Generalization via Derandomization

Jul 12, 2020

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We propose to study the generalization error of a learned predictor h^ in terms of that of a surrogate (potentially randomized) classifier that is coupled to h^ and designed to trade empirical risk for control of generalization error. In the case where h^ interpolates the data, it is interesting to consider theoretical surrogate classifiers that are partially derandomized or rerandomized, e.g., fit to the training data but with modified label noise. We show that replacing h^ by its conditional distribution with respect to an arbitrary sigma-field is a viable method to derandomize. We give an example, inspired by the work of Nagarajan and Kolter (2019), where the learned classifier h^ interpolates the training data with high probability, has small risk, and, yet, does not belong to a nonrandom class with a tight uniform bound on two-sided generalization error. At the same time, we bound the risk of h^ in terms of a surrogate that is constructed by conditioning and shown to belong to a nonrandom class with uniformly small generalization error.

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About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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