Adaptive randomized pivoting and volume sampling

arXiv stat.ML / 4/6/2026

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Key Points

The paper revisits Adaptive Randomized Pivoting (ARP), a column subset selection algorithm, and shows it can be reinterpreted through the lens of volume sampling for matrix-related sampling.
It draws formal connections between ARP and active learning algorithms for linear regression, providing a unified theoretical view of the underlying sampling/selection principles.
The authors use these connections to derive new analysis results for ARP, improving understanding of its behavior and effectiveness.
The work also introduces faster ARP implementations via rejection sampling, aiming to reduce computational overhead while retaining performance.
The announcement indicates this is a revised version (v2), replacing the prior posting with updated analysis and implementation details.

Abstract

Adaptive randomized pivoting (ARP) is a recently proposed and highly effective algorithm for column subset selection. This paper reinterprets the ARP algorithm by drawing connections to the volume sampling distribution and active learning algorithms for linear regression. As consequences, this paper presents new analysis for the ARP algorithm and faster implementations using rejection sampling.