Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age

TL;DR

This paper introduces new optimization-based variable selection methods for complex biomedical data, demonstrating significant improvements in accuracy and speed across various models and data types, with a focus on clinical applications.

Contribution

It proposes a general, optimization-based variable selection framework applicable to diverse data types and models, outperforming existing methods in accuracy and computational efficiency.

Findings

Outperforms state-of-the-art methods in accuracy.

Achieves several orders of magnitude faster computation.

Applicable to various data types including functional and graph data.

Abstract

Many problems within personalized medicine and digital health rely on the analysis of continuous-time functional biomarkers and other complex data structures emerging from high-resolution patient monitoring. In this context, this work proposes new optimization-based variable selection methods for multivariate, functional, and even more general outcomes in metrics spaces based on best-subset selection. Our framework applies to several types of regression models, including linear, quantile, or non parametric additive models, and to a broad range of random responses, such as univariate, multivariate Euclidean data, functional, and even random graphs. Our analysis demonstrates that our proposed methodology outperforms state-of-the-art methods in accuracy and, especially, in speed-achieving several orders of magnitude improvement over competitors across various type of statistical responses as the case of mathematical functions. While our framework is general and is not designed for a specific regression and scientific problem, the article is self-contained and focuses on biomedical applications. In the clinical areas, serves as a valuable resource for professionals in biostatistics, statistics, and artificial intelligence interested in variable selection problem in this new technological AI-era.