Model complexity validation for PDF estimation using Gaussian mixtures

A test carried on the training set to validate the model choice and if the selected model is required to give a calibrated prediction, if it predicts the frequencies of the training sample reasonably well, the penalty term adopted is accepted otherwise it is relaxed.

Abstract

Semiparametric density estimation using Gaussian mixtures is a powerful means that can give as good performance as a nonparametric estimator, without its heavy computational burden. A maximum penalised likelihood principle was previously proposed by the authors (1996) for selecting the best approximating mixture for an unknown density function. We propose here a test carried on the training set to validate the model choice. The selected model is required to give a calibrated prediction, i.e. if it predicts the frequencies of the training sample reasonably well, the penalty term adopted is accepted otherwise it is relaxed.