# Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

arXiv: https://arxiv.org/abs/2603.11532 · HTML: https://mlsanity.com/paper/2603.11532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [A Survey of Human-in-the-loop for Machine Learning](https://mlsanity.com/paper/2108.00941/) (2021)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Recent progress in log-concave density estimation](https://mlsanity.com/paper/1709.03154/) (2017)

## Abstract (arXiv)

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.