An effect of selection of a smoothing parameter on the performance of likelihood ratio models for solving classification task

Abstract

The usage of likelihood ratio models is common in both the classification and comparison problem designed especially for evidence evaluation dedicated to physicochemical data. The presence of performance assessment method in the form of empirical cross entropy for such models is considered as an additional advantage. The combination of these two approaches provides the evidence evaluation along with probabilistic interpretation. Likelihood ratio models for physicochemical data are usually constructed with the use of kernel density estimation procedure that exempts from the need for parametric distribution choice. The use of nonparametric approach in the form of kernel density estimation procedure requires the choice of the value of smoothing parameter that targets the proper fitting of probability density estimate to the analysed data. The choice of the value of this parameter allows interference in the model and thus permits influencing its results.In this work, several approaches to the choice of the amount of smoothing are considered for uni- and multivariate classification likelihood ratio models. The impact of these approaches on the results of likelihood ratio models is considered in the context of correct classification rates and parameters derived from empirical cross entropy. The classification problems involved three datasets that can be of scientist's interest, namely the problems include determination of olive oil geographical origin, determination of wine brand designation and the usage category of glass samples.The application of different approaches to smoothing for considered likelihood ratio models shows the possibility of enhancing classification results. A trade-off problem between classification rates and empirical cross entropy parameters is emphasised. The method of constructing multivariate likelihood ratio models based on information-theoretical approach and their superiority over univariate counterparts is highlighted.