Count Data Modeling and Classification Using Statistical Hierarchical Approaches and Multi-topic Models

In this thesis, we propose and develop various statistical models to enhance and improve the efficiency of statistical modeling of count data in various applications. The major emphasis of the work is focused on developing hierarchical models. Various schemes of hierarchical structures are thus developed and analyzed in this work ranging from purely static hierarchies to dynamic models. The second part of the work concerns itself with the development of multitopic statistical models. It has been shown that these models provide more realistic modeling characteristics in comparison to mono topic models. We proceed with developing several multitopic models and we analyze their performance against benchmark models. We show that our proposed models in the majority of instances improve the modeling efficiency in comparison to some benchmark models, without drastically increasing the computational demands. In the last part of the work, we extend our proposed multitopic models to include online learning capability and again we show the relative superiority of our models in comparison to the benchmark models. Various real world applications such as object recognition, scene classification, text classification and action recognition, are used for analyzing the strengths and weaknesses of our proposed models

A variational Bayes model for count data learning and classification

Several machine learning and knowledge discovery approaches have been proposed for count data modeling and classification. In particular, latent Dirichlet allocation (LDA) (Blei et al., 2003a) has received a lot of attention and has been shown to be extremely useful in several applications. Although the LDA is generally accepted to be one of the most powerful generative models, it is based on the Dirichlet assumption which has some drawbacks as we shall see in this paper. Thus, our goal is to enhance the LDA by considering the generalized Dirichlet distribution as a prior. The resulting generative model is named latent generalized Dirichlet allocation (LGDA) to maintain consistency with the original model. The LGDA is learned using variational Bayes which provides computationally tractable posterior distributions over the model׳s hidden variables and its parameters. To evaluate the practicality and merits of our approach, we consider two challenging applications namely text classification and visual scene categorization

Radiomic Texture Analysis Mapping Predicts Areas of True Functional MRI Activity.

Individual analysis of functional Magnetic Resonance Imaging (fMRI) scans requires user-adjustment of the statistical threshold in order to maximize true functional activity and eliminate false positives. In this study, we propose a novel technique that uses radiomic texture analysis (TA) features associated with heterogeneity to predict areas of true functional activity. Scans of 15 right-handed healthy volunteers were analyzed using SPM8. The resulting functional maps were thresholded to optimize visualization of language areas, resulting in 116 regions of interests (ROIs). A board-certified neuroradiologist classified different ROIs into Expected (E) and Non-Expected (NE) based on their anatomical locations. TA was performed using the mean Echo-Planner Imaging (EPI) volume, and 20 rotation-invariant texture features were obtained for each ROI. Using forward stepwise logistic regression, we built a predictive model that discriminated between E and NE areas of functional activity, with a cross-validation AUC and success rate of 79.84% and 80.19% respectively (specificity/sensitivity of 78.34%/82.61%). This study found that radiomic TA of fMRI scans may allow for determination of areas of true functional activity, and thus eliminate clinician bias