Date of Award

Summer 2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Ji Meng Loh

Second Advisor

Zhi Wei

Third Advisor

Antai Wang

Fourth Advisor

Yixin Fang

Fifth Advisor

Yi Chen

Abstract

This dissertation consists of two parts. In the first part, a learning-based method for classification of online reviews that achieves better classification accuracy is extended. Automatic sentiment classification is becoming a popular and effective way to help online users or companies to process and make sense of customer reviews. The method combines two recent developments. First, valence shifters and individual opinion words are combined as bigrams to use in an ordinal margin classifier. Second, relational information between unigrams expressed in the form of a graph is used to constrain the parameters of the classifier. By combining these two components, it is possible to extract more of the unstructured information present in the data than previous methods, like support vector machine, random forest, hence gaining the potential of better performance. Indeed, the results show a higher classification accuracy on empirical real data with ground truth as well as on simulated data.

The second part deals with graphical models. Gaussian graphical models are useful to explore conditional dependence relationships between random variables through estimation of the inverse covariance matrix of a multivariate normal distribution. An estimator for such models appropriate for multiple graphs analysis in two groups is developed. Under this setting, inferring networks separately ignores the common structure, while inferring networks identically would mask the disparity. A generalized method which estimates multiple partial correlation matrices through linear regressions is proposed. The method pursues the sparsity for each matrix, similarities for matrices within each group, and the disparities for matrices between groups. This is achieved by a l1 penalty and a 12 penalty for the pursuit of sparseness and clustering, and a metric that learns the true heterogeneity through optimization procedure. Theoretically, the asymptotic consistency for both constrained l0 method and the proposed method to reconstruct the structures is shown. Its superior performance is illustrated via a number of simulated networks. An application to polychromatic flow cytometry data sets for network inference under different sets of conditions is also included.

Included in

Mathematics Commons

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