Statistical Active Learning Algorithms for Noise Tolerance and Differential Privacy

TL;DR

This paper introduces a framework for designing active learning algorithms that are robust to noise and preserve privacy, achieving optimal noise tolerance and exponential label savings over passive methods.

Contribution

It presents a generic method to convert statistical active learning algorithms into noise-tolerant and differentially-private versions, with optimal complexity and broad applicability.

Findings

Efficient algorithms for learning thresholds, rectangles, and linear separators under noise.

Optimal quadratic dependence on noise rate in complexity.

Exponential label savings in private active learning.

Abstract

We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the sense that they rely on estimates of expectations of functions of filtered random examples. It builds on the powerful statistical query framework of Kearns (1993). We show that any efficient active statistical learning algorithm can be automatically converted to an efficient active learning algorithm which is tolerant to random classification noise as well as other forms of "uncorrelated" noise. The complexity of the resulting algorithms has information-theoretically optimal quadratic dependence on $1/(1-2\eta)$, where $\eta$ is the noise rate. We show that commonly studied concept classes including thresholds, rectangles, and linear separators can be efficiently actively learned in our framework. These results combined with our generic conversion lead to the first computationally-efficient algorithms for actively learning some of these concept classes in the presence of random classification noise that provide exponential improvement in the dependence on the error $\epsilon$ over their passive counterparts. In addition, we show that our algorithms can be automatically converted to efficient active differentially-private algorithms. This leads to the first differentially-private active learning algorithms with exponential label savings over the passive case.