For traditional ridge regression, the loss function is

$loss\_function = ||A\mathbf{x}-\mathbf{b}||_2^2 + ||\Gamma\mathbf{x}||_2^2$


Is there a matrix formalism to extend this such that $\Gamma\mathbf{x}$ is instead a non linear function of $\mathbf{x}$? That is

$loss\_function = ||A\mathbf{x}-\mathbf{b}||_2^2 + ||f(r,\mathbf{x})||_2^2$

Where $f(r,\mathbf{x})$ is a non linear function of $\mathbf{x}$ with $r$ being a set of tunable parameters.


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