Ryan Burn

Ryan Burn

I develop an algorithm to produce the piecewise quadratic that computes leave-one-out cross-validation for the lasso as a function of its hyperparameter. The algorithm can be used to find exact hyperparameters that optimize leave-one-out cross-validation either globally or locally, and its practicality is demonstrated on real-world data sets. I also show how the algorithm can be modified to compute approximate leave-one-out cross-validation, making it suitable for larger data sets.

Ryan Burn

For a large class of regularized models, leave-one-out cross-validation can be efficiently estimated with an approximate leave-one-out formula (ALO). We consider the problem of adjusting hyperparameters so as to optimize ALO. We derive efficient formulas to compute the gradient and hessian of ALO and show how to apply a second-order optimizer to find hyperparameters. We demonstrate the usefulness of the proposed approach by finding hyperparameters for regularized logistic regression and ridge regression on various real-world data sets.