Fused Multinomial Logistic Regression Utilizing Summary-Level External Machine-learning Information

• URL: http://arxiv.org/abs/2604.03939v1
• Date: Sun, 05 Apr 2026 02:37:23 GMT
• Title: Fused Multinomial Logistic Regression Utilizing Summary-Level External Machine-learning Information
• Abstract summary: We propose a general empirical-likelihood framework that incorporates external predictions through moment constraints.<n>We focus on multinomial logistic regression as the primary model and address common data-quality issues in external sources.<n>We provide mild sufficient conditions under which incorporating external predictions delivers a strict efficiency gain relative to the primary-only estimator.
• Score: 3.2819213801147282
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Joint Model and Data Sparsification via the Marginal Likelihood [53.29070892356214]
  We propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification.<n>This symmetric pruning of model and data offers a natural extension that preserves conjugacy.<n> Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
  arXiv  Detail & Related papers  (2026-05-28T13:26:53Z)
• STAR : Bridging Statistical and Agentic Reasoning for Large Model Performance Prediction [78.0692157478247]
  We propose STAR, a framework that bridges data-driven STatistical expectations with knowledge-driven Agentic Reasoning.<n>We show that STAR consistently outperforms all baselines on both score-based and rank-based metrics.
  arXiv  Detail & Related papers  (2026-02-12T16:30:07Z)
• Fast Rates for Nonstationary Weighted Risk Minimization [6.015898117103068]
  This article studies its out-of-sample prediction error under nonstationarity.<n>We provide a general decomposition of the excess risk into a learning term and an error term associated with distribution drift.
  arXiv  Detail & Related papers  (2026-02-05T15:10:07Z)
• Machine-Learning-Assisted Comparison of Regression Functions [6.536054952579518]
  We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference.<n>We propose a new notion of kernel-based conditional mean dependence that provides a new characterization of the null hypothesis of equal regression functions.<n>We develop two novel tests that leverage modern machine learning methods for flexible estimation.
  arXiv  Detail & Related papers  (2025-10-28T17:59:15Z)
• Multiply Robust Conformal Risk Control with Coarsened Data [0.0]
  Conformal Prediction (CP) has recently received a tremendous amount of interest.<n>In this paper, we consider the general problem of obtaining distribution-free valid prediction regions for an outcome given coarsened data.<n>Our principled use of semiparametric theory has the key advantage of facilitating flexible machine learning methods.
  arXiv  Detail & Related papers  (2025-08-21T12:14:44Z)
• Robust Molecular Property Prediction via Densifying Scarce Labeled Data [53.24886143129006]
  In drug discovery, compounds most critical for advancing research often lie beyond the training set.<n>We propose a novel bilevel optimization approach that leverages unlabeled data to interpolate between in-distribution (ID) and out-of-distribution (OOD) data.
  arXiv  Detail & Related papers  (2025-06-13T15:27:40Z)
• Modelling higher education dropouts using sparse and interpretable post-clustering logistic regression [0.8437187555622164]
  Higher education dropout constitutes a critical challenge for tertiary education systems worldwide.<n>The model introduced in this paper is a specialized form of logistic regression, specifically adapted to the context of university dropout analysis.
  arXiv  Detail & Related papers  (2025-05-12T14:05:23Z)
• In-Context Linear Regression Demystified: Training Dynamics and Mechanistic Interpretability of Multi-Head Softmax Attention [52.159541540613915]
  We study how multi-head softmax attention models are trained to perform in-context learning on linear data.<n>Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution.
  arXiv  Detail & Related papers  (2025-03-17T02:00:49Z)
• Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
  This thesis is a series of independent contributions to statistics unified by a model-free perspective.<n>The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning.<n>The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
  arXiv  Detail & Related papers  (2025-02-11T19:24:09Z)
• Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling [53.7117640028211]
  We present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. We incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space. A spectral graph-theoretic method is devised to estimate the number of potential novel classes.
  arXiv  Detail & Related papers  (2024-03-02T00:56:05Z)
• Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction [7.093830786026851]
  This paper proposes a novel clustered reduced-rank learning framework. It imposes two joint matrix regularizations to automatically group the features in constructing predictive factors. It is more interpretable than low-rank modeling and relaxes the stringent sparsity assumption in variable selection.
  arXiv  Detail & Related papers  (2021-12-17T20:11:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.