Reviews: On Optimal Generalizability in Parametric Learning

This paper proposes an efficiently computable approximation of leave-one-out cross validation for parametric learning problems, as well as an algorithm for jointly learning the regularization parameters and model parameters. These techniques seem novel and widely applicable. The paper starts out clearly written, though maybe some less space could have been spent on laying the groundwork, leaving more room for the later sections where the notation is quite dense. Can you say anything about the comparsion between ALOOCV and LOOCV evaluated on only a subset of the data points (as you mention in l137-140), both in terms of computation cost and approximation accuracy? Other comments: l75: are you referring to PRESS?