In order to obtain better generalization performance in supervised learning, model parameters should be determined appropriately, i.e., they should be determined so that the generalization error is minimized. However, since the generalization error is inaccessible in practice, the model parameters are usually determined so that an estimator of the generalization error is minimized. The regularized subspace information criterion (RSIC) is such a generalization error estimator for model selection. RSIC includes an additional regularization parameter and it should be determined appropriately for better model selection. A meta-criterion for determining the regularization parameter has also been proposed and shown to be useful in practice. In this paper, we show that there are several drawbacks in the existing meta-criterion and give an alternative meta-criterion that can solve the problems. Through simulations, we show that the use of the new meta-criterion further improves the model selection performance.

In order to obtain better learning results in supervised learning, it is important to choose model parameters appropriately. Model selection is usually carried out by preparing a finite set of model candidates, estimating a generalization error for each candidate, and choosing the best one from the candidates. If the number of candidates is increased in this procedure, the optimization quality may be improved. However, this in turn increases the computational cost. In this paper, we focus on a generalization error estimator called the regularized subspace information criterion and derive an analytic form of the optimal model parameter over a set of infinitely many model candidates. This allows us to maximize the optimization quality while the computational cost is kept moderate.

For obtaining a higher level of generalization capability in supervised learning, model parameters should be optimized, i.e., they should be determined in such a way that the generalization error is minimized. However, since the generalization error is inaccessible in practice, model parameters are usually determined in such a way that an estimate of the generalization error is minimized. A standard procedure for model parameter optimization is to first prepare a finite set of candidates of model parameter values, estimate the generalization error for each candidate, and then choose the best one from the candidates. If the number of candidates is increased in this procedure, the optimization quality may be improved. However, this in turn increases the computational cost. In this paper, we give methods for analytically finding the optimal model parameter value from a set of infinitely many candidates. This maximally enhances the optimization quality while the computational cost is kept reasonable.