Fundamental Limits for High-Dimensional Factor Regression Models

High-dimensional factor models enable the analysis of complex interactions in structured data. In this paper, we introduce a generalization of the matrix tensor product framework that incorporates covariate information. We rigorously derive fundamental limits for this model by characterizing the asymptotic mutual information and the associated minimum mean-squared error in the Bayes-optimal setting. By leveraging multilinear approximations, our approach extends prior results to settings involving heteroskedastic noise, asymmetric interactions, and higher-order tensors.

Duke Scholars

Author Galen Reeves Electrical and Computer Engineering