Pytorch 多项式回归

一、一般的多项式回归模型：

$y=\beta_{0}+\beta_{1} x+\beta_{2} x^{2}+\beta_{3} x^{3}+\cdots+\beta_{n} x^{n}+\varepsilon$

$\left[\begin{array}{c}y_{1} \\ y_{2} \\ y_{3} \\ \vdots \\ y_{n}\end{array}\right]=\left[\begin{array}{ccccc}1 & x_{1} & x_{1}^{2} & \ldots & x_{1}^{m} \\ 1 & x_{2} & x_{2}^{2} & \ldots & x_{2}^{m} \\ 1 & x_{3} & x_{3}^{2} & \ldots & x_{3}^{m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & x_{n} & x_{n}^{2} & \ldots & x_{n}^{m}\end{array}\right]\left[\begin{array}{c}\beta_{0} \\ \beta_{1} \\ \beta_{2} \\ \vdots \\ \beta_{m}\end{array}\right]+\left[\begin{array}{c}\varepsilon_{1} \\ \varepsilon_{2} \\ \varepsilon_{3} \\ \vdots \\ \varepsilon_{n}\end{array}\right]$

因此，首先我们需要将输入 [x1, x2, ..., xn] 转变成矩阵 $\left[\begin{array}{ccccc}1 & x_{1} & x_{1}^{2} & \ldots & x_{1}^{m} \\ 1 & x_{2} & x_{2}^{2} & \ldots & x_{2}^{m} \\ 1 & x_{3} & x_{3}^{2} & \ldots & x_{3}^{m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & x_{n} & x_{n}^{2} & \ldots & x_{n}^{m}\end{array}\right]$

原文：https://www.cnblogs.com/qinzihao/p/15177453.html