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

arXiv: https://arxiv.org/abs/2501.06868 · HTML: https://mlsanity.com/paper/2501.06868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 102 references that are in the map.
- First posted on arXiv 12 Jan 2025.

## Builds on (most cited first, 30 of 36)

- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Wasserstein Regression](https://mlsanity.com/paper/2006.09660/) (2020)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [False Discoveries Occur Early on the Lasso Path](https://mlsanity.com/paper/1511.01957/) (2015)
- [Sparse Regression: Scalable algorithms and empirical performance](https://mlsanity.com/paper/1902.06547/) (2019)
- [Sparse Classification: a scalable discrete optimization perspective](https://mlsanity.com/paper/1710.01352/) (2017)
- [Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso](https://mlsanity.com/paper/1707.08692/) (2017)
- [Network Regression with Graph Laplacians](https://mlsanity.com/paper/2109.02981/) (2021)
- [Gene Hunting with Knockoffs for Hidden Markov Models](https://mlsanity.com/paper/1706.04677/) (2017)
- [Functional Models for Time-Varying Random Objects](https://mlsanity.com/paper/1907.10829/) (2019)
- [A new perspective on low-rank optimization](https://mlsanity.com/paper/2105.05947/) (2021)
- [Single Index Fr'echet Regression](https://mlsanity.com/paper/2108.05437/) (2021)
- [Wasserstein F-tests and Confidence Bands for the Fr`echet Regression of Density Response Curves](https://mlsanity.com/paper/1910.13418/) (2019)
- [Conditional Wasserstein Barycenters and Interpolation/Extrapolation of Distributions](https://mlsanity.com/paper/2107.09218/) (2021)
- [Nonlinear Sufficient Dimension Reduction for Distribution-on-Distribution Regression](https://mlsanity.com/paper/2207.04613/) (2022)
- [Sliced Wasserstein Regression](https://mlsanity.com/paper/2306.10601/) (2023)
- [Nonlinear global Fr'echet regression for random objects via weak conditional expectation](https://mlsanity.com/paper/2310.07817/) (2023)
- [Modeling Time-Varying Random Objects and Dynamic Networks](https://mlsanity.com/paper/2104.04628/) (2021)
- [Medoid splits for efficient random forests in metric spaces](https://mlsanity.com/paper/2306.17031/) (2023)
- [Multilevel functional distributional models with application to continuous glucose monitoring in diabetes clinical trials](https://mlsanity.com/paper/2403.10514/) (2024)
- [Distributional data analysis via quantile functions and its application to modelling digital biomarkers of gait in Alzheimer's Disease](https://mlsanity.com/paper/2102.10783/) (2021)
- [Universally Consistent Online Learning with Arbitrarily Dependent Responses](https://mlsanity.com/paper/2203.06046/) (2022)
- [Multivariate Scalar on Multidimensional Distribution Regression](https://mlsanity.com/paper/2310.10494/) (2023)
- [Fr'echet Covariance and MANOVA Tests for Random Objects in Multiple Metric Spaces](https://mlsanity.com/paper/2306.12066/) (2023)
- [Geodesic Mixed Effects Models for Repeatedly Observed/Longitudinal Random Objects](https://mlsanity.com/paper/2307.05726/) (2023)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)

## Abstract (arXiv)

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.