Work

A unified approach for estimation of unnormalized models via Stein operators

Year: 2026

Type: preprint

Abstract: In this paper, we develop a unified framework connecting proper scoring rules and Stein's method for the estimation of unnormalized models. We construct a class of proper scoring rules that encompasses score matching, ratio matching, pseudolikelihood, and noise contrastive estimation. We show that these proper scoring rules naturally induce Stein operators. This connection yields a new construction principle for Stein operators, and enables us to study estimators based on these scoring rules through the geometry associated with the induced Stein operators. Using this geometric perspective, we provide a unified characterization of the asymptotic efficiency of the resulting estimators.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29510

Authors: Nagai, Mitsuki, Yano, Keisuke

Institutions: The Graduate University for Advanced Studies, SOKENDAI, The Institute of Statistical Mathematics

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology

Award: G9001175560

OpenAlex ID: W7223204603

Cites: 9

Cited by:

Related to: 10