On Bayesian Methods in Network Regression

There has been a growing interest during recent years in connectomics, which is the study of interconnections or networks within the human brain. This interest has been spurred by the development of new imaging technologies, which allow researchers to peer non-invasively into the human brain and obtain data on connections. Motivated by these datasets, this dissertation develops a novel class of Bayesian regression models which study the relationships between neuro-scientific phenotypes and brain connectome networks of individuals.First, we introduce a novel approach that develops a regression framework of the brain network (represented in the form of a symmetric matrix) on a continuous phenotypic response. We propose a novel network shrinkage prior on the network predictor coefficient matrix. The proposed framework is able to identify nodes or functional regions in the brain network and interconnections between different regions, significantly related to the phenotypic response. To the best of our knowledge, our framework is the first principled Bayesian framework that enables identification of network nodes and edges significantly relatedto the response. The performance of the proposed model is evaluated with respect to a wide range of existing competitors available in the high dimensional frequentist and Bayesian literature using a variety of simulation studies. The proposed model identifies important brain regions and interconnections significantly associated with creativity for a group of subjects.Next, we extend our model to build network classifiers when a brain connectome network along with a binary response is provided for a group of individuals. Here we develop a broader class of global-local network shrinkage priors which includes the novel prior distribution specified earlier as a special case. We specifically consider two different global-local network shrinkage priors from this class of priors and investigate them using simulation studies. In particular, we assess their performance in terms of network classification and identifying influential network nodes and edges for the purpose of classification. We also demonstrate superior performance of our proposed network classifiers over state-of-the-art high dimensional classification techniques. Another major contribution remains developing theoretical conditions to guarantee asymptotically consistent classification for the proposed framework. In particular, we derive conditions on the number of network nodes, sparsity in the network coefficient matrix as a function of the sample size to achieve asymptotically optimal classification. While theoretical results on high dimensional binary regression with ordinary shrinkage priors have emerged recently, developing theory for our network classifier model involves several additional challenges due to the complex nature of the global local shrinkage prior developed here. The framework is used to classify individuals into high and low IQ groups based on their brain connectomes.Notably, the work discussed in the last two paragraphs tacitly assumes that all nodes and edges have similar impact on a phenotype for every individual. In our next project, we study a brain connectome data where this assumption is violated. In fact, there is a relatively less developed literature in neuroscience that argues for different groups of individuals having shared relationships between brain networks and phenotypes, though this literature lacks a principled Bayesian approach that takes into account different relationships of nodes and edges with the response for different groups of individuals and facilitates clustering of individuals. Motivated by this problem and our dataset, we have developed a Bayesian network mixture regression model. Simulation studies and analysis of the brain connectome dataset demonstrate superior performance of the proposed approach over the approach described earlier. Simulation studies are also used to evaluate the performance of the proposed approach by varying the true and fitted number of clusters, size of the network and sample size.For these projects, computationally efficient Bayesian sampling algorithms are developed to enable computations even for reasonably large networks in presence of moderately large sample size

Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of variables, BN is naturally a generative model, which is not necessarily discriminative. This may cause the ignorance of subtle but critical network changes that are of investigation values across populations. In this paper, we propose to improve the discriminative power of BN models for continuous variables from two different perspectives. This brings two general discriminative learning frameworks for Gaussian Bayesian networks (GBN). In the first framework, we employ Fisher kernel to bridge the generative models of GBN and the discriminative classifiers of SVMs, and convert the GBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. In the second framework, we employ the max-margin criterion and build it directly upon GBN models to explicitly optimize the classification performance of the GBNs. The advantages and disadvantages of the two frameworks are discussed and experimentally compared. Both of them demonstrate strong power in learning discriminative parameters of GBNs for neuroimaging based brain network analysis, as well as maintaining reasonable representation capacity. The contributions of this paper also include a new Directed Acyclic Graph (DAG) constraint with theoretical guarantee to ensure the graph validity of GBN.Comment: 16 pages and 5 figures for the article (excluding appendix

The robust selection of predictive genes via a simple classifier

Identifying genes that direct the mechanism of a disease from expression data is extremely useful in understanding how that mechanism works. This in turn may lead to better diagnoses and potentially can lead to a cure for that disease. This task becomes extremely challenging when the data are characterised by only a small number of samples and a high number of dimensions, as it is often the case with gene expression data. Motivated by this challenge, we present a general framework that focuses on simplicity and data perturbation. These are the keys for the robust identification of the most predictive features in such data. Within this framework, we propose a simple selective na¨ıve Bayes classifier discovered using a global search technique, and combine it with data perturbation to increase its robustness to small sample sizes. An extensive validation of the method was carried out using two applied datasets from the field of microarrays and a simulated dataset, all confounded by small sample sizes and high dimensionality. The method has been shown capable of identifying genes previously confirmed or associated with prostate cancer and viral infections

Protein (Multi-)Location Prediction: Using Location Inter-Dependencies in a Probabilistic Framework

Knowing the location of a protein within the cell is important for understanding its function, role in biological processes, and potential use as a drug target. Much progress has been made in developing computational methods that predict single locations for proteins, assuming that proteins localize to a single location. However, it has been shown that proteins localize to multiple locations. While a few recent systems have attempted to predict multiple locations of proteins, they typically treat locations as independent or capture inter-dependencies by treating each locations-combination present in the training set as an individual location-class. We present a new method and a preliminary system we have developed that directly incorporates inter-dependencies among locations into the multiple-location-prediction process, using a collection of Bayesian network classifiers. We evaluate our system on a dataset of single- and multi-localized proteins. Our results, obtained by incorporating inter-dependencies are significantly higher than those obtained by classifiers that do not use inter-dependencies. The performance of our system on multi-localized proteins is comparable to a top performing system (YLoc+), without restricting predictions to be based only on location-combinations present in the training set.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013