Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

TL;DR

This paper introduces a method for estimating multiple discrete unimodal distributions under stochastic order constraints, improving accuracy in small-sample scenarios by formulating the problem as a mixed-integer convex quadratic optimization.

Contribution

It presents a novel optimization-based approach that incorporates prior order knowledge to enhance distribution estimation accuracy.

Findings

Reduces Jensen-Shannon divergence by 2.2% on average with small samples.

Performs comparably to existing methods with larger datasets.

Effective in real-world search behavior analysis.

Abstract

We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic order constraints and formulate the estimation task as a mixed-integer convex quadratic optimization problem. Experiments on both synthetic and real datasets show that the proposed method reduces the Jensen-Shannon divergence by 2.2% on average (up to 6.3%) when the sample size is small, while performing comparably to existing methods when sufficient data are available.