Summary of The Polynomial Stein Discrepancy For Assessing Moment Convergence, by Narayan Srinivasan et al.
The Polynomial Stein Discrepancy for Assessing Moment Convergence
by Narayan Srinivasan, Matthew Sutton, Christopher Drovandi, Leah F South
First submitted to arxiv on: 6 Dec 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Computation (stat.CO)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed novel method measures discrepancy between samples and desired posterior distribution for Bayesian inference. The effective sample size is not suitable for scalable Bayesian sampling algorithms like stochastic gradient Langevin dynamics, which are asymptotically biased. Instead, the gold standard uses kernel Stein Discrepancy (KSD), but it’s not scalable due to quadratic cost with number of samples. The KSD and its faster extensions suffer from curse-of-dimensionality and require extensive tuning. To address limitations, the polynomial Stein discrepancy (PSD) is developed along with an associated goodness-of-fit test. The test detects differences in first r moments in the Bernstein-von Mises limit, but it’s not fully convergence-determining. Empirical results show that the test has higher power than competitors at a lower computational cost. Finally, PSD helps practitioners select hyper-parameters of Bayesian sampling algorithms more efficiently than competitors. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper is about finding ways to measure how well samples match what we want them to look like in Bayesian inference. Right now, there’s no good way to do this when using certain types of algorithms that are designed for big datasets. The current “gold standard” method, called kernel Stein Discrepancy (KSD), has some problems too. It’s not fast enough and requires a lot of tweaking to work well. To solve these issues, the authors created a new method called polynomial Stein discrepancy (PSD) that can help us figure out if our samples are good or not. They also developed a test to go along with it that can detect certain kinds of differences between what we want and what we get. |
Keywords
» Artificial intelligence » Bayesian inference
