Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

Yasuhiro Yoshida; Noriyoshi Sukegawa; Jiro Iwanaga

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arXiv · 2603.11532

Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

Yasuhiro Yoshida·Noriyoshi Sukegawa·Jiro Iwanaga

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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.

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Yasuhiro Yoshida, Noriyoshi Sukegawa, Jiro Iwanaga. 2026-03-12. Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints. https://arxiv.org/abs/2603.11532

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