Active Learning for Binary Classification with Abstention

TL;DR

This paper develops and analyzes active learning algorithms for binary classification with abstention, providing theoretical guarantees, adaptive strategies, and computationally efficient variants across various abstention settings and sampling models.

Contribution

It introduces new active learning algorithms for abstention scenarios, establishes their near-optimality, and proposes adaptive and efficient variants for high-dimensional problems.

Findings

Algorithms achieve minimax near-optimal excess risk bounds.

Adaptive strategies effectively handle unknown smoothness parameters.

A computationally efficient variant reduces complexity in high dimensions.

Abstract

We construct and analyze active learning algorithms for the problem of binary classification with abstention. We consider three abstention settings: \emph{fixed-cost} and two variants of \emph{bounded-rate} abstention, and for each of them propose an active learning algorithm. All the proposed algorithms can work in the most commonly used active learning models, i.e., \emph{membership-query}, \emph{pool-based}, and \emph{stream-based} sampling. We obtain upper-bounds on the excess risk of our algorithms in a general non-parametric framework and establish their minimax near-optimality by deriving matching lower-bounds. Since our algorithms rely on the knowledge of some smoothness parameters of the regression function, we then describe a new strategy to adapt to these unknown parameters in a data-driven manner. Since the worst case computational complexity of our proposed algorithms increases exponentially with the dimension of the input space, we conclude the paper with a computationally efficient variant of our algorithm whose computational complexity has a polynomial dependence over a smaller but rich class of learning problems.