Generalized Coverage for More Robust Low-Budget Active Learning

TL;DR

The paper tackles active learning in ultra-low-budget scenarios where labeling is scarce and where traditional uncertainty-based methods falter. It introduces generalized coverage, a flexible objective $C_k(L)=\mathbb{E}_{x}[\max_{x' \in L} k(x, x')]$, and proposes MaxHerding, a greedy algorithm that maximizes this objective and is motivated by kernel herding. The work demonstrates that ProbCover is a special case of MaxHerding (with a top-hat kernel) and provides a non-greedy kernel $k$-medoids variant to connect to existing methods; MaxHerding achieves strong performance with lower computational cost across multiple low-budget image benchmarks and is robust to kernel choice and budget size. These results offer a scalable, robust approach for learning with limited labels, particularly when leveraging self-supervised representations.

Abstract

The ProbCover method of Yehuda et al. is a well-motivated algorithm for active learning in low-budget regimes, which attempts to "cover" the data distribution with balls of a given radius at selected data points. We demonstrate, however, that the performance of this algorithm is extremely sensitive to the choice of this radius hyper-parameter, and that tuning it is quite difficult, with the original heuristic frequently failing. We thus introduce (and theoretically motivate) a generalized notion of "coverage," including ProbCover's objective as a special case, but also allowing smoother notions that are far more robust to hyper-parameter choice. We propose an efficient greedy method to optimize this coverage, generalizing ProbCover's algorithm; due to its close connection to kernel herding, we call it "MaxHerding." The objective can also be optimized non-greedily through a variant of $k$-medoids, clarifying the relationship to other low-budget active learning methods. In comprehensive experiments, MaxHerding surpasses existing active learning methods across multiple low-budget image classification benchmarks, and does so with less computational cost than most competitive methods.

Figures (10)

• Figure 1: Illustration of the connection between our proposed methods (in red) and the existing active learning (in blue) as well as herding methods (in green). We describe (a)--(c) in \ref{['sec:method']}. For (d)--(f), please refer to steinpoints2018chen, probcover2022yehuda, and typiclust2022hacohen, respectively.
• Figure 2: (a) Next choices for different algorithms after selecting the initial orange point. (b) Varying the radius $\delta$ in ProbCover, and Gaussian lengthscale for MaxHerding, for CIFAR10 classification. See text for the definition of purity.
• Figure 3: Comparison on benchmark datasets using 1-NN classifier.
• Figure 4: Comparison on imbalanced datasets using 1-NN classifier.
• Figure 5: (a) compares the greedy (MaxHerding) and non-greedy (kernel $k$-medoids) algorithms on CIFAR100, and (b) compares low budget active learning methods in terms of runtime in seconds per selection on CIFAR100 and TinyImageNet.

Theorems & Definitions (16)

• proposition thmcounterproposition: Kernel herding convergence kherding2010chen
• theorem thmcountertheorem
• corollary thmcountercorollary
• definition thmcounterdefinition: Generalized Coverage
• proposition thmcounterproposition
• proof
• corollary thmcountercorollary
• proposition thmcounterproposition
• proposition thmcounterproposition
• proof