Can we use LASSO for non-linear regression?
By Emma Terry •
I am studying machine learning and would like to apply LASSO. I wonder if it is possible to apply LASSO on a non-linear regression model. I search on the internet but all literature focus on linear setting. If we can apply LASSO on non-linear regression model, are there any relevant references I can follow?
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$\begingroup$Why wouldn't you be able to?
The essential part of LASSO is just adding an L$^1$ norm of the coefficients to the main term,
$$f(x,y,\beta) + \lambda\|\beta\|_1.$$
There's no reason $f$ has to be a linear model. It may not have an analytic solution, or be convex, but there's nothing stopping you from trying it out, and it should still induce sparsity, contingent on a large enough lambda.
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