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Consider one dependent variable 'Y' and 10 independent variables or features- X1, X2, X3, ... X10.

I want to create a non-linear polynomial regression model such that-

Y ~ a1.X1^b1 + a2.X2^b2 + .... + a10.X10^b10

I was wondering is there any algorithm that will determine best possible values for powers of independent variables that is values of b1, b2, ... b10 from data.

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If all you care about is the quality of predictions (as opposed to explanatory power), skip linear models altogether and use gradient boosted trees instead. Gradient boosting can generally learn polynomial splines with ease, and you don't have to manually make a bunch of polynomial predictors yourself.

By the way, gradient boosting is implemented in Python's scikit-learn library, R's caret library, and Java/Scala's Weka library.

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