Symbolic Density Estimation for Discrete Distributions
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Density EstimationSimilar Papers 제목 키워드 기반
Symbolic Density Estimation: A Decompositional Approach
We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicabil…
Density EstimationHierarchical Discrete Distribution Decomposition for Match Density Estimation
Explicit representations of the global match distributions of pixel-wise correspondences between pairs of images are desirable for uncertainty estimation and downstream applications. However, the computation of the match…
Density EstimationOptical Flow EstimationStereo MatchingStereo Matching HandCommunication-Efficient Distributed Learning of Discrete Distributions
We initiate a systematic investigation of distribution learning (density estimation) when the data is distributed across multiple servers. The servers must communicate with a referee and the goal is to estimate the under…
Density EstimationMESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation
We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient…
Density EstimationSymbolic RegressionDiscretely Indexed Flows
In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic tra…
Density EstimationVariational Inference