# Coefficient Shape Alignment in Multiple Functional Linear Regression

arXiv: https://arxiv.org/abs/2312.01925 · HTML: https://mlsanity.com/paper/2312.01925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 4 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [Fast and Provable ADMM for Learning with Generative Priors](https://mlsanity.com/paper/1907.03343/) (2019)
- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)
- [Matrix-Variate Regressions and Envelope Models](https://mlsanity.com/paper/1605.01485/) (2016)
- [Functional time series prediction under partial observation of the future curve](https://mlsanity.com/paper/1906.00281/) (2019)
- [Preconditioned ADMM with nonlinear operator constraint](https://mlsanity.com/paper/1511.00425/) (2015)
- [Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction](https://mlsanity.com/paper/2112.09746/) (2021)
- [Multivariate functional group sparse regression: functional predictor selection](https://mlsanity.com/paper/2107.02146/) (2021)

## Abstract (arXiv)

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this paper, a novel grouped multiple functional regression model with a new regularization approach termed it ``coefficient shape alignment" is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing differences in the shape of the coefficients. We establish conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data.