Generalized score matching

Jiazhen Xu; Janice L. Scealy; Andrew T. A. Wood; Tao Zou

doi:10.1016/j.jmva.2025.105473

Generalized score matching

Jiazhen Xu, Janice L. Scealy, Andrew T. A. Wood, Tao Zou

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Abstract

Score matching is an estimation procedure that has been developed for statistical models whose probability density function or probability mass function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modeling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matching-based inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.

Original language	English
Article number	105473
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Multivariate Analysis
Volume	210
DOIs	https://doi.org/10.1016/j.jmva.2025.105473
Publication status	Published - Nov 2025
Externally published	Yes

Bibliographical note

© 2025 The Author(s). Published by Elsevier Inc. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Auto model
Compositional data analysis
Conway–Maxwell–Poisson regression
Fisher divergence
Intractable normalizing constant

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10.1016/j.jmva.2025.105473Licence: CC BY

Publisher version (open access)Final published version, 2.29 MBLicence: CC BY

Cite this

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title = "Generalized score matching",

abstract = "Score matching is an estimation procedure that has been developed for statistical models whose probability density function or probability mass function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modeling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matching-based inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.",

keywords = "Auto model, Compositional data analysis, Conway–Maxwell–Poisson regression, Fisher divergence, Intractable normalizing constant",

author = "Jiazhen Xu and Scealy, \{Janice L.\} and Wood, \{Andrew T. A.\} and Tao Zou",

note = "{\textcopyright} 2025 The Author(s). Published by Elsevier Inc. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2025",

month = nov,

doi = "10.1016/j.jmva.2025.105473",

language = "English",

volume = "210",

pages = "1--20",

journal = "Journal of Multivariate Analysis",

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publisher = "Academic Press Inc.",

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T1 - Generalized score matching

AU - Xu, Jiazhen

AU - Scealy, Janice L.

AU - Wood, Andrew T. A.

AU - Zou, Tao

N1 - © 2025 The Author(s). Published by Elsevier Inc. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2025/11

Y1 - 2025/11

N2 - Score matching is an estimation procedure that has been developed for statistical models whose probability density function or probability mass function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modeling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matching-based inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.

AB - Score matching is an estimation procedure that has been developed for statistical models whose probability density function or probability mass function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modeling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matching-based inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.

KW - Auto model

KW - Compositional data analysis

KW - Conway–Maxwell–Poisson regression

KW - Fisher divergence

KW - Intractable normalizing constant

UR - http://purl.org/au-research/grants/arc/DP220102232

UR - https://www.scopus.com/pages/publications/105010203019

U2 - 10.1016/j.jmva.2025.105473

DO - 10.1016/j.jmva.2025.105473

M3 - Article

SN - 0047-259X

VL - 210

SP - 1

EP - 20

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 105473

ER -

Generalized score matching

Abstract

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Keywords

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