Summary of Equivalence Of the Empirical Risk Minimization to Regularization on the Family Of F-divergences, by Francisco Daunas et al.
Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences
by Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, H. Vincent Poor
First submitted to arxiv on: 1 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Information Theory (cs.IT); 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 This paper presents a solution to empirical risk minimization with f-divergence regularization (ERM-fDR) under mild conditions on f. The optimal measure is shown to be unique, and examples are provided for specific choices of f. Building on this framework, previously known solutions to common regularization choices can be obtained. For instance, the unique solutions to empirical risk minimization with relative entropy regularization (Type-I and Type-II) can be recovered. The analysis reveals that f-divergence regularization introduces a strong inductive bias that dominates the training data evidence, and any f-divergence regularization is equivalent to another with an appropriate transformation of the empirical risk function. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a problem called empirical risk minimization with f-divergence regularization. It shows that there’s one way to solve this problem that works for many different choices of f. The researchers found that when they use certain types of f, they can get solutions they already knew about. This helps them understand how the method works and what it means. |
Keywords
* Artificial intelligence * Regularization
