A unified approach for estimation of unnormalized models via Stein operators

Mitsuki Nagai, Keisuke Yano · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29510 · cited by 0 works (OpenAlex) · open-access PDF

German

In diesem Papier entwickeln wir einen einheitlichen Rahmen, der die richtigen Scoring-Regeln und die Stein-Methode für die Schätzung nicht normalisierter Modelle verbindet. Wir konstruieren eine Klasse von richtigen Scoring-Regeln, die Scoring-Matching, Ratio-Matching, Pseudolikelihood und Geräuschkontrastschätzung umfasst. Wir zeigen, dass diese richtigen Scoring-Regeln Stein-Operatoren auf natürliche Weise induzieren. Diese Verbindung erzeugt ein neues Konstruktionsprinzip für Stein-Operatoren und ermöglicht es uns, Schätzungen basierend auf diesen Scoring-Regeln durch die mit den induzierten Stein-Operatoren verbundene Geometrie zu studieren.

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Estimator, Mathematics, Connection (principal bundle), Class (philosophy), Construct (python library), Noise (video)

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