Summary of Complexity Of Vector-valued Prediction: From Linear Models to Stochastic Convex Optimization, by Matan Schliserman and Tomer Koren
Complexity of Vector-valued Prediction: From Linear Models to Stochastic Convex Optimization
by Matan Schliserman, Tomer Koren
First submitted to arxiv on: 5 Dec 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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 studies learning vector-valued linear predictors, which are rules that map feature vectors to target vectors. The focus is on convex and Lipschitz loss functions, and the authors present several new theoretical results on the complexity of this problem and its connections to other learning models. Specifically, they provide a tight characterization of the sample complexity of Empirical Risk Minimization (ERM) in vector-valued linear prediction, showing that approximately k/ε^2 examples are needed to achieve excess risk ε. This improves upon recent results by Magen and Shamir (2023) and matches a classical upper bound due to Maurer (2016). The authors also present a black-box conversion from general d-dimensional Stochastic Convex Optimization (SCO) to vector-valued linear prediction, showing that any SCO problem can be embedded as a prediction problem with k=Θ(d) outputs. This work bridges the gap between linear models and general SCO problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about learning rules that connect feature vectors to target vectors. The authors want to understand how many examples we need to train these rules correctly, and they found some surprising answers! They also showed that a type of problem called Stochastic Convex Optimization (SCO) can be transformed into this kind of prediction problem. This is important because it helps us understand the connections between different types of learning problems. |
Keywords
» Artificial intelligence » Optimization
