Summary of On the Nonconvexity Of Some Push-forward Constraints and Its Consequences in Machine Learning, by Lucas De Lara (ut3 et al.
On the nonconvexity of some push-forward constraints and its consequences in machine learning
by Lucas de Lara, Mathis Deronzier, Alberto González-Sanz, Virgile Foy
First submitted to arxiv on: 12 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Probability (math.PR)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 investigates the push-forward operation, which redistributes probability measures through deterministic maps, playing a crucial role in statistics and optimization. The authors identify gaps in current literature regarding the non-convexity of constraints framed as push-forward conditions on learning problems. They provide sufficient and necessary conditions for the convexity or non-convexity of maps transporting probability measures. This finding has significant implications for designing convex optimization problems for generative modeling and group-fair predictors, highlighting critical limitations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how to move a probability measure around using a map. This is important in statistics and optimization because many learning problems involve constraints or penalties that need to be framed as push-forward conditions on the model. The authors want to fill a gap in current knowledge by studying when these constraints are convex or not. They find that most of the time, these constraints are not convex. This has big implications for how we design optimization problems for things like generating models and fair predictors. |
Keywords
* Artificial intelligence * Optimization * Probability
