Active Covering

TL;DR

This paper studies active covering, proposing algorithms that efficiently label positive examples with fewer queries, outperforming offline methods and baselines on image datasets under standard assumptions.

Contribution

It introduces a simple active learning algorithm with improved query complexity and demonstrates its effectiveness on benchmark datasets.

Findings

Active learning method outperforms offline and baseline methods.

Proposed algorithms require only positive labels, offering computational and privacy benefits.

Achieves near-optimal query cost under standard non-parametric assumptions.

Abstract

We analyze the problem of active covering, where the learner is given an unlabeled dataset and can sequentially label query examples. The objective is to label query all of the positive examples in the fewest number of total label queries. We show under standard non-parametric assumptions that a classical support estimator can be repurposed as an offline algorithm attaining an excess query cost of $\widetilde{\Theta}(n^{D/(D+1)})$ compared to the optimal learner, where $n$ is the number of datapoints and $D$ is the dimension. We then provide a simple active learning method that attains an improved excess query cost of $\widetilde{O}(n^{(D-1)/D})$. Furthermore, the proposed algorithms only require access to the positive labeled examples, which in certain settings provides additional computational and privacy benefits. Finally, we show that the active learning method consistently outperforms offline methods as well as a variety of baselines on a wide range of benchmark image-based datasets.