Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917334737747968 |
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| author | Yoshida, Yasuhiro Sukegawa, Noriyoshi Iwanaga, Jiro |
| author_facet | Yoshida, Yasuhiro Sukegawa, Noriyoshi Iwanaga, Jiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints Yoshida, Yasuhiro Sukegawa, Noriyoshi Iwanaga, Jiro Optimization and Control Machine Learning Methodology 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. |
| title | Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints |
| topic | Optimization and Control Machine Learning Methodology |
| url | https://arxiv.org/abs/2603.11532 |