machine learning

Ridge regression is am modified version of linear regression that penelizes the coefficients for being large. It accomplishes this by adding a so-called L2 penalty term to the loss function (e.g. mean squared error): L()=n1i=1n(f^(xi)yi)2+i=1di2 where >0 is a hyperparameter that must be tuned by the user. An appropriate choice of can often help with learning datasets where the input features are highly correlated or it can help with an overfitting problem. (a) Write each part of L() in matrix-vector form where f^ is a LBF expansion regression model. Define each matrix an vector separately by writing their elements with subscripts, and state their dimensions. (b) Solve the following optimization problem by hand for the loss function L above: minRd+1L()