Summary of Trading Off Consistency and Dimensionality Of Convex Surrogates For the Mode, by Enrique Nueve et al.
Trading off Consistency and Dimensionality of Convex Surrogates for the Mode
by Enrique Nueve, Bo Waggoner, Dhamma Kimpara, Jessie Finocchiaro
First submitted to arxiv on: 16 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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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 In a multiclass classification setting, designing a consistent surrogate loss is crucial for accurate predictions. The abstract argues that this consistency requires embedding outcomes into at least n-1-dimensional reals. However, as n grows, optimizing in such high-dimensional spaces becomes impractical. To address this challenge, the paper explores ways to trade off surrogate loss dimension, problem instances, and restricting the region of consistency in the simplex. It proposes an intuitive embedding procedure that maps outcomes onto vertices of convex polytopes in a low-dimensional space. The authors demonstrate how full-dimensional subsets of the simplex exist around each point mass distribution for which consistency holds, but also highlight the phenomenon of hallucination, where the optimal report under the surrogate loss is an outcome with zero probability. They derive a result to check if consistency holds under a given polytope embedding and low-noise assumption, providing insight into when to use a particular embedding. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Multiclass classification is a way for computers to predict one of many outcomes. To do this, it needs a “correct” way to make predictions. The paper talks about how to design a system that makes good predictions, even if the data is noisy or biased. It shows that sometimes you need to use high-dimensional spaces to get good results, but this can be hard to do when there are many possible outcomes. The authors also introduce an idea called hallucination, where the computer thinks it’s correct to predict something that actually has zero chance of happening. They give examples of how to make these predictions work in practice and show that you can even learn from mistakes. |
Keywords
* Artificial intelligence * Classification * Embedding * Hallucination * Probability
