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In sparse regression modeling via regularization such as the lasso, it isimportant to select appropriate values of tuning parameters includingregularization parameters. The choice of tuning parameters can be viewed as amodel selection and evaluation problem. Mallows' $C_p$ type criteria may beused as a tuning parameter selection tool in lasso-type regularization methods,for which the concept of degrees of freedom plays a key role. In the presentpaper, we propose an efficient algorithm that computes the degrees of freedomby extending the generalized path seeking algorithm. Our procedure allows us toconstruct model selection criteria for evaluating models estimated byregularization with a wide variety of convex and non-convex penalties. MonteCarlo simulations demonstrate that our methodology performs well in varioussituations. A real data example is also given to illustrate our procedure.

Efficient algorithm to select tuning parameters in sparse regression modeling with regularization