Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

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.

Figures (4)

• Figure 1: Three search timing distributions for keywords containing body weight on Mamari
• Figure 2: Change in the estimation error (JSD) with respect to sample size using synthetic data
• Figure 3: Visual comparison of estimated distributions with varying sample sizes
• Figure 4: Estimated distributions for two instances