Fused Multinomial Logistic Regression Utilizing Summary-Level External Machine-learning Information
arXiv:2604.03939v1 Announce Type: cross Abstract: In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric machine-learning predictions. Although summary-level external information has been studied in the data integration literature, there is limited methodology for leveraging external nonparametric machine-learning predictions to improve statistical inference in the primary study. We propose a general empirical-likelihood framework that incorporates external predictions through moment constraints. An advantage of nonparametric machine-learning prediction is that it induces a rich class of valid moment restrictions that rema
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Abstract:In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric machine-learning predictions. Although summary-level external information has been studied in the data integration literature, there is limited methodology for leveraging external nonparametric machine-learning predictions to improve statistical inference in the primary study. We propose a general empirical-likelihood framework that incorporates external predictions through moment constraints. An advantage of nonparametric machine-learning prediction is that it induces a rich class of valid moment restrictions that remain robust to covariate shift under a mild overlap condition without requiring explicit density-ratio modeling. We focus on multinomial logistic regression as the primary model and address common data-quality issues in external sources, including coarsened outcomes, partially observed covariates, covariate shift, and heterogeneity in generating mechanisms known as concept shift. We establish large-sample properties of the resulting fused estimator, including consistency and asymptotic normality under regularity conditions. Moreover, we provide mild sufficient conditions under which incorporating external predictions delivers a strict efficiency gain relative to the primary-only estimator. Simulation studies and an application to the National Health and Nutrition Examination Survey on multiclass blood-pressure classification.
Comments: 24 pages, 2 figures
Subjects:
Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)
MSC classes: 62F12, 62H30, 62D20, 68T05
Cite as: arXiv:2604.03939 [stat.ME]
(or arXiv:2604.03939v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2604.03939
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Chi-Shian Dai [view email] [v1] Sun, 5 Apr 2026 02:37:23 UTC (76 KB)
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