Learning sparse mixtures of rankings from noisy information

TL;DR

This paper introduces algorithms for learning mixtures of rankings from noisy data across various models, achieving high accuracy with significantly improved polynomial runtime compared to prior exponential-time methods.

Contribution

The authors develop efficient algorithms for learning mixtures of rankings under multiple noise models, with a runtime of n^{O(log k)} that improves upon previous exponential-time algorithms.

Findings

Algorithms successfully learn mixtures with high accuracy.

Runtime is polynomial in n and logarithmic in k.

Applicable to multiple noise models including heat kernel and Mallows.

Abstract

We study the problem of learning an unknown mixture of $k$ rankings over $n$ elements, given access to noisy samples drawn from the unknown mixture. We consider a range of different noise models, including natural variants of the "heat kernel" noise framework and the Mallows model. For each of these noise models we give an algorithm which, under mild assumptions, learns the unknown mixture to high accuracy and runs in $n^{O(\log k)}$ time. The best previous algorithms for closely related problems have running times which are exponential in $k$.