Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

• URL: http://arxiv.org/abs/2603.11532v1
• Date: Thu, 12 Mar 2026 04:36:25 GMT
• Title: Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints
• Abstract summary: We study the problem of estimating multiple discrete unimodal distributions motivated by search behavior analysis on a real-world platform.<n>To incorporate prior knowledge of precedence relations among distributions, we impose order constraints and formulate the estimation task as a mixed-integer convex optimization problem.<n> 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.
• Score: 1.0323063834827415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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