Partition-Based Functional Ridge Regression for High-Dimensional Data

• URL: http://arxiv.org/abs/2603.11113v1
• Date: Wed, 11 Mar 2026 12:16:22 GMT
• Title: Partition-Based Functional Ridge Regression for High-Dimensional Data
• Abstract summary: This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability.<n>We develop three estimators: the Functional Ridge Estor (FRE), the Functional Ridge Full Model (FRFM), and the Functional Ridge Sub-Model (FRSM)
• Score: 0.45880283710344055
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability in high-dimensional functional linear models. The coefficient function vector \( \boldsymbolβ(s) \) is decomposed into two components, \( \boldsymbolβ_1(s) \) and \( \boldsymbolβ_2(s) \), representing dominant and weaker functional effects. This partition enables differential ridge penalization across functional blocks, so that important signals are preserved while less informative components are more strongly shrunk. The resulting approach improves numerical stability and enhances interpretability without relying on explicit variable selection. We develop three estimators: the Functional Ridge Estimator (FRE), the Functional Ridge Full Model (FRFM), and the Functional Ridge Sub-Model (FRSM). Under standard regularity conditions, we establish consistency and asymptotic normality for all estimators. Simulation results reveal a clear bias--variance trade-off where FRSM performs best in small samples through strong variance reduction, whereas FRFM achieves superior accuracy in moderate to large samples by retaining informative functional structure through adaptive penalization. An empirical application to Canadian weather data further demonstrates improved predictive performance, reduced variance inflation, and clearer identification of influential functional effects. Overall, partition-based ridge regularization provides a practical and theoretically grounded method for high-dimensional functional regression.

Related papers

• Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimality [0.962543698736491]
  Functional data analysis is an important statistical field that treats data as random functions.<n>In practice, the random functions are often not fully observed but instead measured at discrete times.<n>We propose a novel approach, referred to as pooling ridge estimation, which combines the advantages of pooling strategy and RKHS-based method.
  arXiv  Detail & Related papers  (2026-08-26T07:36:39Z)
• Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage [65.51149575007149]
  We present Fun-DDPS, a generative framework that combines function-space diffusion models with differentiable neural operator surrogates for both forward and inverse modeling.<n>Fun-DDPS produces physically consistent realizations free from the high-frequency artifacts observed in joint-state baselines.
  arXiv  Detail & Related papers  (2026-02-12T18:58:12Z)
• FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression [15.00767095565706]
  Functional Attention with a Mixture-of-Experts (FAME) is an end-to-end, fully data-driven framework for function-on-function regression.<n>FAME forms continuous attention by coupling a neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity.<n>Experiments on synthetic and real-world functional-regression benchmarks show that FAME achieves state-of-the-art accuracy, strong robustness to arbitrarily sampled discrete observations.
  arXiv  Detail & Related papers  (2025-10-01T07:53:55Z)
• Identifiable Convex-Concave Regression via Sub-gradient Regularised Least Squares [1.9580473532948397]
  We propose a novel nonparametric regression method that models complex input-relationships as the sum of convex and concave components.<n>The method-ICCNLS-decomposes sub-constrained shape-constrained additive decomposition.
  arXiv  Detail & Related papers  (2025-06-22T15:53:12Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• Optimal Activation Functions for the Random Features Regression Model [7.381113319198103]
  We identify in closed-form the family of Activation Functions (AFs) that minimize a combination of the test error and sensitivity of the Random Features Regression model. We show how using optimal AFs impacts well-established properties of the RFR model.
  arXiv  Detail & Related papers  (2022-05-31T16:41:42Z)
• On the Double Descent of Random Features Models Trained with SGD [78.0918823643911]
  We study properties of random features (RF) regression in high dimensions optimized by gradient descent (SGD) We derive precise non-asymptotic error bounds of RF regression under both constant and adaptive step-size SGD setting. We observe the double descent phenomenon both theoretically and empirically.
  arXiv  Detail & Related papers  (2021-10-13T17:47:39Z)
• Non-parametric Models for Non-negative Functions [48.7576911714538]
  We provide the first model for non-negative functions from the same good linear models. We prove that it admits a representer theorem and provide an efficient dual formulation for convex problems.
  arXiv  Detail & Related papers  (2020-07-08T07:17:28Z)
• Piecewise Linear Regression via a Difference of Convex Functions [50.89452535187813]
  We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. We empirically validate the method, showing it to be practically implementable, and to have comparable performance to existing regression/classification methods on real-world datasets.
  arXiv  Detail & Related papers  (2020-07-05T18:58:47Z)
• Exponentially Weighted l_2 Regularization Strategy in Constructing Reinforced Second-order Fuzzy Rule-based Model [72.57056258027336]
  In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules. We introduce an exponential weight approach inspired by the weight function theory encountered in harmonic analysis.
  arXiv  Detail & Related papers  (2020-07-02T15:42:15Z)
• Multivariate Functional Regression via Nested Reduced-Rank Regularization [2.730097437607271]
  We propose a nested reduced-rank regression (NRRR) approach in fitting regression model with multivariate functional responses and predictors. We show through non-asymptotic analysis that NRRR can achieve at least a comparable error rate to that of the reduced-rank regression. We apply NRRR in an electricity demand problem, to relate the trajectories of the daily electricity consumption with those of the daily temperatures.
  arXiv  Detail & Related papers  (2020-03-10T14:58:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.