From 7632f5cbf4972589dbe9ce29fbbe5680f1b09e2f Mon Sep 17 00:00:00 2001 From: fstrub Date: Thu, 18 Feb 2016 18:48:03 +0100 Subject: [PATCH 01/12] add first idea for post --- blog/_posts/2016-02-21-cfn.md | 461 ++++++++++++++++++++++++++++++ blog/_posts/images/CF/CBF.png | Bin 0 -> 150584 bytes blog/_posts/images/CF/ratings.png | Bin 0 -> 43481 bytes 3 files changed, 461 insertions(+) create mode 100644 blog/_posts/2016-02-21-cfn.md create mode 100644 blog/_posts/images/CF/CBF.png create mode 100644 blog/_posts/images/CF/ratings.png diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md new file mode 100644 index 0000000..4b99393 --- /dev/null +++ b/blog/_posts/2016-02-21-cfn.md @@ -0,0 +1,461 @@ +--- +layout: post +title: Collaborative Filtering with Neural Networks +comments: True +author: florian-strub +excerpt: Collaborative Filtering methods are a key algorithm for Recommender Systems. They are used by major companies such as Netflix, Amazon or Spotify to suggest items to users. While Neural Networks have tremendous success in image and speech recognition, Collaborative Filtering received less attention as it deals with sparse inputs/targets. After a quick introduction to Recommendation Systems, we show how to implement Autoencoders to perform Collaborative Filtering. +picture: http://insidebigdata.com/wp-content/uploads/2014/06/Humor_recommender.jpg +--- + + + +Deep Learning has well-known state-of-the arts results in Computer Vision, Speech Recognition or Natural Language Processing. +This post aims at using Neural Networks on a new topic : Recommender systems and Collaborative Filtering. + +Recommendation systems are a subclass of algorithms that seek to predict the rating that a user would give to an item [Wiki](https://en.wikipedia.org/wiki/Recommender_system). +One of the most successful approach of Recommendation systems is to use the explicit feedback of users. + +Collaborative Filtering + + + + + - Classic fields: Image/Speech Recognition/ + Recommendation system + + - rank items --> rankNet + - predict matrix of ratings -> CF / CB + +This post focus on the implementation part. Underlying motivations, basic maths are explained in the following paper + +## Problem description ## + +Matrix of ratings + +Create autoencoders that will fill this matrix. +--> picture: + +movieLens + + + +## Sparsity ## +Sparsity big constraint +Picture Autoencoder + +Autoencoder ~= dimension reduction + + +First step : use sparse representation +Torch.sparse + +Data sparse +implement parser + + +## Autoencoder -> Forward ## + +Use SparseLinear... Slow +CPU -> use nnsparse.BatchLinear +GPU -> nnsparse.densify() + nn.Linear (Up to 10time faster) + +Better implementation undergoing + + +## Autoencoder -> Loss ## +Unknwon rating??? + -> unknown = no error... + + loss = sum (exist) + + Backward + + +## Autoencoder -> Better ## + +Yes! Use mask noise +--> loss + +Deeper? Yes, harder to train... + + +## Results ## + + +## +This is not deep learning. (look at the title :P) + +Another field where the structure of neural networks return excellent restults +Autoencoders were used differently form what they think to do. + +This is not naive implementation of neural networks, they are actualy clear motivation why it was likely to work. +The real surprise is : how well they work! + +![ratings](/home/fstrub/Projects/torch.github.io/blog/_posts/images/CF) + + + + + + + +```lua +module = nn.SpatialGlimpse(size, depth, scale) +``` + +Basically, if you feed it an image, say the classic `3x512x512` Lenna image: + +![lenna](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/lenna.png) + +And you run this code on it: + +```lua +require 'dpnn' +require 'image' + +img = image.lena() +loc = torch.Tensor{0,0} -- 0.0 is the center of the image + +sg = nn.SpatialGlimpse(64, 3, 2) + +output = sg:forward{img, loc} +print(output:size()) -- 9 x 64 x 64 + + +-- unroll the glimpse onto its different depths +outputs = torch.chunk(output, 3) +display = image.toDisplayTensor(outputs) +image.save("glimpse-output.png", display) +``` + +You will end up with the following (unrolled) glimpse : + +![glimpse](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/glimpse-output.png) + +While the input is a `3x512x512` image (786432 scalars), +the output is very small : `9x64x64` (36864 scalars), or about +5% the size of the original image. +Since the glimse here has a `depth=3` (i.e. it uses 3 patches), +each successive patch is `scale` times the size of the prevous one. +So we end up with a high-resolution patch of a small area, +and successively lower-resolution (i.e. downscaled) patches of larger areas. +This carries fascinating parallels to how our own human attention mechanism may possibly work. +Quite often, we humans can vividly see the details of what we focus our attention on, +while nevertheless maintaining a blurry sense of the outskirts. + +Although not necessary for reproducing this paper, +the `SpatialGlimpse` can also be partially backpropagated through. +While the gradient w.r.t. the `img` tensor can be obtained, +the gradients w.r.t. the `location` (i.e. the `x,y` coordinates of the glimpse) will be zero. +This is because the glimpse operation cannot be differentiated w.r.t. the `location`. +Which brings us to the main difficulty of attention models : +how can we teach the network to glimpse at the right `locations`? + +## REINFORCE algorithm ## + +Some attention models use a fully differentiable attention mechanism, +like the recent DRAW paper [[2]](#rmva.ref). +But the RAM model uses a non-differentiable attention mechanism. +Specifically, it uses a the REINFORCE algorithm [[3]](#rmva.ref). +This algorithm allows one to train stochastic units through reinforcement learning. + +The REINFORCE algorithm is very powerful as it can be +used to optimize stochastic units (conditioned on an input), +such that they minimize an objective function (i.e. a reward function). +*Unlike backpropagation [[4]](#rmva.ref), this objective need not be differentiable*. + +The RAM model uses the REINFORCE algorithm to train the `locator` network : + +```lua +-- actions (locator) +locator = nn.Sequential() +locator:add(nn.Linear(opt.hiddenSize, 2)) +locator:add(nn.HardTanh()) -- bounds mean between -1 and 1 +locator:add(nn.ReinforceNormal(2*opt.locatorStd)) -- sample from normal, uses REINFORCE learning rule +locator:add(nn.HardTanh()) -- bounds sample between -1 and 1 +locator:add(nn.MulConstant(opt.unitPixels*2/ds:imageSize("h"))) +``` + +The input is the previous recurrent hidden state `h[t-1]`. +During training, the output is sampled from a normal +distribution with fixed standard deviation. +The mean is conditioned on `h[t-1]` through an affine transform (i.e. `Linear` module). +During evaluation, instead of sampling from the distribution, the output is taken to be the input, i.e. the mean. + +The [ReinforceNormal](https://github.com/nicholas-leonard/dpnn#nn.ReinforceNormal) module +implements the REINFORCE algorithm for the normal distribution. +Unlike most `Modules`, `ReinforceNormal` ignores the `gradOutput` when `backward` is called. +This is because the units it embodies are in fact stochastic. +So then how does it generate `gradInputs` when the `backward` is called? +It uses the REINFORCE algorithm, which requires that a reward function be defined. +The reward used by the paper is very simple, and yet not differentiable (eq. 1) : + +``` +R = I(y=t) +``` + +where `R` is the raw reward, `I(x)` is `1` when `x` is true and `0` otherwise +(see [indicator function](https://en.wikipedia.org/wiki/Indicator_function)), +`y` is the predicted class, `t` is the target class. +Or in Lua : + +```lua +R = (y==t) and 1 or 0 +``` + +The REINFORCE algorithm requires that we differentiate the +probability density or mass function (PDF/PMF) of the distribution +w.r.t. the parameters. So given the following variables : + + * `f` : normal probability density function + * `x` : the sampled values (i.e. `ReinforceNormal.output`) + * `u` : mean (`input` to `ReinforceNormal`) + * `s` : standard deviation (`ReinforceNormal.stdev`) + +the derivative of log normal w.r.t. mean `u` is : + +``` +d ln(f(x,u)) (x - u) +------------ = ------- + d u s^2 +``` + +So where does `d ln(f(x,u,s) / d u` fit in with the reward? +Well, in order to obtain a gradient of the reward `R` w.r.t. +to input `u`, we apply the following equation (eq. 2, i.e. the REINFORCE algorithm): + +``` +d R d ln(f(x,u)) +--- = a * (R - b) * -------------- +d u d u +``` + +where + + * `a` (alpha) is just a scaling factor like the learning rate ; and + * `b` is a baseline reward used to reduce the variance of the gradient. + * `f` is the PMF/PDF + * `u` is the parameter w.r.t. which you want to get a gradient + * `x` is the sampled value. + +In the paper, they take `b` to be the expected reward `E[R]`. +They approximate the expectation by making `b` a (conditionally independent) parameter of the model . +For each example, the mean square error between `R` and `b` is minimized by +backpropagation. The beauty of doing this, instead of, +say, making `b` a moving average of `R`, is that *the baseline reward `b` +learns at the same rate as the rest of the model*. + +We decided to implement the `reward = a * (R - b)` part of eq. 2 +within a [VRClassReward](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.VRClassReward) criterion, +which also implements the paper's varianced-reduced classification reward function (eq. 1): + +```lua +vcr = nn.VRClassReward(module [, scale, criterion]) +``` + +The nn package was primarily built for backpropagation, so we had to find a not-too-hacky way of +broadcasting the `reward` to the different +[Reinforce](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.Reinforce) modules. +We did this by having the criterion take the `module` as argument, +and adding the [Module:reinforce(reward)](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.Module.reinforce) +method. The latter allows the `Reinforce` modules (like `ReinforceNormal`) to +hold on to the criterion's broadcasted `reward` for later. Later being when `backward` is called +and the `Reinforce` module(s) compute(s) the `gradInput` +(i.e. `d R / d U`) using the REINFORCE algorithm (eq. 2). +And then `nn` is happy, because with the `gradInput`, it can continue +the backpropagation from the `Reinforce` module to its predecessors. + +So to summarize, if you can differentiate the PMF/PDF w.r.t. to its parameters, +then you can use the REINFORCE algorithm on it. We have already implemented +modules for the categorical and bernoulli distributions : + + * [ReinforceCategorical](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.ReinforceCategorical) + * [ReinforceBernoulli](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.ReinforceBernoulli) + +## Recurrent Attention Model + +![rva](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/rva-diagram.png) + +Okay, so we discussed the glimpse module and the REINFORCE algorithm, +lets talk about the recurrent attention model. We can divide the model +into its respective components : + +The location sensor. Its inputs are the `x`, `y` coordinates of the current glimpse location, +so the network knows *where* its looking at each time-step : + +```lua +locationSensor = nn.Sequential() +locationSensor:add(nn.SelectTable(2)) +locationSensor:add(nn.Linear(2, opt.locatorHiddenSize)) +locationSensor:add(nn[opt.transfer]()) +``` + +The glimpse sensor is *what* it's looking at : + +```lua +glimpseSensor = nn.Sequential() +glimpseSensor:add(nn.DontCast(nn.SpatialGlimpse(opt.glimpsePatchSize, opt.glimpseDepth, opt.glimpseScale):float(),true)) +glimpseSensor:add(nn.Collapse(3)) +glimpseSensor:add(nn.Linear(ds:imageSize('c')*(opt.glimpsePatchSize^2)*opt.glimpseDepth, opt.glimpseHiddenSize)) +glimpseSensor:add(nn[opt.transfer]()) +``` + +The glimpse network is where the glimpse and location sensor mix through +a hidden layer to form the input layer of the Recurrent Neural Network (RNN) : + +```lua +glimpse = nn.Sequential() +glimpse:add(nn.ConcatTable():add(locationSensor):add(glimpseSensor)) +glimpse:add(nn.JoinTable(1,1)) +glimpse:add(nn.Linear(opt.glimpseHiddenSize+opt.locatorHiddenSize, opt.imageHiddenSize)) +glimpse:add(nn[opt.transfer]()) +glimpse:add(nn.Linear(opt.imageHiddenSize, opt.hiddenSize)) +``` + +The RNN is the where the glimpse network and the recurrent layer come together. +The output of the `rnn` module is the hidden state `h[t]` where `t` indexes the time-step. +We used the [rnn](https://github.com/Element-Research/rnn) package to build it : + +```lua +-- rnn recurrent layer +recurrent = nn.Linear(opt.hiddenSize, opt.hiddenSize) + +-- recurrent neural network +rnn = nn.Recurrent(opt.hiddenSize, glimpse, recurrent, nn[opt.transfer](), 99999) +``` + +We have already seen the locator network above, but here it is again : + +```lua +-- actions (locator) +locator = nn.Sequential() +locator:add(nn.Linear(opt.hiddenSize, 2)) +locator:add(nn.HardTanh()) -- bounds mean between -1 and 1 +locator:add(nn.ReinforceNormal(2*opt.locatorStd)) -- sample from normal, uses REINFORCE learning rule +locator:add(nn.HardTanh()) -- bounds sample between -1 and 1 +locator:add(nn.MulConstant(opt.unitPixels*2/ds:imageSize("h"))) +``` + +The locator's task is to sample the next location `l[t]` (or action) +given the previous hidden state `h[t-1]`, i.e. the previous output of the `rnn`. +For the first step, we use `h[0] = 0` (a tensor of zeros) for the previous hidden state. +We should also bring your attention to the `opt.unitPixels` variable, +as it is very important and not specified in the paper. +This variable basically outlines how far (in pixels) near the borders the +center of each glimpse can reach with respect to the center. +So a value of 13 (the default) means that the center of the glimpse can +be anywhere between the 2rd and 27th pixel (for a `1x28x28` MNIST example). +So glimpses of the corner will have fewer zero-padding values then if `opt.unitPixels = 14`. + +We need to encapsulate the `rnn` and `locator` into a module that would +capture the essence of the RAM model. +So we decided to implement a module that took the full image as input, +and output the sequence of hidden states `h`. +As its name implies, this module is a general purpose +[RecurrentAttention](https://github.com/Element-Research/rnn#rnn.RecurrentAttention) module : + +```lua +attention = nn.RecurrentAttention(rnn, locator, opt.rho, {opt.hiddenSize}) +``` + +It's so general-purpose that you can use it with an +[LSTM](https://github.com/Element-Research/rnn#rnn.LSTM) module, +and different glimpse or locator modules. As long as these respectively preserve +the same `{input, action} -> output` interfaces (glimpse) and use the REINFORCE algorithm (locator), of course. + +Next we build an agent by stacking a classifier on top of the `RecurrentAttention` module. +The classifier's input is the last hidden state `h[T]`, +where `T` is the total number of time-steps (i.e. glimpses to take): + +```lua +-- model is a reinforcement learning agent +agent = nn.Sequential() +agent:add(nn.Convert(ds:ioShapes(), 'bchw')) +agent:add(attention) + +-- classifier : +agent:add(nn.SelectTable(-1)) +agent:add(nn.Linear(opt.hiddenSize, #ds:classes())) +agent:add(nn.LogSoftMax()) +``` + +You might recall that the REINFORCE algorithm requires a baseline reward `b`? +This is where that happens (yes, it requires a little bit of `nn` kung-fu): + +```lua +-- add the baseline reward predictor +seq = nn.Sequential() +seq:add(nn.Constant(1,1)) +seq:add(nn.Add(1)) +concat = nn.ConcatTable():add(nn.Identity()):add(seq) +concat2 = nn.ConcatTable():add(nn.Identity()):add(concat) + +-- output will be : {classpred, {classpred, basereward}} +agent:add(concat2) +``` + +At this point, the model is ready for training. +The `agent` instance is effectively the RAM model detailed in the paper. + +## Training + +Training is pretty straight-forward after that. +The script can be launched with the default hyper-parameters. +It should take 1-2 runs to find a validation minima that +reproduces the MNIST test results of the paper. We are still working on +reproducing the Translated and Cluttered MNIST results. + +## Results + +In the paper, they get 1.07% error on MNIST with 7 glimpses. +We got 0.85% error after 853 epochs of training (early-stopped on the validation set of course). +Here are some glimpse sequences. Note how the first frames start at the same location : + +![locations](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_8PHJ4z.gif) + +And this is what the model sees for those sequences: + +![glimpses](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_Onbzrk.gif) + +So basically, REINFORCE did a good job of teaching the module to focus +its attention on different regions given different inputs. +A failure mode (bad) would have been to see the model do this : + +![fail](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_6kgOs1.gif) + +In that particular case, the `opt.unitPixels` was set to 6 instead of 12 +(so the attention was limited to a small region in the center of the image). +You don't want this to happen because it means the attention is conditionally independent of the input (i.e. dumb). + +Here are some results for the Translated MNIST dataset : + +![translatedmnist](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_52iFki.gif) + +For this dataset, the images are of size `1x60x60` where each image contains a randomly placed `1x28x28` MNIST digit. +The `3x12x12` glimpse uses a depth of 3 scales +where each successive patch is twice the height and width of the previous one. +Training with this dataset was started about 3 days prior to this blog post. +For 7 glimpses, after 193 epochs, we get 1.223% error. Note that the model is still training. +The paper gets 1.22% and 1.2% error for 6 and 8 glimpses, respectively. + +Note : you can evaluate your models with the [evaluation script](https://github.com/Element-Research/rnn/blob/master/scripts/evaluate-rva.lua). +It will generate a sample of glimpse sequences and print the confusion matrix results for the test set. + +## Conclusion + +This blog discussed a concrete implementation of a Recurrent Model for Visual Attention +using the REINFORCE algorithm. The REINFORCE algorithm is very powerful as it +can learn non-differentiable criterions through reinforcement learning. +However, like many reinforcement learning algorithms, it does take a long time to converge. +Nevertheless, as demonstrated here and in the original paper, +the ability to train a model to learn where to focus its attention +can provide significant performance improvements. + + + +## References + +1. *Volodymyr Mnih, Nicolas Heess, Alex Graves, Koray Kavukcuoglu*, Recurrent Models of Visual Attention, [NIPS 2014](http://papers.nips.cc/paper/5542-recurrent-models-of-visual-attention) +2. *Gregor, Karol, et al.*, DRAW: A recurrent neural network for image generation, [Arxiv 2015](http://arxiv.org/abs/1502.04623) +3. *Williams, Ronald J.*, Simple statistical gradient-following algorithms for connectionist reinforcement learning, [Machine learning 8.3-4 (1992): 229-256](http://link.springer.com/article/10.1007/BF00992696). +4. *Rumelhart, David E., Geoffrey E. Hinton, and Ronald J. 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--- blog/_posts/images/CF/Matrixratings.png | Bin 0 -> 666 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 blog/_posts/images/CF/Matrixratings.png diff --git a/blog/_posts/images/CF/Matrixratings.png b/blog/_posts/images/CF/Matrixratings.png new file mode 100644 index 0000000000000000000000000000000000000000..e1dfdfbe48cfd26725bfb59ba56b78cd5132ab25 GIT binary patch literal 666 zcmeAS@N?(olHy`uVBq!ia0y~yU}^%gCvh+V$++7#AAl5dv6E*A2M5RPhyD+M@CYG#TEp2H4(!j7U@$V{VUUz&Yv|!+b~x6? usE~Y^VZz2lh7&go7*a;1M}q|^If!vYu_$`?-hT~DYz&^RelF{r5}E+;lfWqe literal 0 HcmV?d00001 From 1a815269da30cdc1d5de98bc0c2d13d301a49f3d Mon Sep 17 00:00:00 2001 From: fstrub Date: Fri, 19 Feb 2016 17:20:20 +0100 Subject: [PATCH 03/12] Add introduction --- blog/_posts/2016-02-21-cfn.md | 397 +++------------------------------- 1 file changed, 30 insertions(+), 367 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 4b99393..81f8805 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -10,23 +10,38 @@ picture: http://insidebigdata.com/wp-content/uploads/2014/06/Humor_recommender.j Deep Learning has well-known state-of-the arts results in Computer Vision, Speech Recognition or Natural Language Processing. -This post aims at using Neural Networks on a new topic : Recommender systems and Collaborative Filtering. +This post aims at using Neural Networks on a different topic : Recommender systems and Collaborative Filtering. +It turns out that Neural Networks also perform among the best Collaborative Fitering algorithms. -Recommendation systems are a subclass of algorithms that seek to predict the rating that a user would give to an item [Wiki](https://en.wikipedia.org/wiki/Recommender_system). -One of the most successful approach of Recommendation systems is to use the explicit feedback of users. +#Introduction# -Collaborative Filtering +Recommendation systems are a subclass of algorithms that seek to predict the rating that a user would give to an item. +A good recommendation system may dramatically increase the amount of sales of a firm or retain customers. For instance, 80% of movies watched on Netflix come from the recommender system of the company +One of the most successful approach of Recommendation systems is to use the explicit feedback of users to build a Matrix of ratings. This technique is known as Collaborative Filtering. +For instance, if we gather the feedback of all users into a matrix, we obtain a sparse matrix of ratings. Note that sparsity is induced by unknown values. + +![ratings](http://florian-strub.com/tmp/initialMatrix.png) + +In this case, should we recommend Bob to watch _The Exorcist_ or _Titanic_? + +Collaborative Filtering aims at estimating the ratings a user would have given to other movies by using the ratings of all the other users. +Inherent features of users or items such as the genre, age, actors or some descriptions are _not_ take into account. +The goal is then to turn the previous sparse matrix of ratings into a dense one: + +![ratings](http://florian-strub.com/tmp/finalMatrix.png) + +Therefore, the Recommender System will advise Bob to watch _The Exorcist_. + +If Bob eventually rates _The Exorcist_, the matrix is re-estimated and so on... +In practice, the matrix of ratings is very sparse. IMDB currently inventors around 1,7 millions movies while users rarely rate more than a few hundreds movies. + +In addition to this sparsity constraint, Collaborative Filtering faces several limitations such as the cold-start problem (How to recommend an item that has no rating), scalability issue (Millions of users/products) or lack of external information (how to append side information to help the system). +A good overview can be found in the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) + +In this post, we will focus on the general case and the network implementation for clarity purpose. - - - Classic fields: Image/Speech Recognition/ - Recommendation system - - - rank items --> rankNet - - predict matrix of ratings -> CF / CB - -This post focus on the implementation part. Underlying motivations, basic maths are explained in the following paper ## Problem description ## @@ -39,6 +54,7 @@ movieLens + ## Sparsity ## Sparsity big constraint Picture Autoencoder @@ -91,371 +107,18 @@ Autoencoders were used differently form what they think to do. This is not naive implementation of neural networks, they are actualy clear motivation why it was likely to work. The real surprise is : how well they work! -![ratings](/home/fstrub/Projects/torch.github.io/blog/_posts/images/CF) - - - - - - - -```lua -module = nn.SpatialGlimpse(size, depth, scale) -``` - -Basically, if you feed it an image, say the classic `3x512x512` Lenna image: - -![lenna](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/lenna.png) - -And you run this code on it: - -```lua -require 'dpnn' -require 'image' - -img = image.lena() -loc = torch.Tensor{0,0} -- 0.0 is the center of the image - -sg = nn.SpatialGlimpse(64, 3, 2) - -output = sg:forward{img, loc} -print(output:size()) -- 9 x 64 x 64 - --- unroll the glimpse onto its different depths -outputs = torch.chunk(output, 3) -display = image.toDisplayTensor(outputs) -image.save("glimpse-output.png", display) -``` - -You will end up with the following (unrolled) glimpse : - -![glimpse](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/glimpse-output.png) - -While the input is a `3x512x512` image (786432 scalars), -the output is very small : `9x64x64` (36864 scalars), or about -5% the size of the original image. -Since the glimse here has a `depth=3` (i.e. it uses 3 patches), -each successive patch is `scale` times the size of the prevous one. -So we end up with a high-resolution patch of a small area, -and successively lower-resolution (i.e. downscaled) patches of larger areas. -This carries fascinating parallels to how our own human attention mechanism may possibly work. -Quite often, we humans can vividly see the details of what we focus our attention on, -while nevertheless maintaining a blurry sense of the outskirts. -Although not necessary for reproducing this paper, -the `SpatialGlimpse` can also be partially backpropagated through. -While the gradient w.r.t. the `img` tensor can be obtained, -the gradients w.r.t. the `location` (i.e. the `x,y` coordinates of the glimpse) will be zero. -This is because the glimpse operation cannot be differentiated w.r.t. the `location`. -Which brings us to the main difficulty of attention models : -how can we teach the network to glimpse at the right `locations`? -## REINFORCE algorithm ## -Some attention models use a fully differentiable attention mechanism, -like the recent DRAW paper [[2]](#rmva.ref). -But the RAM model uses a non-differentiable attention mechanism. -Specifically, it uses a the REINFORCE algorithm [[3]](#rmva.ref). -This algorithm allows one to train stochastic units through reinforcement learning. -The REINFORCE algorithm is very powerful as it can be -used to optimize stochastic units (conditioned on an input), -such that they minimize an objective function (i.e. a reward function). -*Unlike backpropagation [[4]](#rmva.ref), this objective need not be differentiable*. - -The RAM model uses the REINFORCE algorithm to train the `locator` network : - -```lua --- actions (locator) -locator = nn.Sequential() -locator:add(nn.Linear(opt.hiddenSize, 2)) -locator:add(nn.HardTanh()) -- bounds mean between -1 and 1 -locator:add(nn.ReinforceNormal(2*opt.locatorStd)) -- sample from normal, uses REINFORCE learning rule -locator:add(nn.HardTanh()) -- bounds sample between -1 and 1 -locator:add(nn.MulConstant(opt.unitPixels*2/ds:imageSize("h"))) -``` -The input is the previous recurrent hidden state `h[t-1]`. -During training, the output is sampled from a normal -distribution with fixed standard deviation. -The mean is conditioned on `h[t-1]` through an affine transform (i.e. `Linear` module). -During evaluation, instead of sampling from the distribution, the output is taken to be the input, i.e. the mean. - -The [ReinforceNormal](https://github.com/nicholas-leonard/dpnn#nn.ReinforceNormal) module -implements the REINFORCE algorithm for the normal distribution. -Unlike most `Modules`, `ReinforceNormal` ignores the `gradOutput` when `backward` is called. -This is because the units it embodies are in fact stochastic. -So then how does it generate `gradInputs` when the `backward` is called? -It uses the REINFORCE algorithm, which requires that a reward function be defined. -The reward used by the paper is very simple, and yet not differentiable (eq. 1) : - -``` -R = I(y=t) -``` - -where `R` is the raw reward, `I(x)` is `1` when `x` is true and `0` otherwise -(see [indicator function](https://en.wikipedia.org/wiki/Indicator_function)), -`y` is the predicted class, `t` is the target class. -Or in Lua : - -```lua -R = (y==t) and 1 or 0 -``` - -The REINFORCE algorithm requires that we differentiate the -probability density or mass function (PDF/PMF) of the distribution -w.r.t. the parameters. So given the following variables : - - * `f` : normal probability density function - * `x` : the sampled values (i.e. `ReinforceNormal.output`) - * `u` : mean (`input` to `ReinforceNormal`) - * `s` : standard deviation (`ReinforceNormal.stdev`) - -the derivative of log normal w.r.t. mean `u` is : - -``` -d ln(f(x,u)) (x - u) ------------- = ------- - d u s^2 -``` - -So where does `d ln(f(x,u,s) / d u` fit in with the reward? -Well, in order to obtain a gradient of the reward `R` w.r.t. -to input `u`, we apply the following equation (eq. 2, i.e. the REINFORCE algorithm): - -``` -d R d ln(f(x,u)) ---- = a * (R - b) * -------------- -d u d u -``` - -where - - * `a` (alpha) is just a scaling factor like the learning rate ; and - * `b` is a baseline reward used to reduce the variance of the gradient. - * `f` is the PMF/PDF - * `u` is the parameter w.r.t. which you want to get a gradient - * `x` is the sampled value. - -In the paper, they take `b` to be the expected reward `E[R]`. -They approximate the expectation by making `b` a (conditionally independent) parameter of the model . -For each example, the mean square error between `R` and `b` is minimized by -backpropagation. The beauty of doing this, instead of, -say, making `b` a moving average of `R`, is that *the baseline reward `b` -learns at the same rate as the rest of the model*. -We decided to implement the `reward = a * (R - b)` part of eq. 2 -within a [VRClassReward](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.VRClassReward) criterion, -which also implements the paper's varianced-reduced classification reward function (eq. 1): ```lua -vcr = nn.VRClassReward(module [, scale, criterion]) -``` - -The nn package was primarily built for backpropagation, so we had to find a not-too-hacky way of -broadcasting the `reward` to the different -[Reinforce](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.Reinforce) modules. -We did this by having the criterion take the `module` as argument, -and adding the [Module:reinforce(reward)](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.Module.reinforce) -method. The latter allows the `Reinforce` modules (like `ReinforceNormal`) to -hold on to the criterion's broadcasted `reward` for later. Later being when `backward` is called -and the `Reinforce` module(s) compute(s) the `gradInput` -(i.e. `d R / d U`) using the REINFORCE algorithm (eq. 2). -And then `nn` is happy, because with the `gradInput`, it can continue -the backpropagation from the `Reinforce` module to its predecessors. - -So to summarize, if you can differentiate the PMF/PDF w.r.t. to its parameters, -then you can use the REINFORCE algorithm on it. We have already implemented -modules for the categorical and bernoulli distributions : - - * [ReinforceCategorical](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.ReinforceCategorical) - * [ReinforceBernoulli](https://github.com/nicholas-leonard/dpnn/blob/master/README.md#nn.ReinforceBernoulli) - -## Recurrent Attention Model - -![rva](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/rva-diagram.png) - -Okay, so we discussed the glimpse module and the REINFORCE algorithm, -lets talk about the recurrent attention model. We can divide the model -into its respective components : - -The location sensor. Its inputs are the `x`, `y` coordinates of the current glimpse location, -so the network knows *where* its looking at each time-step : - -```lua -locationSensor = nn.Sequential() -locationSensor:add(nn.SelectTable(2)) -locationSensor:add(nn.Linear(2, opt.locatorHiddenSize)) -locationSensor:add(nn[opt.transfer]()) -``` - -The glimpse sensor is *what* it's looking at : - -```lua -glimpseSensor = nn.Sequential() -glimpseSensor:add(nn.DontCast(nn.SpatialGlimpse(opt.glimpsePatchSize, opt.glimpseDepth, opt.glimpseScale):float(),true)) -glimpseSensor:add(nn.Collapse(3)) -glimpseSensor:add(nn.Linear(ds:imageSize('c')*(opt.glimpsePatchSize^2)*opt.glimpseDepth, opt.glimpseHiddenSize)) -glimpseSensor:add(nn[opt.transfer]()) -``` - -The glimpse network is where the glimpse and location sensor mix through -a hidden layer to form the input layer of the Recurrent Neural Network (RNN) : - -```lua -glimpse = nn.Sequential() -glimpse:add(nn.ConcatTable():add(locationSensor):add(glimpseSensor)) -glimpse:add(nn.JoinTable(1,1)) -glimpse:add(nn.Linear(opt.glimpseHiddenSize+opt.locatorHiddenSize, opt.imageHiddenSize)) -glimpse:add(nn[opt.transfer]()) -glimpse:add(nn.Linear(opt.imageHiddenSize, opt.hiddenSize)) -``` - -The RNN is the where the glimpse network and the recurrent layer come together. -The output of the `rnn` module is the hidden state `h[t]` where `t` indexes the time-step. -We used the [rnn](https://github.com/Element-Research/rnn) package to build it : - -```lua --- rnn recurrent layer -recurrent = nn.Linear(opt.hiddenSize, opt.hiddenSize) - --- recurrent neural network -rnn = nn.Recurrent(opt.hiddenSize, glimpse, recurrent, nn[opt.transfer](), 99999) -``` - -We have already seen the locator network above, but here it is again : - -```lua --- actions (locator) -locator = nn.Sequential() -locator:add(nn.Linear(opt.hiddenSize, 2)) -locator:add(nn.HardTanh()) -- bounds mean between -1 and 1 -locator:add(nn.ReinforceNormal(2*opt.locatorStd)) -- sample from normal, uses REINFORCE learning rule -locator:add(nn.HardTanh()) -- bounds sample between -1 and 1 -locator:add(nn.MulConstant(opt.unitPixels*2/ds:imageSize("h"))) -``` - -The locator's task is to sample the next location `l[t]` (or action) -given the previous hidden state `h[t-1]`, i.e. the previous output of the `rnn`. -For the first step, we use `h[0] = 0` (a tensor of zeros) for the previous hidden state. -We should also bring your attention to the `opt.unitPixels` variable, -as it is very important and not specified in the paper. -This variable basically outlines how far (in pixels) near the borders the -center of each glimpse can reach with respect to the center. -So a value of 13 (the default) means that the center of the glimpse can -be anywhere between the 2rd and 27th pixel (for a `1x28x28` MNIST example). -So glimpses of the corner will have fewer zero-padding values then if `opt.unitPixels = 14`. - -We need to encapsulate the `rnn` and `locator` into a module that would -capture the essence of the RAM model. -So we decided to implement a module that took the full image as input, -and output the sequence of hidden states `h`. -As its name implies, this module is a general purpose -[RecurrentAttention](https://github.com/Element-Research/rnn#rnn.RecurrentAttention) module : - -```lua -attention = nn.RecurrentAttention(rnn, locator, opt.rho, {opt.hiddenSize}) -``` - -It's so general-purpose that you can use it with an -[LSTM](https://github.com/Element-Research/rnn#rnn.LSTM) module, -and different glimpse or locator modules. As long as these respectively preserve -the same `{input, action} -> output` interfaces (glimpse) and use the REINFORCE algorithm (locator), of course. - -Next we build an agent by stacking a classifier on top of the `RecurrentAttention` module. -The classifier's input is the last hidden state `h[T]`, -where `T` is the total number of time-steps (i.e. glimpses to take): - -```lua --- model is a reinforcement learning agent -agent = nn.Sequential() -agent:add(nn.Convert(ds:ioShapes(), 'bchw')) -agent:add(attention) - --- classifier : -agent:add(nn.SelectTable(-1)) -agent:add(nn.Linear(opt.hiddenSize, #ds:classes())) -agent:add(nn.LogSoftMax()) -``` - -You might recall that the REINFORCE algorithm requires a baseline reward `b`? -This is where that happens (yes, it requires a little bit of `nn` kung-fu): - -```lua --- add the baseline reward predictor -seq = nn.Sequential() -seq:add(nn.Constant(1,1)) -seq:add(nn.Add(1)) -concat = nn.ConcatTable():add(nn.Identity()):add(seq) -concat2 = nn.ConcatTable():add(nn.Identity()):add(concat) - --- output will be : {classpred, {classpred, basereward}} -agent:add(concat2) +module = nn.SpatialGlimpse(size, depth, scale) ``` -At this point, the model is ready for training. -The `agent` instance is effectively the RAM model detailed in the paper. - -## Training - -Training is pretty straight-forward after that. -The script can be launched with the default hyper-parameters. -It should take 1-2 runs to find a validation minima that -reproduces the MNIST test results of the paper. We are still working on -reproducing the Translated and Cluttered MNIST results. - -## Results - -In the paper, they get 1.07% error on MNIST with 7 glimpses. -We got 0.85% error after 853 epochs of training (early-stopped on the validation set of course). -Here are some glimpse sequences. Note how the first frames start at the same location : -![locations](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_8PHJ4z.gif) - -And this is what the model sees for those sequences: - -![glimpses](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_Onbzrk.gif) - -So basically, REINFORCE did a good job of teaching the module to focus -its attention on different regions given different inputs. -A failure mode (bad) would have been to see the model do this : - -![fail](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_6kgOs1.gif) - -In that particular case, the `opt.unitPixels` was set to 6 instead of 12 -(so the attention was limited to a small region in the center of the image). -You don't want this to happen because it means the attention is conditionally independent of the input (i.e. dumb). - -Here are some results for the Translated MNIST dataset : - -![translatedmnist](https://raw.githubusercontent.com/torch/torch.github.io/master/blog/_posts/images/output_52iFki.gif) - -For this dataset, the images are of size `1x60x60` where each image contains a randomly placed `1x28x28` MNIST digit. -The `3x12x12` glimpse uses a depth of 3 scales -where each successive patch is twice the height and width of the previous one. -Training with this dataset was started about 3 days prior to this blog post. -For 7 glimpses, after 193 epochs, we get 1.223% error. Note that the model is still training. -The paper gets 1.22% and 1.2% error for 6 and 8 glimpses, respectively. - -Note : you can evaluate your models with the [evaluation script](https://github.com/Element-Research/rnn/blob/master/scripts/evaluate-rva.lua). -It will generate a sample of glimpse sequences and print the confusion matrix results for the test set. - -## Conclusion - -This blog discussed a concrete implementation of a Recurrent Model for Visual Attention -using the REINFORCE algorithm. The REINFORCE algorithm is very powerful as it -can learn non-differentiable criterions through reinforcement learning. -However, like many reinforcement learning algorithms, it does take a long time to converge. -Nevertheless, as demonstrated here and in the original paper, -the ability to train a model to learn where to focus its attention -can provide significant performance improvements. - - - ## References - -1. *Volodymyr Mnih, Nicolas Heess, Alex Graves, Koray Kavukcuoglu*, Recurrent Models of Visual Attention, [NIPS 2014](http://papers.nips.cc/paper/5542-recurrent-models-of-visual-attention) -2. *Gregor, Karol, et al.*, DRAW: A recurrent neural network for image generation, [Arxiv 2015](http://arxiv.org/abs/1502.04623) -3. *Williams, Ronald J.*, Simple statistical gradient-following algorithms for connectionist reinforcement learning, [Machine learning 8.3-4 (1992): 229-256](http://link.springer.com/article/10.1007/BF00992696). -4. *Rumelhart, David E., Geoffrey E. Hinton, and Ronald J. Williams.* Learning internal representations by error propagation, [No. ICS-8506](http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA164453) +1. *Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, (8), 30-37., From ccfc099a9081dcfd4c439ba97ba975ef33bdb5ee Mon Sep 17 00:00:00 2001 From: fstrub Date: Fri, 19 Feb 2016 19:38:26 +0100 Subject: [PATCH 04/12] add model + implem (part1) --- blog/_posts/2016-02-21-cfn.md | 124 ++++++++++++++++++++++------------ 1 file changed, 82 insertions(+), 42 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 81f8805..38068f4 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -37,88 +37,128 @@ Therefore, the Recommender System will advise Bob to watch _The Exorcist_. If Bob eventually rates _The Exorcist_, the matrix is re-estimated and so on... In practice, the matrix of ratings is very sparse. IMDB currently inventors around 1,7 millions movies while users rarely rate more than a few hundreds movies. -In addition to this sparsity constraint, Collaborative Filtering faces several limitations such as the cold-start problem (How to recommend an item that has no rating), scalability issue (Millions of users/products) or lack of external information (how to append side information to help the system). -A good overview can be found in the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) +For more details about Collaborative Filtering, I recommend the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) that provide a great insight about the major challenges (Latent factors, Cold-Sart Problem, Hybrid Systems etc.) -In this post, we will focus on the general case and the network implementation for clarity purpose. +In this post, we will introduce a Collaborative Filtering approach based on Stacked Denoising Autoencoders. - -## Problem description ## +# Understanding the model # -Matrix of ratings +As a short reminder, Autoencoders are unsupervised Networks where the output of the Network aims at reconstructing the initial input. +The Network is constrained to use narrow hidden layers, forcing a dimensionality reduction on the data. -Create autoencoders that will fill this matrix. ---> picture: +In a Collaborative Filtering task, the goal is to turn the sparse matrix of ratings into a dense one. +To do so, we are going to decompose the matrix by either its lines or columns. +The Autoencoder is then fed these sparse vectors, its ouput will be our line/column estimate. -movieLens + ![ratings](http://florian-strub.com/tmp/UV.png) +Note that the input/output size will depend on the matrix dimension. +Before implemeting the Autoencoder, we need to define how to handle unknwon values. +In the forward pass, a naive but efficient approach is to turn unkwown values into zero values. +This is strictly equivalent to remove the neuron from the network. In other words, unknown values are ignored. -## Sparsity ## -Sparsity big constraint -Picture Autoencoder +In the backward pass, the same idea can be applied. When no rating exist, the error is set to zero as it cannot be computed. -Autoencoder ~= dimension reduction + ![ratings](http://florian-strub.com/tmp/training1-small.png) +Beware that for real datasets, more than 95% of the ratings are missing. Thus, the bottleneck of the autoencoder is often greater than the input vector! +The autoencoder is also divert from its original purpose. It does not aim to reconstruct the input, it aims at predicting it. -First step : use sparse representation -Torch.sparse - -Data sparse -implement parser +# Implementation # -## Autoencoder -> Forward ## +Let's start the interesting part! -Use SparseLinear... Slow -CPU -> use nnsparse.BatchLinear -GPU -> nnsparse.densify() + nn.Linear (Up to 10time faster) +First, we need to install the nnsparse package to have basic tools to handle sparse data. -Better implementation undergoing +``` +luarocks install nnsparse +``` -## Autoencoder -> Loss ## -Unknwon rating??? - -> unknown = no error... - - loss = sum (exist) - - Backward +## The data ## +We are going to work on a small but classic dataset called [movieLens-1M](http://grouplens.org/datasets/movielens/). +This dataset contains 1 million ratings from 1 to 5 given by 6040 users on 3700 movies. +```lua -## Autoencoder -> Better ## + train, test = {}, {} -Yes! Use mask noise ---> loss + -- Step 1 : Load file + local ratesfile = io.open("ml-1m/ratings.dat, "r") -Deeper? Yes, harder to train... + -- Step 2 : Retrieve ratings + for line in ratesfile:lines() do + -- parse the file by using regex + local userIdStr, movieIdStr, ratingStr, _ = line:match('(%d+)::(%d+)::(%d%.?%d?)::(%d+)') -## Results ## + local userId = tonumber(userIdStr) + local itemId = tonumber(movieIdStr) + local rating = tonumber(ratingStr) + -- normalize the rating between [-1, 1] + rating = (rating-3)/2 -## -This is not deep learning. (look at the title :P) + -- we are going to autoencode the item with a training ratio of 0.9 + if torch.uniform() < 0.9 do + train[itemId] = train[itemId] or nnsparse.DynamicSparseTensor() + train[itemId]:append(torch.Tensor{userId, rating}) + else + test[itemId] = test[itemId] or nnsparse.DynamicSparseTensor() + test[itemId]:append(torch.Tensor{userId, rating}) + end -Another field where the structure of neural networks return excellent restults -Autoencoders were used differently form what they think to do. + end -This is not naive implementation of neural networks, they are actualy clear motivation why it was likely to work. -The real surprise is : how well they work! +``` +Given the toy matrix in the first section, the full dataset would be encoded this way: +|train["Exorcist" = 1] | train["Inception"= 2] | train["Psycho"= 3] |train["Titanic"= 4] | +|----------------------------------|---------------------------------|----------------------------------|----------------------------------| +| 3 : 5 | 1 : 3 | 1 : 5 | 2 : 5 | +| 4 : 2 | 2 : 5 | 3 : 4 | 4 : 4 | +| | | 4 : 1 | | +## The Network ## +We will first implement a shallow Autoencoder with sparse inputs. Deeper Autoencoder can be used, but the final results will only be increased by a small margin. +So let keep thing simple! +- On CPU: +```lua +local network = nn.Sequential() +network:add(nnsparse.SparseLinearBatch(6040, 500)) --There are 6040 users in movieLens-1M +network:add(nn.Tanh()) +network:add(nn.Linear(500, 6040)) +network:add(nn.Tanh()) +``` +- On GPU: ```lua -module = nn.SpatialGlimpse(size, depth, scale) +local network = nn.Sequential() +network:add(nnsparse.Densify(6040)) --GPU does not handle sparse data, so we densify the input on the fly +network:add(nn.Linear(6040, 500)) +network:add(nn.Tanh()) +network:add(nn.Linear(500, 6040)) +network:add(nn.Tanh()) +network:cuda() ``` +## The Loss ## + + + + + + + ## References 1. *Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, (8), 30-37., From 42df3d9d3f6aef514189ebf6be9440614034c5bb Mon Sep 17 00:00:00 2001 From: fstrub Date: Mon, 29 Feb 2016 19:27:56 +0100 Subject: [PATCH 05/12] add code! --- blog/_posts/2016-02-21-cfn.md | 218 +++++++++++++++++++++++++++++----- 1 file changed, 186 insertions(+), 32 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 38068f4..618c79e 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -13,7 +13,7 @@ Deep Learning has well-known state-of-the arts results in Computer Vision, Speec This post aims at using Neural Networks on a different topic : Recommender systems and Collaborative Filtering. It turns out that Neural Networks also perform among the best Collaborative Fitering algorithms. -#Introduction# +#Collaborative Filtering# Recommendation systems are a subclass of algorithms that seek to predict the rating that a user would give to an item. A good recommendation system may dramatically increase the amount of sales of a firm or retain customers. For instance, 80% of movies watched on Netflix come from the recommender system of the company @@ -22,7 +22,7 @@ One of the most successful approach of Recommendation systems is to use the expl For instance, if we gather the feedback of all users into a matrix, we obtain a sparse matrix of ratings. Note that sparsity is induced by unknown values. -![ratings](http://florian-strub.com/tmp/initialMatrix.png) +![initialMatrix](http://florian-strub.com/tmp/initialMatrix.png) In this case, should we recommend Bob to watch _The Exorcist_ or _Titanic_? @@ -30,7 +30,7 @@ Collaborative Filtering aims at estimating the ratings a user would have given t Inherent features of users or items such as the genre, age, actors or some descriptions are _not_ take into account. The goal is then to turn the previous sparse matrix of ratings into a dense one: -![ratings](http://florian-strub.com/tmp/finalMatrix.png) +![finalMatrix](http://florian-strub.com/tmp/finalMatrix.png) Therefore, the Recommender System will advise Bob to watch _The Exorcist_. @@ -50,7 +50,7 @@ In a Collaborative Filtering task, the goal is to turn the sparse matrix of rati To do so, we are going to decompose the matrix by either its lines or columns. The Autoencoder is then fed these sparse vectors, its ouput will be our line/column estimate. - ![ratings](http://florian-strub.com/tmp/UV.png) + ![UV](http://florian-strub.com/tmp/UV.png) Note that the input/output size will depend on the matrix dimension. @@ -61,15 +61,33 @@ This is strictly equivalent to remove the neuron from the network. In other word In the backward pass, the same idea can be applied. When no rating exist, the error is set to zero as it cannot be computed. - ![ratings](http://florian-strub.com/tmp/training1-small.png) + ![training1](http://florian-strub.com/tmp/training1-small.png) -Beware that for real datasets, more than 95% of the ratings are missing. Thus, the bottleneck of the autoencoder is often greater than the input vector! -The autoencoder is also divert from its original purpose. It does not aim to reconstruct the input, it aims at predicting it. +Beware that more than 95% of the ratings are missing in real datasets. Thus, the bottleneck of the autoencoder is often greater than the number of ratings in the input vector! +The autoencoder is also diverted from its original purpose. It does not aim to reconstruct the initial input anymore, it aims at predicting the missing data. +By keeping this idea in mind, we applied the Denoising loss [2] to empahisize the prediction aspect during the training. +A few input ratings are masked on every input vector, thus, it simulates missing ratings. +Finally, a higher error is provided when the output rating is erroneously predicted. + +The training loss becomes + ![DAELoss](http://florian-strub.com/tmp/DAELoss-small.png) + + + +where \tilde{x} is the corrupted input x, J are the indices of the corrupted elements of x, nn(x)_j is the jth output of the Network, K(x) are the indices of known values of x. +The loss is based on two main hyperparameters Alpha, Beta. They balance whether the Network would focus on denoising the input (alpha) or reconstructing the input (beta). + +Finally, the full training process is described below + + ![training1](http://florian-strub.com/tmp/training2-small.png) + + +Now, let's start the interesting part! # Implementation # -Let's start the interesting part! + First, we need to install the nnsparse package to have basic tools to handle sparse data. @@ -82,52 +100,65 @@ luarocks install nnsparse We are going to work on a small but classic dataset called [movieLens-1M](http://grouplens.org/datasets/movielens/). This dataset contains 1 million ratings from 1 to 5 given by 6040 users on 3700 movies. +To avoid memory explosition, data must be stored in sparse tensors. Given the toy matrix in the first section, the sparse matrix of users/items would be: + + ![training1](http://florian-strub.com/tmp/dense2sparse.png) + + +The following code parse the movieLens-1M dataset and turn it into a sparse reprensation of items + + ```lua - train, test = {}, {} + local train, test = {}, {} -- Step 1 : Load file - local ratesfile = io.open("ml-1m/ratings.dat, "r") + local ratesfile = io.open("ml-1m/ratings.dat", "r") -- Step 2 : Retrieve ratings for line in ratesfile:lines() do - -- parse the file by using regex + -- parse the file by using regex local userIdStr, movieIdStr, ratingStr, _ = line:match('(%d+)::(%d+)::(%d%.?%d?)::(%d+)') local userId = tonumber(userIdStr) local itemId = tonumber(movieIdStr) local rating = tonumber(ratingStr) - -- normalize the rating between [-1, 1] + -- normalize the rating between [-1, 1] rating = (rating-3)/2 - -- we are going to autoencode the item with a training ratio of 0.9 - if torch.uniform() < 0.9 do - train[itemId] = train[itemId] or nnsparse.DynamicSparseTensor() - train[itemId]:append(torch.Tensor{userId, rating}) - else - test[itemId] = test[itemId] or nnsparse.DynamicSparseTensor() - test[itemId]:append(torch.Tensor{userId, rating}) - end + -- we are going to autoencode the item with a training ratio of 0.9 + if torch.uniform() < 0.9 then + train[itemId] = train[itemId] or nnsparse.DynamicSparseTensor() + train[itemId]:append(torch.Tensor{userId, rating}) + else + test[itemId] = test[itemId] or nnsparse.DynamicSparseTensor() + test[itemId]:append(torch.Tensor{userId, rating}) + end end -``` - -Given the toy matrix in the first section, the full dataset would be encoded this way: + -- Step 3 : Build the final sparse matrices + for k, oneTrain in pairs(train) do train[k] = oneTrain:build():ssortByIndex() end + for k, oneTest in pairs(test) do test[k] = oneTest:build():ssortByIndex() end +``` -|train["Exorcist" = 1] | train["Inception"= 2] | train["Psycho"= 3] |train["Titanic"= 4] | -|----------------------------------|---------------------------------|----------------------------------|----------------------------------| -| 3 : 5 | 1 : 3 | 1 : 5 | 2 : 5 | -| 4 : 2 | 2 : 5 | 3 : 4 | 4 : 4 | -| | | 4 : 1 | | - +Unbias the training mean by lines/columns increase the final results. + +```lua +-- Step 4 : remove mean +for k, oneTrain in pairs(train) do + local mean = oneTrain[{ {},2 }]:mean() + train[k][{ {},2 }]:add(-mean) + test[k] [{ {},2 }]:add(-mean) +end +``` ## The Network ## -We will first implement a shallow Autoencoder with sparse inputs. Deeper Autoencoder can be used, but the final results will only be increased by a small margin. -So let keep thing simple! +We will first implement a shallow Autoencoder with sparse inputs for items. Deeper Autoencoder can be used, but the final results will only be increased by a small margin. +So let keep things simple! - On CPU: @@ -151,11 +182,134 @@ network:add(nn.Tanh()) network:cuda() ``` -## The Loss ## +## Training Loss ## +As described above, training the autoencoder requires to use a Denoising Loss. +The ```nnsparse``` package offers a full Denoising Loss (Gaussian Noise/Masking Noise/ Salt&Paper Noise) for CPU and a Masking Loss that both work on CPU/GPU. +We will use on the latter since we are want to focus on the prediction aspect. +This is the most verbose part but we try to keep the code as simple as possible. +```lua + + -- define the Loss function + lossFct = nnsparse.MaskCriterion(nn.MSECriterion(), { + alpha = 1, + beta = 0.5, + hideRatio = 0.25, + }) + lossFct.inputDim = 6040 --require for sparse inputs + lossFct.sizeAverage = false + + -- Create minibatch + local input, minibatch = {}, {} + + --shuffle the indices of the inputs to create the minibatch + local shuffle = torch.randperm(#train) + shuffle:apply(function(k) + if train[k] then + input[#input+1] = train[k] + if #input == batchSize then + minibatch[#minibatch+1] = input + input = {} + end + end + end) + + local w, dw = network:getParameters() + + -- Classic training + for _, input in pairs(minibatch) do + local function feval(x) + + -- Reset gradients and losses + network:zeroGradParameters() + + -- AutoEncoder targets + local target = input + + -- Compute noisy input for Denoising autoencoders + local noisyInput = lossFct:prepareInput(input) + + -- FORWARD + local output = network:forward(noisyInput) + local loss = lossFct:forward(output, target) + + -- BACKWARD + local dloss = lossFct:backward(output, target) + local _ = network:backward(noisyInput, dloss) + + -- Return loss and gradients + return loss/batchSize, dw:div(batchSize) + end + + sgdConfiguration.evalCounter = currentEpoch + optim.sgd (feval, w, sgdConfiguration ) + + end +``` + +## Testing Loss ## + +Torch criterions do not handle Sparse target by default. Thus, it is necessary to wrap them into another criterion. +The ```nnsparse.SparseCriterion``` takes a dense output and a sparse target as parameters. +It then computes the loss/dloss regarding the indices of the target. + + +```lua + -- Create minibatch + local noRatings = 0 + local input, target, minibatch = {}, {}, {} + + for k, _ in pairs(train) do + if test[k] ~= nil then --ignore when there is no target + input [#input +1] = train[k] + target[#target +1] = test[k] + + noRatings = noRatings + test[k]:size(1) + + if #input == batchSize then + minibatch[#minibatch+1] = {input = input, target = target} + input, target = {}, {} + end + end + end + + -- define the testing criterion + local criterion = nnsparse.SparseCriterion(nn.MSECriterion()) + criterion.sizeAverage = false + + -- Compute the RMSE by predicting the testing dataset thanks to the training dataset + local err = 0 + for _, oneBatch in pairs(minibatch) do + local output = self.network:forward(oneBatch.input) + err = err + criterion:forward(output, oneBatch.target) + end + + err = err/noRatings + +``` + +The full code can be found here: + +A more advanced implementation can be found here; + + +# Results # + +For movieLens-1M, the network should be trained in a few minutes (~20 epoches). +The final RMSE should be around 0.839 with the following hyperparameters. Deeper Networks can go up to a RMSE of 0.831. + +```lua +local sgdConfiguration = { + learningRate = 0.07, + learningRateDecay = 0.9, + weightDecay = 0.05, +} +``` +As a benchmark, Alternative Least squares is a widely used Collaborative algorithm. It has a final RMSE around 0.850 on movieLens-1M - cf [Mahout](http://mahout.apache.org/) + [Script](https://github.com/apache/mahout/blob/master/examples/bin/factorize-movielens-1M.sh) +Furthermore, the bigger is the dataset, the better will be the Autoencoder. State of the art results can be computed with movieLens-10/20M. From aad1b97079d1e58a33989f884bba55f0da7bc0b0 Mon Sep 17 00:00:00 2001 From: fstrub Date: Tue, 1 Mar 2016 18:19:27 +0100 Subject: [PATCH 06/12] V1.0 --- blog/_posts/2016-02-21-cfn.md | 104 ++++++++++++++++++++-------------- 1 file changed, 60 insertions(+), 44 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 618c79e..4338385 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -3,24 +3,25 @@ layout: post title: Collaborative Filtering with Neural Networks comments: True author: florian-strub -excerpt: Collaborative Filtering methods are a key algorithm for Recommender Systems. They are used by major companies such as Netflix, Amazon or Spotify to suggest items to users. While Neural Networks have tremendous success in image and speech recognition, Collaborative Filtering received less attention as it deals with sparse inputs/targets. After a quick introduction to Recommendation Systems, we show how to implement Autoencoders to perform Collaborative Filtering. +excerpt: Collaborative Filtering methods are key algorithms for Recommender Systems. They are used by major companies such as Netflix, Amazon or Spotify to suggest items to users. While Neural Networks have tremendous success in image and speech recognition, Collaborative Filtering received less attention as it deals with sparse inputs/targets. After a quick introduction to Recommendation Systems, we show how to implement a well-defined Autoencoders to perform Collaborative Filtering. picture: http://insidebigdata.com/wp-content/uploads/2014/06/Humor_recommender.jpg --- Deep Learning has well-known state-of-the arts results in Computer Vision, Speech Recognition or Natural Language Processing. -This post aims at using Neural Networks on a different topic : Recommender systems and Collaborative Filtering. -It turns out that Neural Networks also perform among the best Collaborative Fitering algorithms. +This post intends at using Neural Networks on a different topic : Recommender systems and Collaborative Filtering. +It turns out that a well-defined Autoencoder can perform among the best Collaborative Fitering algorithms. +This post is focused on understating and implementing such Autoencoders. #Collaborative Filtering# Recommendation systems are a subclass of algorithms that seek to predict the rating that a user would give to an item. -A good recommendation system may dramatically increase the amount of sales of a firm or retain customers. For instance, 80% of movies watched on Netflix come from the recommender system of the company +A good recommendation system may dramatically increase the amount of sales of a firm or retain customers. For instance, 80% of movies watched on Netflix come from the recommender system of the company. One of the most successful approach of Recommendation systems is to use the explicit feedback of users to build a Matrix of ratings. This technique is known as Collaborative Filtering. -For instance, if we gather the feedback of all users into a matrix, we obtain a sparse matrix of ratings. Note that sparsity is induced by unknown values. +For instance, if we gather the feedback of movies of all users into a matrix, we obtain a sparse matrix of ratings. Note that sparsity is induced by unknown values. ![initialMatrix](http://florian-strub.com/tmp/initialMatrix.png) @@ -37,18 +38,19 @@ Therefore, the Recommender System will advise Bob to watch _The Exorcist_. If Bob eventually rates _The Exorcist_, the matrix is re-estimated and so on... In practice, the matrix of ratings is very sparse. IMDB currently inventors around 1,7 millions movies while users rarely rate more than a few hundreds movies. -For more details about Collaborative Filtering, I recommend the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) that provide a great insight about the major challenges (Latent factors, Cold-Sart Problem, Hybrid Systems etc.) +I would recommend the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) [1] to curious people which provide a great insight regarding the challenges of the field (Latent factors, Cold-Sart Problem, Hybrid Systems etc.) In this post, we will introduce a Collaborative Filtering approach based on Stacked Denoising Autoencoders. +A preliminary and (excellent work!) was first pulished in 2007 by Ruslan Salakhutdinov [2]. # Understanding the model # -As a short reminder, Autoencoders are unsupervised Networks where the output of the Network aims at reconstructing the initial input. +As a short reminder, Autoencoders are unsupervised Networks where the output of the Network plan to reconstruct the initial input. The Network is constrained to use narrow hidden layers, forcing a dimensionality reduction on the data. In a Collaborative Filtering task, the goal is to turn the sparse matrix of ratings into a dense one. To do so, we are going to decompose the matrix by either its lines or columns. -The Autoencoder is then fed these sparse vectors, its ouput will be our line/column estimate. +The Autoencoder is fed with these sparse vectors; its ouput will finally complete the line/column one after the other. ![UV](http://florian-strub.com/tmp/UV.png) @@ -61,7 +63,7 @@ This is strictly equivalent to remove the neuron from the network. In other word In the backward pass, the same idea can be applied. When no rating exist, the error is set to zero as it cannot be computed. - ![training1](http://florian-strub.com/tmp/training1-small.png) + ![training1](http://florian-strub.com/tmp/training3-small.png) Beware that more than 95% of the ratings are missing in real datasets. Thus, the bottleneck of the autoencoder is often greater than the number of ratings in the input vector! The autoencoder is also diverted from its original purpose. It does not aim to reconstruct the initial input anymore, it aims at predicting the missing data. @@ -73,8 +75,6 @@ Finally, a higher error is provided when the output rating is erroneously predic The training loss becomes ![DAELoss](http://florian-strub.com/tmp/DAELoss-small.png) - - where \tilde{x} is the corrupted input x, J are the indices of the corrupted elements of x, nn(x)_j is the jth output of the Network, K(x) are the indices of known values of x. The loss is based on two main hyperparameters Alpha, Beta. They balance whether the Network would focus on denoising the input (alpha) or reconstructing the input (beta). @@ -82,6 +82,8 @@ Finally, the full training process is described below ![training1](http://florian-strub.com/tmp/training2-small.png) +A more advanced description is described in our paper [4]. +Importantly, we explain in tis paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. Now, let's start the interesting part! @@ -145,7 +147,7 @@ The following code parse the movieLens-1M dataset and turn it into a sparse repr ``` -Unbias the training mean by lines/columns increase the final results. +It is important to unbias the lines/columns by the training mean to increase the final results. ```lua -- Step 4 : remove mean @@ -175,9 +177,9 @@ network:add(nn.Tanh()) ```lua local network = nn.Sequential() network:add(nnsparse.Densify(6040)) --GPU does not handle sparse data, so we densify the input on the fly -network:add(nn.Linear(6040, 500)) +network:add(nn.Linear(6040, 750)) network:add(nn.Tanh()) -network:add(nn.Linear(500, 6040)) +network:add(nn.Linear(750, 6040)) network:add(nn.Tanh()) network:cuda() ``` @@ -186,8 +188,7 @@ network:cuda() As described above, training the autoencoder requires to use a Denoising Loss. The ```nnsparse``` package offers a full Denoising Loss (Gaussian Noise/Masking Noise/ Salt&Paper Noise) for CPU and a Masking Loss that both work on CPU/GPU. -We will use on the latter since we are want to focus on the prediction aspect. -This is the most verbose part but we try to keep the code as simple as possible. +We will use the latter since we want to focus on the prediction aspect. ```lua @@ -204,7 +205,7 @@ This is the most verbose part but we try to keep the code as simple as possible. local input, minibatch = {}, {} --shuffle the indices of the inputs to create the minibatch - local shuffle = torch.randperm(#train) + local shuffle = torch.randperm(inputSize) shuffle:apply(function(k) if train[k] then input[#input+1] = train[k] @@ -214,10 +215,13 @@ This is the most verbose part but we try to keep the code as simple as possible. end end end) - - local w, dw = network:getParameters() - + if #input > 0 then + minibatch[#minibatch+1] = input + end + -- Classic training + local w, dw = network:getParameters() + for _, input in pairs(minibatch) do local function feval(x) @@ -241,57 +245,63 @@ This is the most verbose part but we try to keep the code as simple as possible. -- Return loss and gradients return loss/batchSize, dw:div(batchSize) end - - sgdConfiguration.evalCounter = currentEpoch + + sgdConfiguration.evalCounter = t optim.sgd (feval, w, sgdConfiguration ) - end + end ``` ## Testing Loss ## -Torch criterions do not handle Sparse target by default. Thus, it is necessary to wrap them into another criterion. +Torch criterions do not handle sparse targets by default. Thus, it is necessary to wrap them into another criterion. The ```nnsparse.SparseCriterion``` takes a dense output and a sparse target as parameters. It then computes the loss/dloss regarding the indices of the target. - ```lua -- Create minibatch local noRatings = 0 local input, target, minibatch = {}, {}, {} for k, _ in pairs(train) do - if test[k] ~= nil then --ignore when there is no target - input [#input +1] = train[k] - target[#target +1] = test[k] - - noRatings = noRatings + test[k]:size(1) - - if #input == batchSize then - minibatch[#minibatch+1] = {input = input, target = target} - input, target = {}, {} - end - end + + if test[k] ~= nil then --ignore when there is no target + input [#input +1] = train[k] + target[#target +1] = test[k] + + noRatings = noRatings + test[k]:size(1) + + if #input == batchSize then + minibatch[#minibatch+1] = {input = input, target = target} + input, target = {}, {} + end + end + end + if #input > 0 then + minibatch[#minibatch+1] = {input = input, target = target} end -- define the testing criterion local criterion = nnsparse.SparseCriterion(nn.MSECriterion()) criterion.sizeAverage = false - + -- Compute the RMSE by predicting the testing dataset thanks to the training dataset local err = 0 for _, oneBatch in pairs(minibatch) do - local output = self.network:forward(oneBatch.input) - err = err + criterion:forward(output, oneBatch.target) + local output = network:forward(oneBatch.input) + err = err + criterion:forward(output, oneBatch.target) end err = err/noRatings + print("Current RMSE : " .. math.sqrt(err) * 2) -- The RMSE is rescaled ``` -The full code can be found here: +Here we are! The shallow autoencoder can be trained. + +The full code can be found [here](https://github.com/fstrub95/Autoencoders_cf/blob/master/src/tutorial.lua) -A more advanced implementation can be found here; +A more advanced implementation can be found [here]((https://github.com/fstrub95/Autoencoders_cf/). # Results # @@ -307,12 +317,18 @@ local sgdConfiguration = { } ``` -As a benchmark, Alternative Least squares is a widely used Collaborative algorithm. It has a final RMSE around 0.850 on movieLens-1M - cf [Mahout](http://mahout.apache.org/) + [Script](https://github.com/apache/mahout/blob/master/examples/bin/factorize-movielens-1M.sh) +As a benchmark, Alternative Least Squares [3] is a widely used Collaborative algorithm. It has a final RMSE around 0.850 on movieLens-1M - cf [Mahout](http://mahout.apache.org/) + [Script](https://github.com/apache/mahout/blob/master/examples/bin/factorize-movielens-1M.sh) -Furthermore, the bigger is the dataset, the better will be the Autoencoder. State of the art results can be computed with movieLens-10/20M. +Furthermore, the bigger is the dataset, the better will be the Autoencoder. The current state of the art results can be obtained with a shallow autoencoder for movieLens-10/20M. +Once you have your network, you are free to implement your recommendation system! +More advanced Network can be built to integrate side information such as movie tags, age/sex/job etc. [4] +Boosting can also be used to mix both User/Item-autoencoders to compute a single matrice. ## References -1. *Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, (8), 30-37., +1. *Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, (8), 30-37.,* +2. *Salakhutdinov, R., Mnih, A., & Hinton, G. (2007, June). Restricted Boltzmann machines for collaborative filtering. In Proceedings of the 24th international conference on Machine learning (pp. 791-798). ACM.* +3. *Zhou, Y., Wilkinson, D., Schreiber, R., & Pan, R. (2008). Large-scale parallel collaborative filtering for the netflix prize. In Algorithmic Aspects in Information and Management (pp. 337-348). Springer Berlin Heidelberg.* +4. *Strub, F., Mary, J., Gaudel R., (2016). Collaborative Filterings and Neural Networks. Under review* From b55755a6abdea8e4e7a25708aac362c78a42d4df Mon Sep 17 00:00:00 2001 From: fstrub Date: Tue, 1 Mar 2016 19:21:28 +0100 Subject: [PATCH 07/12] fix typo (thx PV) --- blog/_posts/2016-02-21-cfn.md | 42 +++++++++++++++++------------------ 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 4338385..1e717c8 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -9,10 +9,10 @@ picture: http://insidebigdata.com/wp-content/uploads/2014/06/Humor_recommender.j -Deep Learning has well-known state-of-the arts results in Computer Vision, Speech Recognition or Natural Language Processing. +Deep Learning has well-known state-of-the-art results in Computer Vision, Speech Recognition or Natural Language Processing. This post intends at using Neural Networks on a different topic : Recommender systems and Collaborative Filtering. -It turns out that a well-defined Autoencoder can perform among the best Collaborative Fitering algorithms. -This post is focused on understating and implementing such Autoencoders. +It turns out that a well-defined Autoencoder can compete with the best Collaborative Fitering algorithms. +This post focus on understating and implementing such Autoencoders. #Collaborative Filtering# @@ -21,14 +21,14 @@ A good recommendation system may dramatically increase the amount of sales of a One of the most successful approach of Recommendation systems is to use the explicit feedback of users to build a Matrix of ratings. This technique is known as Collaborative Filtering. -For instance, if we gather the feedback of movies of all users into a matrix, we obtain a sparse matrix of ratings. Note that sparsity is induced by unknown values. +For instance, if we gather the feedback of movies of all users into a matrix, we obtain a sparse matrix of ratings. Note that the sparsity is induced by unknown values. ![initialMatrix](http://florian-strub.com/tmp/initialMatrix.png) In this case, should we recommend Bob to watch _The Exorcist_ or _Titanic_? Collaborative Filtering aims at estimating the ratings a user would have given to other movies by using the ratings of all the other users. -Inherent features of users or items such as the genre, age, actors or some descriptions are _not_ take into account. +Inherent features of users or items such as the genre, age, actors or some descriptions are _not_ taken into account. The goal is then to turn the previous sparse matrix of ratings into a dense one: ![finalMatrix](http://florian-strub.com/tmp/finalMatrix.png) @@ -36,12 +36,12 @@ The goal is then to turn the previous sparse matrix of ratings into a dense one: Therefore, the Recommender System will advise Bob to watch _The Exorcist_. If Bob eventually rates _The Exorcist_, the matrix is re-estimated and so on... -In practice, the matrix of ratings is very sparse. IMDB currently inventors around 1,7 millions movies while users rarely rate more than a few hundreds movies. +In practice, the matrix of ratings is very sparse. IMDB currently indexes around 1,7 millions movies while users rarely rate more than a few hundreds movies. I would recommend the [following paper](https://datajobs.com/data-science-repo/Recommender-Systems-%5BNetflix%5D.pdf) [1] to curious people which provide a great insight regarding the challenges of the field (Latent factors, Cold-Sart Problem, Hybrid Systems etc.) In this post, we will introduce a Collaborative Filtering approach based on Stacked Denoising Autoencoders. -A preliminary and (excellent work!) was first pulished in 2007 by Ruslan Salakhutdinov [2]. +A preliminary (and excellent!) work was first pulished in 2007 by Ruslan Salakhutdinov [2]. # Understanding the model # @@ -49,8 +49,8 @@ As a short reminder, Autoencoders are unsupervised Networks where the output of The Network is constrained to use narrow hidden layers, forcing a dimensionality reduction on the data. In a Collaborative Filtering task, the goal is to turn the sparse matrix of ratings into a dense one. -To do so, we are going to decompose the matrix by either its lines or columns. -The Autoencoder is fed with these sparse vectors; its ouput will finally complete the line/column one after the other. +To do so, we are going to decompose the matrix by either its lines or columns and feed them to the Autoencoder. +The output layer will reconstruct the lines/columns and complete them. ![UV](http://florian-strub.com/tmp/UV.png) @@ -59,7 +59,7 @@ Note that the input/output size will depend on the matrix dimension. Before implemeting the Autoencoder, we need to define how to handle unknwon values. In the forward pass, a naive but efficient approach is to turn unkwown values into zero values. -This is strictly equivalent to remove the neuron from the network. In other words, unknown values are ignored. +This is strictly equivalent to removing the neurons from the network. In other words, unknown values are ignored. In the backward pass, the same idea can be applied. When no rating exist, the error is set to zero as it cannot be computed. @@ -68,22 +68,22 @@ In the backward pass, the same idea can be applied. When no rating exist, the er Beware that more than 95% of the ratings are missing in real datasets. Thus, the bottleneck of the autoencoder is often greater than the number of ratings in the input vector! The autoencoder is also diverted from its original purpose. It does not aim to reconstruct the initial input anymore, it aims at predicting the missing data. -By keeping this idea in mind, we applied the Denoising loss [2] to empahisize the prediction aspect during the training. -A few input ratings are masked on every input vector, thus, it simulates missing ratings. -Finally, a higher error is provided when the output rating is erroneously predicted. +By keeping this idea in mind, we applied the Denoising loss [2] to emphasize the prediction aspect during the training. +First, a few input ratings are masked on every input vector to simulate missing ratings. +And then, a higher error is returned when the output rating is erroneously predicted. The training loss becomes ![DAELoss](http://florian-strub.com/tmp/DAELoss-small.png) where \tilde{x} is the corrupted input x, J are the indices of the corrupted elements of x, nn(x)_j is the jth output of the Network, K(x) are the indices of known values of x. -The loss is based on two main hyperparameters Alpha, Beta. They balance whether the Network would focus on denoising the input (alpha) or reconstructing the input (beta). +The loss is based on two main hyperparameters Alpha, Beta. They balance the evolution of the Network between denoising the input (alpha) and reconstructing the input (beta). Finally, the full training process is described below ![training1](http://florian-strub.com/tmp/training2-small.png) A more advanced description is described in our paper [4]. -Importantly, we explain in tis paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. +Importantly, we explain in this paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders and propose ideas that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. Now, let's start the interesting part! @@ -91,7 +91,7 @@ Now, let's start the interesting part! -First, we need to install the nnsparse package to have basic tools to handle sparse data. +First, we need to install the nnsparse package. It will provide us with the basic tools to handle sparse data. ``` luarocks install nnsparse @@ -102,12 +102,12 @@ luarocks install nnsparse We are going to work on a small but classic dataset called [movieLens-1M](http://grouplens.org/datasets/movielens/). This dataset contains 1 million ratings from 1 to 5 given by 6040 users on 3700 movies. -To avoid memory explosition, data must be stored in sparse tensors. Given the toy matrix in the first section, the sparse matrix of users/items would be: +To avoid memory overflow, data must be stored in sparse tensors. Given the toy matrix in the first section, the sparse matrix of users/items would be: ![training1](http://florian-strub.com/tmp/dense2sparse.png) -The following code parse the movieLens-1M dataset and turn it into a sparse reprensation of items +The following code parses the movieLens-1M dataset and turns it into a sparse reprensation of items ```lua @@ -160,7 +160,7 @@ end ## The Network ## We will first implement a shallow Autoencoder with sparse inputs for items. Deeper Autoencoder can be used, but the final results will only be increased by a small margin. -So let keep things simple! +So let's keep things simple! - On CPU: @@ -299,9 +299,9 @@ It then computes the loss/dloss regarding the indices of the target. Here we are! The shallow autoencoder can be trained. -The full code can be found [here](https://github.com/fstrub95/Autoencoders_cf/blob/master/src/tutorial.lua) +The full code can be found [here](https://github.com/fstrub95/Autoencoders_cf/blob/master/src/tutorial.lua). -A more advanced implementation can be found [here]((https://github.com/fstrub95/Autoencoders_cf/). +A more advanced implementation can be found [here](https://github.com/fstrub95/Autoencoders_cf/). # Results # From 132594de85134882107295c3c19d84a6d64739e4 Mon Sep 17 00:00:00 2001 From: Florian STRUB Date: Wed, 2 Mar 2016 18:27:42 +0100 Subject: [PATCH 08/12] Fix paper title --- blog/_posts/2016-02-21-cfn.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 1e717c8..615645a 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -82,7 +82,7 @@ Finally, the full training process is described below ![training1](http://florian-strub.com/tmp/training2-small.png) -A more advanced description is described in our paper [4]. +A more advanced description is described in our paper [4]). Importantly, we explain in this paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders and propose ideas that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. Now, let's start the interesting part! @@ -331,4 +331,4 @@ Boosting can also be used to mix both User/Item-autoencoders to compute a single 1. *Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, (8), 30-37.,* 2. *Salakhutdinov, R., Mnih, A., & Hinton, G. (2007, June). Restricted Boltzmann machines for collaborative filtering. In Proceedings of the 24th international conference on Machine learning (pp. 791-798). ACM.* 3. *Zhou, Y., Wilkinson, D., Schreiber, R., & Pan, R. (2008). Large-scale parallel collaborative filtering for the netflix prize. In Algorithmic Aspects in Information and Management (pp. 337-348). Springer Berlin Heidelberg.* -4. *Strub, F., Mary, J., Gaudel R., (2016). Collaborative Filterings and Neural Networks. Under review* +4. *Strub, F., Mary, J., Gaudel R., (2016). Hybrid Collaborative Filterings and Neural Networks. Under review* From 4e8a5ce010c63396580b5c7334cccd5f11950cab Mon Sep 17 00:00:00 2001 From: Florian STRUB Date: Wed, 2 Mar 2016 19:20:58 +0100 Subject: [PATCH 09/12] Add link to HAL --- blog/_posts/2016-02-21-cfn.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 615645a..ff69b34 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -82,7 +82,7 @@ Finally, the full training process is described below ![training1](http://florian-strub.com/tmp/training2-small.png) -A more advanced description is described in our paper [4]). +A more advanced description is described in our (paper)[https://hal.archives-ouvertes.fr/hal-01281794] [4]). Importantly, we explain in this paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders and propose ideas that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. Now, let's start the interesting part! From db2be438c13d2a279d36fd8eaca803fce699e2d6 Mon Sep 17 00:00:00 2001 From: Florian STRUB Date: Wed, 2 Mar 2016 19:21:37 +0100 Subject: [PATCH 10/12] Add link to HAL --- blog/_posts/2016-02-21-cfn.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index ff69b34..943b5e0 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -82,7 +82,7 @@ Finally, the full training process is described below ![training1](http://florian-strub.com/tmp/training2-small.png) -A more advanced description is described in our (paper)[https://hal.archives-ouvertes.fr/hal-01281794] [4]). +A more advanced description is described in our [paper](https://hal.archives-ouvertes.fr/hal-01281794) [4]). Importantly, we explain in this paper the underlying idea that links classic Collaborative Filtering techniques and Autoencoders and propose ideas that __may explain__ why neural Networks performs well in Collaborative Filtering tasks. Now, let's start the interesting part! From de215d7b44d17f38045ceef96730dcae3861d542 Mon Sep 17 00:00:00 2001 From: fstrub Date: Wed, 9 Mar 2016 17:14:05 +0100 Subject: [PATCH 11/12] Add real size network --- blog/_posts/2016-02-21-cfn.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/blog/_posts/2016-02-21-cfn.md b/blog/_posts/2016-02-21-cfn.md index 1e717c8..cc4d0bf 100644 --- a/blog/_posts/2016-02-21-cfn.md +++ b/blog/_posts/2016-02-21-cfn.md @@ -65,8 +65,13 @@ In the backward pass, the same idea can be applied. When no rating exist, the er ![training1](http://florian-strub.com/tmp/training3-small.png) +At first sight, there is very few constraint in such Autoencoders. Actually, dropout already removed 50% of the weights. Beware that more than 95% of the ratings are missing in real datasets. Thus, the bottleneck of the autoencoder is often greater than the number of ratings in the input vector! -The autoencoder is also diverted from its original purpose. It does not aim to reconstruct the initial input anymore, it aims at predicting the missing data. +If we change the toys example by a bit more realistic autoencoder. It is not straightfroward that the network will be able to learn a useful representation from a very sparse representation. + + ![error](http://florian-strub.com/tmp/realNetworks.png) + +The autoencoder is acctually diverted from its original purpose. It does not aim to reconstruct the initial input anymore, it aims at predicting the missing data. By keeping this idea in mind, we applied the Denoising loss [2] to emphasize the prediction aspect during the training. First, a few input ratings are masked on every input vector to simulate missing ratings. From 4e9073fef3a3eb20fcc92d12c7c22ae1afdfc87b Mon Sep 17 00:00:00 2001 From: fstrub Date: Wed, 9 Mar 2016 17:18:19 +0100 Subject: [PATCH 12/12] Add pictures require for the post : cfn --- blog/_posts/images/CF/CBF.png | Bin 150584 -> 0 bytes blog/_posts/images/CF/Matrixratings.png | Bin 666 -> 0 bytes blog/_posts/images/CF/ratings.png | Bin 43481 -> 0 bytes blog/_posts/images/cfn/DAELoss-small.png | Bin 0 -> 25685 bytes blog/_posts/images/cfn/Humor_recommender.jpg | Bin 0 -> 32193 bytes blog/_posts/images/cfn/UV.png | Bin 0 -> 38055 bytes blog/_posts/images/cfn/dense2sparse.png | Bin 0 -> 126596 bytes blog/_posts/images/cfn/finalMatrix.png | Bin 0 -> 158441 bytes blog/_posts/images/cfn/initialMatrix.png | Bin 0 -> 177232 bytes blog/_posts/images/cfn/realNetworks.png | Bin 0 -> 128517 bytes blog/_posts/images/cfn/training1-small.png | Bin 0 -> 64594 bytes blog/_posts/images/cfn/training2-small.png | Bin 0 -> 69036 bytes blog/_posts/images/cfn/training3-small.png | Bin 0 -> 68824 bytes 13 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 blog/_posts/images/CF/CBF.png delete mode 100644 blog/_posts/images/CF/Matrixratings.png delete mode 100644 blog/_posts/images/CF/ratings.png create mode 100644 blog/_posts/images/cfn/DAELoss-small.png create mode 100644 blog/_posts/images/cfn/Humor_recommender.jpg create mode 100644 blog/_posts/images/cfn/UV.png create mode 100644 blog/_posts/images/cfn/dense2sparse.png create mode 100644 blog/_posts/images/cfn/finalMatrix.png create mode 100644 blog/_posts/images/cfn/initialMatrix.png create mode 100644 blog/_posts/images/cfn/realNetworks.png create mode 100644 blog/_posts/images/cfn/training1-small.png create mode 100644 blog/_posts/images/cfn/training2-small.png create mode 100644 blog/_posts/images/cfn/training3-small.png diff --git a/blog/_posts/images/CF/CBF.png b/blog/_posts/images/CF/CBF.png deleted file mode 100644 index ff5d4b8b47b08cf271ed0f0ab3d5a57cf1479941..0000000000000000000000000000000000000000 GIT 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