Convergence Analysis of function-on-function Polynomial regression model

Naveen Gupta; Sivananthan Sampath

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arXiv · 2512.00549

Convergence Analysis of function-on-function Polynomial regression model

Naveen Gupta·Sivananthan Sampath

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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.

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Naveen Gupta, Sivananthan Sampath. 2025-11-29. Convergence Analysis of function-on-function Polynomial regression model. https://arxiv.org/abs/2512.00549

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