Summary of Transient Anisotropic Kernel For Probabilistic Learning on Manifolds, by Christian Soize and Roger Ghanem
Transient anisotropic kernel for probabilistic learning on manifolds
by Christian Soize, Roger Ghanem
First submitted to arxiv on: 31 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 The paper proposes a novel method called PLoM (Probabilistic Learning on Manifolds) for handling small training datasets. This approach uses an Itô equation as the MCMC generator, with the KDE-estimated probability measure from the training dataset being the invariant measure. The authors introduce a new ISDE projection vector basis built from a transient anisotropic kernel, which provides an alternative to the traditional DMAPS basis for improving statistical surrogates on stochastic manifolds with heterogeneous data. This new basis is shown to better represent statistical dependencies in the learned probability measure, and three applications demonstrate its effectiveness across varying levels of complexity and heterogeneity. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper talks about a new way to deal with small groups of data points that are hard to learn from because they’re noisy or spread out. The method uses math from physics to create a special kind of map that helps the computer understand the patterns in the data better. This map is made by combining two different types of math problems: one that looks at how things move over time and another that helps us figure out what’s important about each piece of data. By using this new map, we can learn more accurate patterns from small groups of data points. The authors tested their method on three different types of data and showed that it works well even when the data is noisy or mixed up. |
Keywords
* Artificial intelligence * Probability
