Symbolic Density Estimation for Discrete Distributions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911709013213184 |
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| author | Liu, Ziwen Li, Meng |
| author_facet | Liu, Ziwen Li, Meng |
| contents | Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE), an unsupervised framework that automatically recovers closed-form probability mass functions by composing elementary analytic operations within a structured search space. Our method integrates domain-specific structural priors with evolutionary search and a validity-aware inference stage, and it extends to richer distribution families such as zero inflation and finite mixtures. To support systematic evaluation and future research, we contribute a benchmark dataset spanning a broad collection of commonly used discrete distributions. The proposed algorithm recovers all benchmark families with accurate parameter estimates. A real data application shows that it identifies concise and interpretable mixture models that improve goodness-of-fit over standard models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21813 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symbolic Density Estimation for Discrete Distributions Liu, Ziwen Li, Meng Machine Learning Methodology Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE), an unsupervised framework that automatically recovers closed-form probability mass functions by composing elementary analytic operations within a structured search space. Our method integrates domain-specific structural priors with evolutionary search and a validity-aware inference stage, and it extends to richer distribution families such as zero inflation and finite mixtures. To support systematic evaluation and future research, we contribute a benchmark dataset spanning a broad collection of commonly used discrete distributions. The proposed algorithm recovers all benchmark families with accurate parameter estimates. A real data application shows that it identifies concise and interpretable mixture models that improve goodness-of-fit over standard models. |
| title | Symbolic Density Estimation for Discrete Distributions |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2605.21813 |