Over the past five years neural network models have been successful across a range of computational linguistic tasks. However, these triumphs have been concentrated in languages with significant resources such as large datasets. Thus, many languages, which are commonly referred to as under-resourced languages, have received little attention and have yet to benefit from recent advances. This investigation aims to evaluate the implications of recent advances in neural network language modelling techniques for under-resourced South African languages. Rudimentary, single layered recurrent neural networks (RNN) were used to model four South African text corpora. The accuracy of these models were compared directly to legacy approaches. A suite of hybrid models was then tested. Across all four datasets, neural networks led to overall better performing language models either directly or as part of a hybrid model. A short examination of punctuation marks in text data revealed that performance metrics for language models are greatly overestimated when punctuation marks have not been excluded. The investigation concludes by appraising the sensitivity of RNN language models (RNNLMs) to the size of the datasets by artificially constraining the datasets and evaluating the accuracy of the models. It is recommended that future research endeavours within this domain are directed towards evaluating more sophisticated RNNLMs as well as measuring their impact on application focused tasks such as speech recognition and machine translation.

Includes bibliographical references (p. 92-93).

Count data are ubiquitous in modern statistical applications. How to modeling such data remains a challenging task in machine learning. In this study, we consider various aspects of statistical modeling on Poisson count data. Concerned with computational burdens for maximum likelihood estimation of the mean, we revisit the classical iterative proportional scaling and propose a set of methods that achieve computational scalability in high dimensional applications with regularized extensions for feature selection. In order to capture association effects given multivariate count data, we utilize the tool of non-Gaussian graph learning. We perform comprehensive empirical studies on synthetic data and real world data to demonstrate its power. Based on the concept of data depth, we investigate a non-parametric approach for modeling multivariate data. We utilize modern optimization techniques to provide scalable algorithms in high dimensional depth and depth median computations. Real-world examples are given to show the effectiveness of the proposed methods. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / June 19, 2018. / Includes bibliographical references. / Yiyuan She, Professor Directing Dissertation; Giray Okten, University Representative; Dan McGee, Committee Member; Xufeng Niu, Committee Member; Minjing Tao, Committee Member.

abstract: Functional brain imaging experiments are widely conducted in many fields for study- ing the underlying brain activity in response to mental stimuli. For such experiments, it is crucial to select a good sequence of mental stimuli that allow researchers to collect informative data for making precise and valid statistical inferences at minimum cost. In contrast to most existing studies, the aim of this study is to obtain optimal designs for brain mapping technology with an ultra-high temporal resolution with respect to some common statistical optimality criteria. The first topic of this work is on finding optimal designs when the primary interest is in estimating the Hemodynamic Response Function (HRF), a function of time describing the effect of a mental stimulus to the brain. A major challenge here is that the design matrix of the statistical model is greatly enlarged. As a result, it is very difficult, if not infeasible, to compute and compare the statistical efficiencies of competing designs. For tackling this issue, an efficient approach is built on subsampling the design matrix and the use of an efficient computer algorithm is proposed. It is demonstrated through the analytical and simulation results that the proposed approach can outperform the existing methods in terms of computing time, and the quality of the obtained designs. The second topic of this work is to find optimal designs when another set of popularly used basis functions is considered for modeling the HRF, e.g., to detect brain activations. Although the statistical model for analyzing the data remains linear, the parametric functions of interest under this setting are often nonlinear. The quality of the de- sign will then depend on the true value of some unknown parameters. To address this issue, the maximin approach is considered to identify designs that maximize the relative efficiencies over the parameter space. As shown in the case studies, these maximin designs yield high performance for detecting brain activation compared to the traditional designs that are widely used in practice. / Dissertation/Thesis / Doctoral Dissertation Statistics 2019

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