# FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions

arXiv: https://arxiv.org/abs/2303.14801 · HTML: https://mlsanity.com/paper/2303.14801/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 92 references that are in the map.
- First posted on arXiv 26 Mar 2023.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Unified Approach to Error Bounds for Structured Convex Optimization Problems](https://mlsanity.com/paper/1512.03518/) (2015)
- [A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems](https://mlsanity.com/paper/1607.05428/) (2016)
- [In Defense of the Indefensible: A Very Naive Approach to High-Dimensional Inference](https://mlsanity.com/paper/1705.05543/) (2017)
- [Nonlinear Sufficient Dimension Reduction for Distribution-on-Distribution Regression](https://mlsanity.com/paper/2207.04613/) (2022)
- [Primal-Dual Rates and Certificates](https://mlsanity.com/paper/1602.05205/) (2016)
- [On function-on-function regression: Partial least squares approach](https://mlsanity.com/paper/1912.06995/) (2019)
- [Smooth Lasso Estimator for the Function-on-Function Linear Regression Model](https://mlsanity.com/paper/2007.00529/) (2020)
- [An Efficient Semi-smooth Newton Augmented Lagrangian Method for Elastic Net](https://mlsanity.com/paper/2006.03970/) (2020)

## Built on by (most cited first, 4 of 4)

- [Forging Time Series with Language: A Large Language Model Approach to Synthetic Data Generation](https://mlsanity.com/paper/2505.17103/) (2025)
- [A new computationally efficient algorithm to solve Feature Selection for Functional Data Classification in high-dimensional spaces](https://mlsanity.com/paper/2401.05765/) (2024)
- [Functional Graph Convolutional Networks: A unified multi-task and multi-modal learning framework to facilitate health and social-care insights](https://mlsanity.com/paper/2403.10158/) (2024)
- [A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomes](https://mlsanity.com/paper/2602.11118/) (2026)

## Abstract (arXiv)

Functional regression analysis is an established tool for many contemporary scientific applications. Regression problems involving large and complex data sets are ubiquitous, and feature selection is crucial for avoiding overfitting and achieving accurate predictions. We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse high dimensional function-on-function regression problem, and we show how to extend it to the scalar-on-function framework. Our method, called FAStEN, combines functional data, optimization, and machine learning techniques to perform feature selection and parameter estimation simultaneously. We exploit the properties of Functional Principal Components and the sparsity inherent to the Dual Augmented Lagrangian problem to significantly reduce computational cost, and we introduce an adaptive scheme to improve selection accuracy. In addition, we derive asymptotic oracle properties, which guarantee estimation and selection consistency for the proposed FAStEN estimator. Through an extensive simulation study, we benchmark our approach to the best existing competitors and demonstrate a massive gain in terms of CPU time and selection performance, without sacrificing the quality of the coefficients' estimation. The theoretical derivations and the simulation study provide a strong motivation for our approach. Finally, we present an application to brain fMRI data from the AOMIC PIOP1 study. Complete FAStEN code is provided at https://github.com/IBM/funGCN.