This thesis is focused on sentiment analysis of unstructured text and its practical application on the real data downloaded from website Yelp.com The objectives of the theoretical part of this thesis is to sum up the information related to history, methods and possible applications of sentiment analysis. A reader is acquainted with important terms and processes of sentiment analysis. Theoretical part is focused on Naive Bayes classifier, that will be used in practical part of this thesis. In practical part there is detailed description of data set, construction and testing of model. At the end there are presented pros and cons of the chosen model and described some possibilities of its usage.

Nonparametric Bayesian inference has widespread applications in statistics and machine learning. In this thesis, we examine the most popular priors used in Bayesian non-parametric inference. The Dirichlet process and its extensions are priors on an infinite-dimensional space. Originally introduced by Ferguson (1983), its conjugacy property allows a tractable posterior inference which has lately given rise to a significant developments in applications related to machine learning. Another yet widespread prior used in nonparametric Bayesian inference is the Beta process and its extensions. It has originally been introduced by Hjort (1990) for applications in survival analysis. It is a prior on the space of cumulative hazard functions and it has recently been widely used as a prior on an infinite dimensional space for latent feature models. Our contribution in this thesis is to collect many diverse groups of nonparametric Bayesian tools and explore algorithms to sample from them. We also explore machinery behind the theory to apply and expose some distinguished features of these procedures. These tools can be used by practitioners in many applications.

This paper studies symbolic dynamical systems {0, 1}G, where G is a countably infinite group, {0, 1}G has the product topology, and G acts on {0, 1}G by shifts. It is proven that for every countably infinite group G the union of the minimal free subflows of {0, 1}G is dense. In fact, a stronger result is obtained which states that if G is a countably infinite group and U is an open subset of {0, 1}G, then there is a collection of size continuum consisting of pairwise disjoint minimal free subflows intersecting U.

<div>Dynamic treatment regimes (DTRs) are often considered for the medical care of chronic diseases and complex conditions. They consist of multistage treatment decisions, each based on the individual's health information and their treatment and response history. In this dissertation, we consider this setting with binary responses (i.e., either respond favorably or unfavorably to a treatment) and highlight one type of heterogeneity, specifically the existence of subgroups of patients who respond favorably to only a distinct subset of study treatments. </div><div>Currently, most works employ model-free approaches to find the optimal DTR. In contrast, we propose a model-based approach, which focuses more on describing heterogeneity in treatment responses. We first consider the scenario when baseline covariates are not included. A mixture of mixed logit models is proposed along with an EM alogorithm to estimate these subgroup proportions and the probabilities of a favorable response. We describe how an optimal dynamic treatment regime can be determined given the model information. We also discuss the necessary identifiability conditions (i.e., what sets of parameters are necessary for DTR determination). </div><div><div>Then, we extend the proposed model to incorporate baseline covariates. Specifically, we include certain baseline covariates in the logistic model for the probabilities of a favorable response and develop a multivariate Bernoulli model to incorporate the remaining covariates in the determination of subgroup proportions. Furthermore, time effects are considered in the model to allow for a potential overall decline in response effectiveness over time. </div><div>In each setting, simulation studies are performed to demonstrate the effectiveness of the proposed method in both parameter and DTR estimation. We also compare our approach with another competing method, Q-learning, and provide the scenarios when our mixture model outperforms Q-learning in terms of finding the optimal DTR.</div></div>

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In this dissertation, a new numerical method for solving the fractional dynamical systems, is presented. We first introduce Riemann-Liouville fractional integral operator for hybrid functions. Then we will show the spectral accuracy of the present method for solving fractional-order differential equations, and we will extend the present method for solving nonlinear fractional integro-differential equations, fractional Bagley-Torvik equation, distributed order fractional differential equations, two-dimensional fractional partial differential equations, and fractional optimal control problems. In all cases, we will show the rate of convergence is more than some existing numerical methods which were used to solve these kind of problems in the literature. Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this dissertation, a new numerical method for solving some problems on the semiinfinite domain is presented. The method is based upon the modified rational Bernoulli functions. These functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then derived and are utilized to reduce the solution of the equations to a system of algebraic equations. This method is used to solve the following problems: Lane-Emden type equations, Volterra’s population model, Blasius equation, and MHD Falkner-Skan equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Fast and high quality classifications of cells inflicted with malignant mutations is essential for diagnosing patients with different forms of leukemia, to quickly be able give patients the crucial care they need. Convolutional neural networks (CNNs) can be trained and used for this purpose. This thesis studies CNNs and the application of regularization to create better performing and generalised models, with the purpose of generating highly accurate classifications for nine different forms of malignant white blood cells from the myeloid lineage. This is done to asses what method of dropout regularization is best suited for this type of cell data. To achieve this, three different methods of dropout regularization were studied: Bernoulli dropout; Gaussian dropout; and spatial dropout. This was conducted using a dataset consisting of 106,472 images from 945 patients. The results indicate that models using Gaussian dropout and Bernoulli dropout, respectively, produce the best results, with 87.39\% being the highest accuracy achieved. These two models are also statistically different from a benchmark model not utilizing any form of dropout. This suggests that one of these techniques may be optimal for this type of data. Further studies may be needed to determine which is the best of the two.

This dissertation concerns with the formulation of an improved multi-target multi-Bernoulli (MeMBer) filter and the use of the joint multi-target (JoM) estimator in an effective and efficient manner for a specific implementation of MeMBer filters. After reviewing random finite set (RFS) formalism for multi-target tracking problems and the related Bayes estimators the major contributions of this dissertation are explained in detail. The second chapter of this dissertation is dedicated to the analysis of the relationship between the multi-Bernoulli RFS distribution and the MeMBer corrector. This analysis leads to the formulation of an unbiased MeMBer filter without making any limiting assumption. Hence, as opposed to the popular cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter, the proposed MeMBer filter can be employed under the cases when sensor detection probability is moderate to low. Furthermore, a statistical refinement process is introduced to improve the stability of the estimated cardinality of targets obtained from the proposed MeMBer filter. The results from simulations demonstrate the effectiveness of the improved MeMBer filter. In Chapters III and IV, the Bayesian optimal estimators proposed for the RFS based multi-target tracking filters are examined in detail. First, an optimal solution to the unknown constant in the definition of the JoM estimator is determined by solving a multi-objective optimization problem. Thus, the JoM estimator can be implemented for tracking of a Bernoulli target using the optimal joint target detection and tracking (JoTT) filter. The results from simulations confirm assertions about its performance obtained by theoretical analysis in the literature. Finally, in the third chapter of this dissertation, the proposed JoM estimator is reformulated for RFS multi-Bernoulli distributions. Hence, an effective and efficient implementation of the JoM estimator is proposed for the Gaussian mixture implementations of the MeMBer filters. Simulation results demonstrate the robustness of the proposed JoM estimator under low-observable conditions. / Thesis / Doctor of Philosophy (PhD)

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