Efficient and Accurate Top-$K$ Recovery from Choice Data

TL;DR

This paper introduces the choice-based Borda count algorithm for efficient and accurate top-$K$ item recovery from choice data, demonstrating optimal sample complexity and practical speed advantages over traditional methods.

Contribution

The paper proposes a novel choice-based Borda count algorithm that achieves optimal sample complexity for top-$K$ recovery under broad models and is faster and simpler than maximum likelihood methods.

Findings

The algorithm matches the top-$K$ estimates of MLE in the limit.

It is several orders of magnitude faster than existing ranking algorithms.

Experiments show competitive accuracy with improved efficiency.

Abstract

The intersection of learning to rank and choice modeling is an active area of research with applications in e-commerce, information retrieval and the social sciences. In some applications such as recommendation systems, the statistician is primarily interested in recovering the set of the top ranked items from a large pool of items as efficiently as possible using passively collected discrete choice data, i.e., the user picks one item from a set of multiple items. Motivated by this practical consideration, we propose the choice-based Borda count algorithm as a fast and accurate ranking algorithm for top $K$-recovery i.e., correctly identifying all of the top $K$ items. We show that the choice-based Borda count algorithm has optimal sample complexity for top-$K$ recovery under a broad class of random utility models. We prove that in the limit, the choice-based Borda count algorithm produces the same top-$K$ estimate as the commonly used Maximum Likelihood Estimate method but the former's speed and simplicity brings considerable advantages in practice. Experiments on both synthetic and real datasets show that the counting algorithm is competitive with commonly used ranking algorithms in terms of accuracy while being several orders of magnitude faster.