Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints
This work addresses the challenge of estimating distributions with prior knowledge for applications like search behavior analysis, but it is incremental as it builds on existing methods with specific constraints.
The paper tackled the problem of estimating multiple discrete unimodal distributions with stochastic order constraints, motivated by search behavior analysis, and achieved a reduction in Jensen-Shannon divergence by 2.2% on average (up to 6.3%) for small sample sizes while performing comparably to existing methods with sufficient data.
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.