关于正则化多项式函数回归

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-03-24 DOI:10.1016/j.jco.2024.101853

Markus Holzleitner , Sergei V. Pereverzyev

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引用次数: 0

摘要

本文全面论述了多项式函数回归，最终建立了一个新颖的有限样本约束。该约束包含多个方面，包括一般平滑条件、容量条件和正则化技术。在此过程中，它还扩展和概括了线性函数回归中的一些发现。我们还提供了数值证据，证明使用高阶多项式项可以提高性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On regularized polynomial functional regression

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity conditions, and regularization techniques. In doing so, it extends and generalizes several findings from the context of linear functional regression as well. We also provide numerical evidence that using higher order polynomial terms can lead to an improved performance.

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.