Summary of Piecewise Deterministic Generative Models, by Andrea Bertazzi et al.
Piecewise deterministic generative models
by Andrea Bertazzi, Dario Shariatian, Umut Simsekli, Eric Moulines, Alain Durmus
First submitted to arxiv on: 28 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs). PDMPs combine deterministic motion with random jumps at random times, allowing for time reversals that are also PDMPs. We apply this concept to three existing PDMPs: Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. Our results show that the jump rates and kernels of these time reversals can be expressed explicitly using conditional densities. This leads to efficient training procedures for learning these characteristics and approximate simulation of the reverse process. We also provide total variation distance bounds between the data distribution and our model’s resulting distribution when the base distribution is a standard Gaussian. The proposed class of models shows promising results, warranting further investigation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary We’re introducing new types of computer programs that can create fake data that looks like real data. These programs use a combination of predictable movements and random jumps to generate this fake data. We’ve applied this idea to three existing programs that do something similar, and we’ve found ways to make these programs work more efficiently. Our results show that we can express the key characteristics of these programs mathematically, which helps us learn how they work and create even better versions. This new class of programs has promising possibilities for creating realistic fake data. |
