A Maximum Likelihood Approach For Selecting Sets of Alternatives

TL;DR

This paper introduces a maximum likelihood approach for selecting optimal subsets of alternatives based on noisy evaluations, providing theoretical insights and practical algorithms for identifying the strongest options.

Contribution

It generalizes classical methods for identifying the best alternatives to subset selection under noisy conditions, with proven optimality in high-noise scenarios.

Findings

Intuitive methods are optimal when noise is high.

The approach generalizes classical ranking and selection results.

Experimental results demonstrate practical effectiveness.

Abstract

We consider the problem of selecting a subset of alternatives given noisy evaluations of the relative strength of different alternatives. We wish to select a k-subset (for a given k) that provides a maximum likelihood estimate for one of several objectives, e.g., containing the strongest alternative. Although this problem is NP-hard, we show that when the noise level is sufficiently high, intuitive methods provide the optimal solution. We thus generalize classical results about singling out one alternative and identifying the hidden ranking of alternatives by strength. Extensive experiments show that our methods perform well in practical settings.