Convergence Analysis of function-on-function Polynomial regression model

2025/11/29 by Naveen Gupta, Gupta, Naveen, S. Sivananthan +1
Mathematics · Computer Science · Engineering · #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2512.00549

Abstract

In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regularization under a general smoothness condition without imposing any additional conditions on the index function. We also establish lower bounds for any learning algorithm to explain the optimality of our convergence rates.

Citations

• Optimal Rates for Functional Linear Regression with General Regularization
• Functional linear and single-index models: A unified approach via Gaussian Stein identity
• Regularized divergences between covariance operators and Gaussian\n measures on Hilbert spaces
• Functional Regression
• Minimax Prediction for Functional Linear Regression with Functional Responses in Reproducing Kernel Hilbert Spaces

Related

• Online Regularized Learning Algorithm for Functional Data
• Nonparametric local polynomial regression for functional covariates
• Model selection of polynomial kernel regression
• Statistical inference for function-on-function linear regression
• Convergence rates of vector-valued local polynomial regression