Python中的加权非负最小二乘线性回归 [英] Weighted Non-negative Least Square Linear Regression in python

问题描述

我知道有一个加权OLS求解器和 受约束的OLS求解器.

是否有将两者结合起来的例程?

Is there a routine that combines the two?

推荐答案

您可以通过修改 X 和 y 输入来模拟OLS加权.在OLS中，您为

β 求解

You can simulate OLS weighting by modifying the X and y inputs. In OLS, you solve β for

X ^t Xβ = X ^t y .

X^tX β = X^ty.

在加权OLS中，您可以解决

X ^t X Wβ = X ^t W y .

X^tX W β = X^t W y.

其中 W 是具有非负项的对角矩阵.因此，存在 W ^0.5 ，您可以将其表示为

where W is a diagonal matrix with nonnegative entries. It follows that W^0.5 exists, and you can formulate this as

(X W ^0.5 ) ^t (XW ^0.5 )β =(X W ^0.5 ) ^t (XW ^0.5 )y ，

(X W^0.5)^t(XW^0.5) β = (X W^0.5)^t(XW^0.5) y,

这是具有 X W ^0.5 和 W ^0.5 y 的OLS问题.

which is an OLS problem with X W^0.5 and W^0.5 y.

因此，通过修改输入，可以使用不直接识别权重的非负约束系统.

Consequently, by modifying the inputs, you can use a non-negative constraint system which does not directly recognize weights.

这篇关于Python中的加权非负最小二乘线性回归的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！