Mitsuki Nagai, Keisuke Yano · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.29510 · cited by 0 works (OpenAlex) · open-access PDF
在这篇论文中,我们开发了一个统一的框架,连接了适当的分数规则和施泰恩的模型估计方法。我们构建了一类适当的分数规则,其中包括分数匹配,比例匹配,假定性,和噪音对比估计。我们展示了这些适当的分数规则自然会诱导施泰恩操作员。这种连接为施泰恩操作员提供了新的构建原则,并使我们能够通过与受诱施泰恩操作员相关的几何学来研究基于这些分数规则的估计器。
Machine translation (Meta M2M100); the English original follows.
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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