Summary of Importance Corrected Neural Jko Sampling, by Johannes Hertrich and Robert Gruhlke
Importance Corrected Neural JKO Sampling
by Johannes Hertrich, Robert Gruhlke
First submitted to arxiv on: 29 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Probability (math.PR)
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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 This paper proposes a novel method to sample from unnormalized probability density functions by combining continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. The approach iteratively trains CNFs with regularized velocity fields, which is shown to converge to the Wasserstein gradient flow (WGF). This allows for overcoming local minima and slow convergence of the WGF for multimodal distributions. The method also reduces the reverse Kulback-Leibler (KL) loss function in each step, enables generation of independent and identically distributed (iid) samples, and permits evaluation of the generated underlying density. Numerical examples demonstrate the accuracy and effectiveness of this approach on various test distributions, including high-dimensional multimodal targets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding a way to get random samples from an unknown probability distribution. It’s like trying to guess what a big jar of colored beads might look like if you only have one bead out of many. The researchers combined two ideas: normalizing flows and rejection-resampling steps. They tested this idea on different distributions, including ones with lots of modes (like having multiple colors in the beads). Their method worked well and was better than other methods in most cases. |
Keywords
* Artificial intelligence * Loss function * Probability
