Summary of Uniform Generalization Bounds on Data-dependent Hypothesis Sets Via Pac-bayesian Theory on Random Sets, by Benjamin Dupuis et al.
Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets
by Benjamin Dupuis, Paul Viallard, George Deligiannidis, Umut Simsekli
First submitted to arxiv on: 26 Apr 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 proposed data-dependent uniform generalization bounds approach the problem from a PAC-Bayesian perspective, applying the framework to “random sets” in a rigorous way. This enables proof of data-dependent bounds applicable in various contexts. The method’s power is demonstrated through two applications: a PAC-Bayesian formulation of fractal-dimension-based generalization bounds, which unifies existing results with a single technique, and uniform bounds over trajectories of continuous Langevin dynamics and stochastic gradient Langeville dynamics, providing novel insights into the generalization properties of noisy algorithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research develops new ways to understand how well machine learning models work on unseen data. The approach is based on a mathematical framework called PAC-Bayesian, which helps prove bounds for how well models can generalize. The results are useful in many areas and provide tighter bounds than existing methods. This paper also shows how the approach can be used to study the generalization properties of algorithms that use noisy data. |
Keywords
» Artificial intelligence » Generalization » Machine learning
