Merge pull request #57 from UTAustin-SwarmLab/ssn-cps-updates

minor edits to cps blog

Author: saishankarn

_posts/2025-10-10-CPS.md

@@ -31,7 +31,7 @@ Additionally, for the stocks domain, there are some inherent rules that a genera
 
 <figure style="text-align: center;">
     <img src="{{site.baseurl}}/images/post/cps_intro_fig.png" alt="High level description plot" height="auto" style="margin: auto; display: block;">
-   <figcaption>Figure 1 - High-Level Description of Constrained Posterior Sampling (CPS): Here, we show an example where CPS generates daily stock price time series with natural constraints such as the bounds on the opening and closing prices of the stock.</figcaption>
+   <figcaption>Figure 1 - High-Level Description of Constrained Posterior Sampling (CPS): Here, we show an example where CPS generates a daily stock price time series with natural constraints, such as the bounds on the opening and closing prices of the stock.</figcaption>
    <p></p>
 </figure>
 
@@ -52,11 +52,11 @@ This process continues for all the denoising steps. During projection, CPS perfo
 
 <figure style="text-align: center;">
     <img src="{{site.baseurl}}/images/post/cps_approach_fig.png" alt="CPS Approach" height="auto" style="margin: auto; display: block;">
-   <figcaption>Figure 2 - Constrained Posterior Sampling: We show the graphical model for one step of denoising in CPS: refer Algorithm 1 in our manuscript.</figcaption>
+   <figcaption>Figure 2 - Constrained Posterior Sampling: We show the graphical model for one step of denoising in CPS: check Algorithm 1 in our manuscript.</figcaption>
    <p></p>
 </figure>
 
-To ensure minimal effects on the sample quality, we introduce penalty coefficients that minimize the perturbations of the posterior mean estimate during the initial denoising steps when the signal to noise ratio is very low. Towards the final denoising steps, the penalty coefficients are very large to ensure constraint satisfaction.
+To ensure minimal effects on the sample quality, we introduce penalty coefficients that minimize the perturbations of the posterior mean estimate during the initial denoising steps when the signal-to-noise ratio is very low. Towards the final denoising steps, the penalty coefficients are very large to ensure constraint satisfaction.
 
 Note that CPS satisfies all the requirements listed above for a desired approach.
 
@@ -79,8 +79,8 @@ In our work, we showcase the efficiency of CPS in terms of sample quality and di
 Additionally, in terms of tracking real time series samples, we show that CPS outperforms SOTA methods by 42%. Specifically, CPS does not suffer from sample quality degradation for a large number of constraints, while other approaches break down in such settings (Figure 4). We refer the readers to Figures 3 and 4 to observe the sample quality and tracking abilities of CPS.
 
 <figure style="text-align: center;">
-    <img src="{{site.baseurl}}/images/post/cps_results_1.png" alt="CPS Main Qualitative Results" height="auto" style="margin: auto; display: block;">
-   <figcaption>Figure 4: CPS tracks the real data samples as the number of constraints increases. Increasing the number of constraints reduces the size of the constraint set, and an ideal approach should effectively generate samples that resemble the real time series samples that belong to the constraint set. Here, we show a qualitative example from the Stocks dataset. Observe that CPS accurately tracks the real sample that concurs with the specified constraints while other approaches suffer.</figcaption>
+    <img src="{{site.baseurl}}/images/post/cps_results_2.png" alt="CPS Main Qualitative Results" height="auto" style="margin: auto; display: block;">
+   <figcaption>Figure 4: CPS tracks the real data samples as the number of constraints increases. Increasing the number of constraints reduces the size of the constraint set, and an ideal approach should effectively generate samples that resemble the real time series samples that belong to the constraint set. Here, we show a qualitative example from the Stocks dataset. Observe that CPS accurately tracks the real sample that concurs with the specified constraints, while other approaches suffer.</figcaption>
    <p></p>
 </figure>