Reconstruction of Transcription Regulatory Network (TRN) and Transcription Factor Activity (TFA) from gene expression data is an important problem in systems biology. Currently, there exist various factor analysis methods for TRN reconstruction, but most approaches have specific assumptions not satisfied by real biological data. Network Component Analysis (NCA) can handle such limitations and is considered to be one of the most effective methods. The prerequisite for NCA is knowledge of the structure of TRN. Such structure can be obtained from ChIP-chip or ChIP-seq experiments, which however have quite limited applications. In order to cope with the difficulty, we resort to heuristic optimization algorithm such as Particle Swarm Optimization (PSO), in order to explore the possible structures of TRN and choose the most plausible one. Regarding the structure estimation problem, we extend classical PSO and propose a novel Probabilistic binary PSO. Furthermore, an improved NCA called FastNCA is adopted to compute the objective function accurately and fast, which enables PSO to run efficiently. Since heuristic optimization cannot guarantee global convergence, we run PSO multiple times and integrate the results. Then GCV-LASSO (Generalized Cross Validation - Least Absolute Shrinkage and Selection Operator) is performed to estimate TRN. We apply our approach and other factor analysis methods on the synthetic data. The results indicate that the proposed PSOFastNCA-GCV-LASSO algorithm gives better estimation. In order to incorporate more prior information on TRN structure and gene expression dynamics in the linear factor analysis model for improved estimation of TRN and TFAs, a linear Bayesian framework is adopted. Under the unified Bayesian framework, Bayesian Linear Sparse Factor Analysis Model (BLSFM) and Bayesian Linear State Space Model (BLSSM) are developed for instantaneous and dynamic TRN, respectively. Various approaches to incorporate partial and ambiguous prior network structure information in the Bayesian framework are proposed to improve performance in practical applications. Furthermore, we propose a novel mechanism for estimating the hyper-parameters of the distribution priors in our BLSFM and BLSSM models, which can significantly improve the estimation compared to traditional ways of hyper-parameter setting. With this development, reasonably good estimation of TFAs and TRN can be obtained even without use of any structure prior of TRN. Extensive numerical experiments are performed to investigate our developed methods under various settings, with comparison to some existing alternative approaches. It is demonstrated that our hyper-parameter estimation method improves the estimation of TFA and TRN in most settings and has superior performance, and that structure priors in general leads to improved estimation performance. Regarding application to real biological data, we execute the PSO-FastNCAGCV-LASSO algorithm developed in the thesis using E. Coli microarray data and obtain sensible estimation of TFAs and TRN. We apply BLSFM without structure priors of TRN, BLSSM without structure priors as well as with partial structure priors to Yeast S. cerevisiae microarray data and obtain a reasonable estimation of TFAs and TRN. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics / Master / Master of Social Sciences

This dissertation introduces a new method, Pratt's measure matrix, for interpreting multidimensional oblique factor models in both exploratory and confirmatory contexts. Overall, my thesis, supported by empirical evidence, refutes the currently recommended and practiced methods for understanding an oblique factor model; that is, interpreting the pattern matrix or structure matrix alone or juxtaposing both without integrating the information. Chapter Two reviews the complexities of interpreting a multidimensional factor solution due to factor correlation (i.e., obliquity). Three major complexities highlighted are (1) the inconsistency between the pattern and structure coefficients, (2) the distortion of additive properties, and (3) the inappropriateness of the traditional cut-off rules as being "meaningful". Chapter Three provides the theoretical rationale for adapting Pratt's importance measures from their use in multiple regression to that of factor analysis. The new method is demonstrated and tested with both continuous and categorical data in exploratory factor analysis. The results show that Pratt's measures are applicable to factor analysis and are able to resolve three interpretational complexities arising from factor obliquity. In the context of confirmatory factor analysis, Chapter Four warns researchers that a structure coefficient could be entirely spurious due to factor obliquity as well as zero constraint on its corresponding pattern coefficient. Interpreting such structure coefficients as Graham et al. (2003) suggested can be problematic. The mathematically more justified method is to transform the pattern and structure coefficients into Pratt's measures. The last chapter describes eight novel contributions in this dissertation. The new method is the first attempt ever at ordering the importance of latent variables for multivariate data. It is also the first attempt at demonstrating and explicating the existence, mechanism, and implications of the suppression effect in factor analyses. Specifically, the new method resolves the three interpretational problems due to factor obliquity, assists in identifying a better-fitting exploratory factor model, proves that a structure coefficient in a confirmatory factor analysis with a zero pattern constraint is entirely spurious, avoids the debate over the choice of oblique and orthogonal factor rotation, and last but not least, provides a tool for consolidating the role off actors as the underlying causes.

The first major work to analyze the dimensions of segregation, done in the late 1980s by Massey and Denton, found five dimensions which explained the phenomenon of segregation. Since the original work was done in 1988 it seems relevant to revisit the issue with new data. Massey and Denton used the technique of factor analysis to identify the latent structure underlying the phenomenon. In this research their methodology is applied to a more complete data set from the 1980 Census to confirm their results and extend the methodology. Due to problems identified during the analysis confirmation was not possible. However, a simpler structure was identified which is comprised of only two factors. This structure is replicated when the methodology is applied to the 1990 and 2000 Census data thereby proving the robustness of the methodology.

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Asthma is a heterogeneity disease that is mostly managed successfully using bronchodilators and anti-inflammatory drugs. Around 10%-15% of asthmatics however have difficult or severe asthma which is less responsive to treatments. Asthma and in particular severe asthma are now thought of a description of symptoms which may contain possible sub-groups with possible different pathologies which could be useful for targeting different drugs for different sub-groups. However little statistical work has been carried out to determine these sub-phenotypes. Studies have been carried out to partition severe asthma variables in to a number of sub-groups but the algorithms used in these studies are not based on statistical inference and it is difficult to select the number of best fitting sub-groups using such methods. It is also unclear where the clusters or sub-groups returned are actual sub-groups or reflect a bigger non-normal distribution. In the thesis we have developed a statistical model that combines factor analysis, a method used to obtain independent factors to describe processes allowing for variation over variables, and infinite mixture modelling, a process that involves determining the most probable number of mixtures or clusters thus allowing for variation over individuals. This model created is a Dirichlet process normal mixture latent variable model DPNMLVN and it is capable of determining the correct number of mixtures over each factor. The model was tested with simulations and used to analysis two severe asthma datasets and a cancer clinical trial. Sub-groups were found that reflect a high Eosinophilic group and an average eosinophilic group, a late onset older non atopic group and a highly atopic younger early onset group. In the clinical trial data 3 distinct mixtures were found relating to existing biomarkers not used in the mixture analysis.

This dissertation introduces a new method, Pratt's measure matrix, for interpreting multidimensional oblique factor models in both exploratory and confirmatory contexts. Overall, my thesis, supported by empirical evidence, refutes the currently recommended and practiced methods for understanding an oblique factor model; that is, interpreting the pattern matrix or structure matrix alone or juxtaposing both without integrating the information. Chapter Two reviews the complexities of interpreting a multidimensional factor solution due to factor correlation (i.e., obliquity). Three major complexities highlighted are (1) the inconsistency between the pattern and structure coefficients, (2) the distortion of additive properties, and (3) the inappropriateness of the traditional cut-off rules as being "meaningful". Chapter Three provides the theoretical rationale for adapting Pratt's importance measures from their use in multiple regression to that of factor analysis. The new method is demonstrated and tested with both continuous and categorical data in exploratory factor analysis. The results show that Pratt's measures are applicable to factor analysis and are able to resolve three interpretational complexities arising from factor obliquity. In the context of confirmatory factor analysis, Chapter Four warns researchers that a structure coefficient could be entirely spurious due to factor obliquity as well as zero constraint on its corresponding pattern coefficient. Interpreting such structure coefficients as Graham et al. (2003) suggested can be problematic. The mathematically more justified method is to transform the pattern and structure coefficients into Pratt's measures. The last chapter describes eight novel contributions in this dissertation. The new method is the first attempt ever at ordering the importance of latent variables for multivariate data. It is also the first attempt at demonstrating and explicating the existence, mechanism, and implications of the suppression effect in factor analyses. Specifically, the new method resolves the three interpretational problems due to factor obliquity, assists in identifying a better-fitting exploratory factor model, proves that a structure coefficient in a confirmatory factor analysis with a zero pattern constraint is entirely spurious, avoids the debate over the choice of oblique and orthogonal factor rotation, and last but not least, provides a tool for consolidating the role off actors as the underlying causes.

Thesis (M.A.)--University of Toronto, 2004. / Adviser: Ruth Childs.

Thesis: Ph.D.-- University of Western Sydney, Macarthur, 2000. / [A thesis presented to the Faculty of Informatics, Science and Technology]. References: p. 172-178.