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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

Indonesian

Dalam makalah ini, kami mengembangkan kerangka kerja yang terintegrasi yang menghubungkan aturan penilaian yang tepat dan metode Stein untuk memperkirakan model yang tidak normal. Kami membangun kelas aturan penilaian yang tepat yang mencakup penilaian skor, perbandingan rasio, pseudolikelihood, dan perkiraan kontras suara. Kami menunjukkan bahwa aturan penilaian yang tepat ini secara alami menginduksi operator Stein. Koneksi ini menghasilkan prinsip konstruksi baru untuk operator Stein, dan memungkinkan kami untuk mempelajari perkiraan berdasarkan aturan penilaian ini melalui geometri yang terkait dengan operator Stein yang diinduksi.

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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