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The paper addresses the problem of estimating multiple discrete unimodal distributions under stochastic order constraints, motivated by search behavior analysis. They formulate the estimation as a mixed-integer convex quadratic optimization problem to incorporate precedence relations among the distributions. Experiments demonstrate that the proposed method achieves a reduction in Jensen-Shannon divergence, particularly when dealing with small sample sizes, compared to existing methods.
Impose stochastic order constraints on multiple discrete unimodal distributions to improve estimation accuracy by up to 6.3% when data is scarce.
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.
