Adaptive Multi-Prior Lasso for High-Dimensional Generalized Linear Models

TL;DR

The paper introduces an adaptive Multi-Prior Lasso method that selectively integrates multiple sources of prior information into high-dimensional generalized linear models, enhancing estimation and prediction accuracy.

Contribution

It proposes a novel adaptive regularization technique that assigns data-driven weights to multiple priors, improving model performance by emphasizing reliable sources.

Findings

The method improves estimation, prediction, and variable selection in simulations.

Application to breast cancer data shows enhanced model performance with prior information.

Theoretical guarantees support the effectiveness of the adaptive weighting scheme.

Abstract

Incorporation of external information into high-dimensional modeling for gene expression data has been shown, both theoretically and empirically, to substantially enhance performance. Such external information, sometimes referred to as prior information or priors, has become increasingly accessible from multiple sources, yet its reliability may vary considerably. Existing approaches often integrate these priors without sufficiently accounting for their quality, which may result in unsatisfactory or even misleading results. To effectively and selectively exploit such priors, we propose adaptive Multi-Prior Lasso, a novel regularization approach that simultaneously identifies reliable prior sources and integrates them to improve model performance. For high-dimensional generalized linear models (GLMs), an adaptive data-driven weight is assigned to each prior, so that more reliable sources are emphasized while less credible ones are downweighted. Theoretical guarantees are established, and the proposed method is shown through extensive simulations to improve estimation, prediction, and variable selection. An application to TCGA breast cancer gene expression data further illustrates the practical value of the proposed method, showing that incorporating prior information from PubMed published studies improves model performance.