Symbolic Density Estimation for Discrete Distributions

• URL: http://arxiv.org/abs/2605.21813v1
• Date: Wed, 20 May 2026 23:22:21 GMT
• Title: Symbolic Density Estimation for Discrete Distributions
• Abstract summary: We introduce symbolic density estimation (SDE), an unsupervised framework that automatically recovers closed-form probability mass functions.<n>Our method integrates domain-specific structural priors with evolutionary search and a validity-aware inference stage.<n>A real data application shows that it identifies concise and interpretable mixture models that improve goodness-of-fit over standard models.
• Score: 5.337523703846813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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