自动发现离散分布的闭式概率质量函数，提升可解释性。
Symbolic Density Estimation for Discrete Distributions
- 通过演化搜索与结构先验，自动构造解析表达式。
- 在基准数据集上准确恢复所有分布族及参数。
- 适合需要可解释模型的统计建模研究者。
离散概率分布是统计建模的基础，但数百年来依赖逐案数学推导，可解释分布种类扩展缓慢。我们提出符号密度估计（SDE），一种无监督框架，能在结构化搜索空间中通过组合基本解析运算，自动恢复闭式概率质量函数。方法融合领域特定结构先验、演化搜索与有效性感知推理阶段，可扩展至零膨胀和有限混合等更丰富分布族。为支持系统评估与未来研究，我们构建了一个涵盖常用离散分布的基准数据集。所提算法在该数据集上准确恢复所有分布族及其参数。真实数据应用表明，其能识别简洁且可解释的混合模型，显著优于标准模型的拟合效果。
原文摘要 · Abstract (English)
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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