A hierarchical Naïve Bayes Model for handling sample heterogeneity in classification problems: an application to tissue microarrays

BACKGROUND: Uncertainty often affects molecular biology experiments and data for different reasons. Heterogeneity of gene or protein expression within the same tumor tissue is an example of biological uncertainty which should be taken into account when molecular markers are used in decision making. Tissue Microarray (TMA) experiments allow for large scale profiling of tissue biopsies, investigating protein patterns characterizing specific disease states. TMA studies deal with multiple sampling of the same patient, and therefore with multiple measurements of same protein target, to account for possible biological heterogeneity. The aim of this paper is to provide and validate a classification model taking into consideration the uncertainty associated with measuring replicate samples. RESULTS: We propose an extension of the well-known Naïve Bayes classifier, which accounts for biological heterogeneity in a probabilistic framework, relying on Bayesian hierarchical models. The model, which can be efficiently learned from the training dataset, exploits a closed-form of classification equation, thus providing no additional computational cost with respect to the standard Naïve Bayes classifier. We validated the approach on several simulated datasets comparing its performances with the Naïve Bayes classifier. Moreover, we demonstrated that explicitly dealing with heterogeneity can improve classification accuracy on a TMA prostate cancer dataset. CONCLUSION: The proposed Hierarchical Naïve Bayes classifier can be conveniently applied in problems where within sample heterogeneity must be taken into account, such as TMA experiments and biological contexts where several measurements (replicates) are available for the same biological sample. The performance of the new approach is better than the standard Naïve Bayes model, in particular when the within sample heterogeneity is different in the different classes

Hierarchical Naive Bayes Classifiers for uncertain data ⋆

Abstract. In experimental sciences many classification problems deal with variables with replicated measurements. In this case the replicates are usually summarized by their mean or median. However, such choice does not consider the information about the uncertainty associated with the measurements, thus potentially leading to over or underestimate the probability associated to each classification. In this paper we present an extension of the Naive Bayes classifier which, thanks to a Bayesian hierarchical model, is able to properly deal with replicates and uncertain measurements. We will show how to perform classification and learning with continuous and discrete variables with replicated measurements and we will describe the advantages of the proposed model over the standard Naive Bayes algorithm with a simulation study.