dist_leaf`) to allow only Linear + Periodic leaves also improves forecasts. - However, note that strong priors can be a double-edged sword: they can help when data are scarce, but if they are too tight or the wrong shape they can be a problem. """ - - From dd07d8c4fbb04f4558b91d31967b754d076a87f5 Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Thu, 4 Jun 2026 11:02:58 +0100 Subject: [PATCH 7/8] put in defaults --- src/make_and_fit_model.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/make_and_fit_model.jl b/src/make_and_fit_model.jl index 3d3c08a..605dc9c 100644 --- a/src/make_and_fit_model.jl +++ b/src/make_and_fit_model.jl @@ -14,7 +14,7 @@ This is a secondary safety net for data that is flat even after transformation. common case of a pathological Box-Cox λ on otherwise-fittable data is handled earlier, in [`get_transformations`](@ref), by falling back to a log transformation. """ -function _stabilize_for_fit(y::AbstractVector{<:Real}; flat_threshold) +function _stabilize_for_fit(y::AbstractVector{<:Real}; flat_threshold = 1.0e-3) n = length(y) n > 1 || return y scale = abs(sum(y) / n) + 1 @@ -76,7 +76,7 @@ for these copy-and-update edits if you have it in your environment (`config = @set GPConfig().prior[:period][:mu] = log(1.0)`); it is not a dependency of this package. """ function make_and_fit_model( - data::TData; n_particles, smc_data_proportion, + data::TData; n_particles = 1, smc_data_proportion = 0.1, flat_threshold = 1.0e-3, config = AutoGP.GP.GPConfig(), kwargs... ) n_train = length(data.y) From 15a2c5996e428171791ac7276bd3dcbaf46cbf4b Mon Sep 17 00:00:00 2001 From: Samuel Brand <48288458+SamuelBrand1@users.noreply.github.com> Date: Thu, 4 Jun 2026 11:06:57 +0100 Subject: [PATCH 8/8] typos and mistaken comment out Co-authored-by: Copilot Autofix powered by AI <175728472+Copilot@users.noreply.github.com> --- docs/make_vignettes.jl | 4 ++-- docs/vignettes/setting-priors.jl | 8 ++++---- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/make_vignettes.jl b/docs/make_vignettes.jl index ea39b4e..2c208a2 100644 --- a/docs/make_vignettes.jl +++ b/docs/make_vignettes.jl @@ -1,7 +1,7 @@ using Literate vignettes_to_make = [ - # "getting-started.jl", - # "use-percentages.jl", + "getting-started.jl", + "use-percentages.jl", "setting-priors.jl", ] diff --git a/docs/vignettes/setting-priors.jl b/docs/vignettes/setting-priors.jl index 5ee7dff..c29a963 100644 --- a/docs/vignettes/setting-priors.jl +++ b/docs/vignettes/setting-priors.jl @@ -55,7 +55,7 @@ default_config = GPConfig() default_config.node_dist_leaf md""" -So by default, the `SquaredExponential` primitive (index 3) has **zero** prior mass, and is treated as superceded by +So by default, the `SquaredExponential` primitive (index 3) has **zero** prior mass, and is treated as superseded by the `GammaExponential` (index 4), which recovers it as a special case when the `gamma` lengthscale exponent is exactly 2. The `Linear` (index 2) and `Periodic` (index 5) primitives have equal prior mass with the `GammaExponential` (index 4), and the `Constant` (index 1) has zero mass. @@ -85,7 +85,7 @@ We will show how to build a strong seasonal prior into the model in two ways: 1. Re-centring the period prior on an annual cycle for that window. 2. Restricting the leaf-kernel distribution to only allow Linear + Periodic kernels. -To demonstate, we simulate three years of synthetic weekly observations using a simple log-linear model +To demonstrate, we simulate three years of synthetic weekly observations using a simple log-linear model with annual sinusoidal variation around a linear trend with multiplicative noise. """ @@ -152,7 +152,7 @@ md""" seasonal_example.prior[:gamma] == GPConfig().prior[:gamma] md""" -#### Alterating the leaf-kernel distribution +#### Altering the leaf-kernel distribution The leaf-kernel distribution is a simple probability vector over the primitive kernels. We can use `@set` to change it, for example to specialise on only Linear + Periodic kernels (indices 2 and 5): @@ -290,7 +290,7 @@ end md""" We see that incorporating our prior knowledge of seasonality substantially improves forecasts. However, this improvement is not uniform; at the first report date, when only one year of data is available, there is insufficient information to learn the secular trend underneath the seasonal variation. -By one and a half years, the change in compared to the previous season is clearer, and the strong seasonal prior allows the model to extrapolate that pattern forward. +By one and a half years, the change compared to the previous season is clearer, and the strong seasonal prior allows the model to extrapolate that pattern forward. This is especially pronounced when we restrict the leaf-kernel distribution to only allow `Linear` + `Periodic` primitives. Later on, the model has locked onto a combination of kernels that captures the trend and seasonality, so the restriction to `Linear` + `Periodic` leaves makes less difference.

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