Summary of Asymmetry Of the Relative Entropy in the Regularization Of Empirical Risk Minimization, by Francisco Daunas et al.
Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization
by Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, H. Vincent Poor
First submitted to arxiv on: 2 Oct 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 The paper analyzes the impact of relative entropy asymmetry on empirical risk minimization (ERM) with relative entropy regularization (ERM-RER). It considers two types of regularizations: Type-I ERM-RER, which measures the relative entropy of the measure to be optimized with respect to a reference measure; and Type-II ERM-RER, which measures the relative entropy of the reference measure with respect to the measure to be optimized. The main result is the characterization of the solution to the Type-II ERM-RER problem and its key properties. Comparing the two types, the paper highlights the effects of entropy asymmetry. Regularization by relative entropy forces the solution’s support to collapse into the support of the reference measure, introducing a strong inductive bias that can overshadow the evidence provided by the training data. Type-II regularization is equivalent to Type-I regularization with an appropriate transformation of the empirical risk function. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how making things more similar or different affects how we learn from data. It’s about finding the best answer based on what we know, but also considering how important certain answers are. The main idea is that if we make things too similar or different, it can affect our results and not give us a good answer. This is shown by comparing two different ways of doing this: one where we compare what we want to learn with something we already know, and the other where we compare what we want to learn with something that’s very different. |
Keywords
» Artificial intelligence » Regularization
