arXiv:2605.21813v1 Announce Type: new 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 rich
The accelerating pace of AI research, coupled with advancements in symbolic AI and computational search methods, enables novel approaches to fundamental statistical problems.
This development could significantly enhance the interpretability and robustness of AI models, particularly in domains requiring explicit probabilistic reasoning, by automating the discovery of foundational statistical distributions.
The ability to automatically generate closed-form probability mass functions could reduce the reliance on empirical methods for distribution fitting and broaden the application of interpretable statistical models.
- · AI researchers
- · Data scientists
- · Financial modeling
- · Healthcare analytics
- · Traditional statistical software
- · Empirical data modelers
Increased efficiency in statistical model development and validation through automated discovery of underlying distributions.
Improved interpretability and trustworthiness of AI systems in regulated industries due to transparent probabilistic foundations.
The development of entirely new classes of algorithms and applications that leverage symbolic distributional knowledge to solve complex, previously intractable problems.
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