Summary of Laplace Transform Based Low-complexity Learning Of Continuous Markov Semigroups, by Vladimir R. Kostic et al.
Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroups
by Vladimir R. Kostic, Karim Lounici, Hélène Halconruy, Timothée Devergne, Pietro Novelli, Massimiliano Pontil
First submitted to arxiv on: 18 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Statistics Theory (math.ST)
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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 data-driven approach for learning Markov processes through spectral decomposition of their infinitesimal generator (IG). The IG’s unbounded nature complicates traditional methods, while existing techniques are computationally expensive or limited in scope. Our proposed method leverages the IG’s resolvent and is robust to time-lag variations, ensuring accurate eigenvalue learning even for small time-lags. This approach applies to a broader class of Markov processes than current methods, reducing computational complexity from quadratic to linear in the state dimension. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how we can learn about random processes that happen in real life. Right now, we have some ways to do this, but they’re not very good and take a long time. This new approach uses something called the “infinitesimal generator” to help us learn more quickly and accurately. It works well even when the process is changing slowly over time. The authors tested it on two different experiments and showed that it’s effective. |
