Inference in high-dimensional logistic regression under tensor network dependence

2026-03-20

AI Summary

This study addresses the challenge of conducting valid statistical inference in high-dimensional logistic regression when observations exhibit higher-order tensor dependence structures induced by a Markov random field. Existing methods are limited either to pairwise interactions or to estimation consistency without inferential guarantees. To overcome these limitations, this work proposes a two-stage inference framework: first, a regularized maximum pseudo-likelihood estimator is constructed, and then a bias-corrected estimator is derived to achieve asymptotic normality, thereby enabling confidence interval construction and hypothesis testing. This approach represents the first method capable of delivering valid inference under high-dimensional tensor network dependence. Theoretical analysis establishes both consistency and asymptotic normality of the proposed estimator, and numerical experiments demonstrate its strong finite-sample performance.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise interaction models such as the Ising model, we consider a framework to accommodate more general tensor structures that capture higher-order dependencies. We develop a two-step procedure for low-dimensional linear and quadratic functionals. The first step constructs a regularized maximum pseudolikelihood estimator, for which we establish consistency under high-dimensional features. However, as in other classical high-dimensional regression problems, this estimator is biased and cannot be directly used for valid statistical inference. The second step introduces a bias-correction that yields an asymptotically normal estimator from which one can construct confidence intervals and test hypotheses. Our results move beyond the existing literature, where only estimation guarantees were available or only for pairwise interaction models. We complement our theoretical analysis with simulation studies confirming the effectiveness of the proposed method.

Problem

• high-dimensional logistic regression
• tensor network dependence
• statistical inference
• Markov random field
• higher-order dependencies

Innovation

• tensor network dependence
• high-dimensional logistic regression
• bias correction
• asymptotic normality
• Markov random field