Prediction Errors for Penalized Regressions based on Generalized Approximate Message Passing. (arXiv:2206.12832v2 [stat.ML] UPDATED)

We discuss the prediction accuracy of assumed statistical models in terms of
prediction errors for the generalized linear model and penalized maximum
likelihood methods. We derive the forms of estimators for the prediction
errors: $C_p$ criterion, information criteria, and leave-one-out cross
validation (LOOCV) error, using the generalized approximate message passing
(GAMP) algorithm and replica method. These estimators coincide with each other
when the number of model parameters is sufficiently small; however, there is a
discrepancy between them in particular in …

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