Weighted Non-negative Least Square Linear Regression in python [closed]

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Closed 3 years ago.

I know there is an weighted OLS solver, and a constrained OLS solver.

Is there a routine that combines the two?

Answer 1

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

X^tX β = X^ty.

In Weighted OLS, you solve

X^tX W β = X^t W y.

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,

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

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