Beyond Global and Individual Models: Tensorized Multitask Regression for Personalized Learning from High-Dimensional Data

Effective modeling of heterogeneous subpopulations presents a significant challenge due to variations in individual characteristics and behaviors. This challenge is exacerbated in high-dimensional settings where each subpopulation may not have enough samples to construct fully individualized models. This paper proposes an approach to address this issue by leveraging concepts from multitask learning (MTL) and low-rank tensor decomposition. The proposed approach aims to enhance personalized modeling by leveraging shared structures across similar tasks (regression models) while accounting for subpopulation-specific variations. We introduce a framework where low-rank decomposition decomposes the collection of task model parameters into a low-rank structure that captures commonalities and variations across tasks and subpopulations. This approach enables efficient learning of personalized models by sharing knowledge across similar tasks while preserving the unique characteristics of each subpopulation. Experimental results on simulated and real-world data sets demonstrate the superior performance of the proposed method compared with several benchmarks, particularly in scenarios with high variability among subpopulations. The proposed framework not only improves prediction accuracy but also enhances interpretability by revealing underlying patterns that contribute to model personalization.

History: Yu Ding served as the senior editor for this article.

Funding: M. Reisi Gahrooei was partially supported by the National Science Foundation [Award 2212878].

Data Ethics & Reproducibility Note: The code capsule is available at https://github.com/elifkonyar/TenMTR.git and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.20245.0097).