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The present section revisits some usual regression techniques, widely considered in the next sections. In general—at least in the most basic setting—regression assumes that the quantity of interest (output) of our learning process, y, depends on the inputs \(x_k\) , \(k=1, \dots , \mathtt P\) through a polynomial law [1, 2]. The simplest choice is to assume that this dependence is linear with respect to the features \(x_i\) , i.e. \(y(\textbf{x}) = \beta _0 + \beta _1 x_1 + \cdots + \beta _\mathtt P x_{\mathtt P}, \) where the \(\mathtt P+1\) coefficients \(\beta _k\) are chosen to provide the best fit to the available data.

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Regression: Basics

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Francisco Chinesta,
  • Elías Cueto,
  • Victor Champaney,
  • Chady Ghnatios,
  • Amine Ammar,
  • Nicolas Hascoët,
  • David González,
  • Icíar Alfaro,
  • Daniele Di Lorenzo,
  • Angelo Pasquale,
  • Dominique Baillargeat

摘要

The present section revisits some usual regression techniques, widely considered in the next sections. In general—at least in the most basic setting—regression assumes that the quantity of interest (output) of our learning process, y, depends on the inputs \(x_k\) , \(k=1, \dots , \mathtt P\) through a polynomial law [1, 2]. The simplest choice is to assume that this dependence is linear with respect to the features \(x_i\) , i.e. \(y(\textbf{x}) = \beta _0 + \beta _1 x_1 + \cdots + \beta _\mathtt P x_{\mathtt P}, \) where the \(\mathtt P+1\) coefficients \(\beta _k\) are chosen to provide the best fit to the available data.