Selecting an optimal set of parameters using an Akaike like criterion

The selection of an optimal set of parameters from a larger one is a well known identification problem in classification or clustering algorithms. The Akaike criterion has been developed to estimate the (Markov) order in auto regressive models. This criterion, which by itself extends the maximum likelihood method to test composite hypotheses, is replaced by the Modified Information Criterion (MIC). This criterion balances bias caused insufficient modeling and the additional variance caused by superfluous parameters. Using this criterion the probability of selecting a model with too many parameters can, without the need of extensively evaluating the bias/variance syndrome, a priori be chosen.