Paper links scoring rules and Stein operators for unnormalized models
Original title: A unified approach for estimation of unnormalized models via Stein operators
The framework covers score matching, ratio matching, pseudolikelihood and noise contrastive estimation, then characterizes estimator efficiency.
An arXiv paper proposes a unified way to estimate unnormalized models by connecting proper scoring rules with Stein's method. The authors build a class of proper scoring rules that includes score matching, ratio matching, pseudolikelihood and noise contrastive estimation, and show these rules induce Stein operators. They use that geometry to characterize the asymptotic efficiency of the resulting estimators.
- The scoring-rule class includes score matching, ratio matching, pseudolikelihood and noise contrastive estimation.
- Proper scoring rules are shown to induce Stein operators, giving a new construction principle.
- Asymptotic efficiency of the estimators is characterized through the induced geometry.
From the original article
1 min read at arxiv.orgIn 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.
By Mitsuki Nagai · arxiv.org
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