A General Method for Robust Learning from Batches

TL;DR

This paper introduces a comprehensive framework for robust learning from batch data, addressing challenges posed by corrupt or adversarial batches across various domains, and presents new efficient algorithms for classification and distribution estimation.

Contribution

It generalizes robust learning to arbitrary domains and provides the first computationally-efficient algorithms for several complex distribution classes.

Findings

Established limits for robust classification and distribution estimation.

Developed the first efficient algorithms for piecewise-interval classification.

Designed robust algorithms for complex distribution families like Gaussian mixtures.

Abstract

In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of robust learning from batches, and determine the limits of both classification and distribution estimation over arbitrary, including continuous, domains. Building on these results, we derive the first robust agnostic computationally-efficient learning algorithms for piecewise-interval classification, and for piecewise-polynomial, monotone, log-concave, and gaussian-mixture distribution estimation.