Summary of Deterministic Fokker-planck Transport — with Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo, by Ilja Klebanov
Deterministic Fokker-Planck Transport – With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo
by Ilja Klebanov
First submitted to arxiv on: 11 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA); Statistics Theory (math.ST); Methodology (stat.ME)
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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 paper proposes a novel approach to particle flow methods by reformulating the Fokker-Planck equation as a continuity equation. This formulation naturally yields a velocity field that can be used to define a gradient flow of the Kullback-Leibler divergence between current and target densities with respect to the 2-Wasserstein distance. However, this approach relies on evaluating the current probability density, which is typically intractable in practical applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper takes an existing method, the Fokker-Planck equation, and gives it a new twist by turning it into a continuity equation. This leads to some useful properties, like being able to measure how far two densities are from each other. The problem is that this method requires knowing the current probability density, which is usually very hard to figure out. |
Keywords
» Artificial intelligence » Probability
