Beyond Tweedie's Formula: Conditional Score Modeling for Empirical Bayes Inference

2026-09-10

AI Summary

本文提出条件f-建模框架，通过直接估计条件边缘得分函数解决经验贝叶斯推理中的协变量效应问题。

Abstract

We propose conditional f-modeling (Cf-modeling), a framework for empirical Bayes inference with covariates. A central identity shows that the conditional marginal score function determines not only the posterior mean through Tweedie's formula, but also the posterior moment-generating function, providing a basis for recovering posterior quantities without explicit prior modeling. Motivated by this observation, we treat the conditional marginal score as the primary object of inference and estimate it directly using an energy-based representation and Hyvärinen score matching, thereby avoiding potentially intractable covariate-dependent normalizing constants. The resulting framework flexibly accommodates covariate effects and heteroscedasticity and provides a practical approach to posterior moment estimation and uncertainty quantification. We demonstrate the effectiveness of the proposed method through simulations and an RNA-seq application.

Problem

• empirical Bayes inference
• covariates
• posterior quantities
• Tweedie's formula
• score matching

Innovation

• conditional f-modeling
• empirical Bayes inference
• Hyvärinen score matching
• covariates