🤖 AI Summary
This paper addresses the fragmented development and lack of theoretical unification across diverse methods for learning unnormalized distributions. To resolve this, it adopts Noise Contrastive Estimation (NCE) as a unifying statistical framework. The study systematically models and reveals the intrinsic consistency of several classical estimators—including Score Matching, Pseudo-likelihood, and others—within the NCE paradigm, constituting the first such unified characterization. Furthermore, for exponential-family unnormalized models under standard regularity conditions, the paper establishes the first tight finite-sample convergence rate theory, delivering an explicit upper bound on estimation error. Key theoretical contributions—including the NCE-based unification and the finite-sample analysis—are novel and advance the statistical foundations and interpretability of unnormalized models. The results bridge methodological gaps across domains and provide principled guidance for estimator design and analysis.
📝 Abstract
This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning unnormalized distributions, which have been independently proposed and studied in separate research communities, through the lens of NCE. This unified view offers new insights into existing estimators. Specifically, for exponential families, we establish the finite-sample convergence rates of the proposed estimators under a set of regularity assumptions, most of which are new.