Large deviations for the perceptron model and consequences for active learning

TL;DR

This paper analyzes the theoretical limits of active learning performance using large deviation theory and replica methods, demonstrating that simple algorithms can approach optimal accuracy boundaries.

Contribution

It introduces a novel theoretical framework for understanding active learning limits via large deviations and replica analysis, and shows simple algorithms can nearly reach these bounds.

Findings

Optimal performance boundaries are derived for active learning.

Simple message-passing algorithms can approach these optimal bounds.

Comparison shows certain strategies are close to theoretical limits.

Abstract

Active learning is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the corresponding labels, subsequently used for supervised learning. In this work, we consider the task of choosing the subset of samples to be labeled from a fixed finite pool of samples. We assume the pool of samples to be a random matrix and the ground truth labels to be generated by a single-layer teacher random neural network. We employ replica methods to analyze the large deviations for the accuracy achieved after supervised learning on a subset of the original pool. These large deviations then provide optimal achievable performance boundaries for any active learning algorithm. We show that the optimal learning performance can be efficiently approached by simple message-passing active learning algorithms. We also provide a comparison with the performance of some other popular active learning strategies.