← 研踪 PaperTrailarXiv:2610.37611 · v2
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
首次提交 2026-10-28 01:41
版本更新 2026-10-30 00:17
雷达观测 2026-10-30 13:28
摘要
Artificial intelligence offers statisticians a new paradigm for modelling and analysing complex datasets. Agents based on large language models can reason about data and automate key stages of the statistical modelling workflow, from model fitting to validation. In this paper we propose a method that uses such an agent to estimate the conditional density of a response given a vector of covariates from an iid sample. The agent examines the sample, chooses a model for the conditional distribution of the response and the procedure to fit it, and returns the estimator as a short computer program. The program is built from a library of probability distributions. The returned law can therefore be a parametric distribution, a mixture or a multivariate factorization, with distribution parameters given by explicit formulas in the covariates. We call this approach agentic distributional regression (ADR). Unlike in the classical approach, the statistician no longer chooses the estimator, but asks an agent to build one. Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under assumptions on the number of admissible models and on the accuracy of the agent's fit, and an oracle inequality for the selection of a model among fitted candidates using independent validation data. Finally, assuming that, as the sample size grows, the agent selects the same smooth parametric model with probability tending to one and fits it accurately, we show that the estimated parameters are asymptotically normal. In simulation studies, on twelve real datasets and on a new dataset whose responses postdate the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the existing methods from the statistical literature with which it is compared.
作者备注：47 pages, 6 figures, 11 tables
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v2 · 2026-10-30 00:17 · 最新观测版本
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
Artificial intelligence offers statisticians a new paradigm for modelling and analysing complex datasets. Agents based on large language models can reason about data and automate key stages of the statistical modelling workflow, from model fitting to validation. In this paper we propose a method that uses such an agent to estimate the conditional density of a response given a vector of covariates from an iid sample. The agent examines the sample, chooses a model for the conditional distribution of the response and the procedure to fit it, and returns the estimator as a short computer program. The program is built from a library of probability distributions. The returned law can therefore be a parametric distribution, a mixture or a multivariate factorization, with distribution parameters given by explicit formulas in the covariates. We call this approach agentic distributional regression (ADR). Unlike in the classical approach, the statistician no longer chooses the estimator, but asks an agent to build one. Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under assumptions on the number of admissible models and on the accuracy of the agent's fit, and an oracle inequality for the selection of a model among fitted candidates using independent validation data. Finally, assuming that, as the sample size grows, the agent selects the same smooth parametric model with probability tending to one and fits it accurately, we show that the estimated parameters are asymptotically normal. In simulation studies, on twelve real datasets and on a new dataset whose responses postdate the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the existing methods from the statistical literature with which it is compared.
查看此版本解读 →查看此版本原文 ↗v1 · 2026-10-28 01:41
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
In this paper we propose a method for estimating conditional densities from an iid sample using a language-model agent. The agent writes the estimator as a short program that, for each covariate value, returns the estimated conditional distribution of the response. The program is built from a library of probability distributions, so the returned law can be a parametric distribution, a mixture or a multivariate factorization, with parameters given by explicit functions of the covariates. Since the number of operations and constants in the program is limited, the fitted conditional density is a formula that can be inspected and evaluated independently of the agent, while the choice of the model structure and of the fitting procedure is left to the agent. We call this approach agentic distributional regression (ADR). Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under explicit complexity and optimization assumptions, and an oracle inequality for selection using independent validation data. For a stably selected regular structure with sufficiently accurate fitting, we obtain asymptotic normality of the fitted constants. In simulation studies, on twelve real datasets and on a new dataset collected after the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the methods considered.
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