Structure learning of Bayesian Networks (BNs) is an important topic in machine learning. Driven by modern applications in genetics and brain sciences, accurate and efficient learning of large-scale BN structures from high-dimensional data becomes a challenging problem. To tackle this challenge, we propose a Sparse Bayesian Network (SBN) structure learning algorithm that employs a novel formulation involving one L1-norm penalty term to impose sparsity and another penalty term to ensure that the learned BN is a Directed Acyclic Graph--a required property of BNs. Through both theoretical analysis and extensive experiments on 11 moderate and large benchmark networks with various sample sizes, we show that SBN leads to improved learning accuracy, scalability, and efficiency as compared with 10 existing popular BN learning algorithms. We apply SBN to a real-world application of brain connectivity modeling for Alzheimer's disease (AD) and reveal findings that could lead to advancements in AD research.

Given a single index, the receiver operational characteristic (ROC) curve analysis is routinely utilized for characterizing performances in distinguishing two conditions/groups in terms of sensitivity and specificity. Given the availability of multiple data sources (referred to as multi-indices), such as multimodal neuroimaging data sets, cognitive tests, and clinical ratings and genomic data in Alzheimer’s disease (AD) studies, the single-index-based ROC underutilizes all available information. For a long time, a number of algorithmic/analytic approaches combining multiple indices have been widely used to simultaneously incorporate multiple sources. In this study, we propose an alternative for combining multiple indices using logical operations, such as “AND,” “OR,” and “at least n” (where n is an integer), to construct multivariate ROC (multiV-ROC) and characterize the sensitivity and specificity statistically associated with the use of multiple indices. With and without the “leave-one-out” cross-validation, we used two data sets from AD studies to showcase the potentially increased sensitivity/specificity of the multiV-ROC in comparison to the single-index ROC and linear discriminant analysis (an analytic way of combining multi-indices). We conclude that, for the data sets we investigated, the proposed multiV-ROC approach is capable of providing a natural and practical alternative with improved classification accuracy as compared to univariate ROC and linear discriminant analysis.

Recent studies have shown that Alzheimer's disease (AD) is related to alteration in brain connectivity networks. One type of connectivity, called effective connectivity, defined as the directional relationship between brain regions, is essential to brain function. However, there have been few studies on modeling the effective connectivity of AD and characterizing its difference from normal controls (NC). In this paper, we investigate the sparse Bayesian Network (BN) for effective connectivity modeling. Specifically, we propose a novel formulation for the structure learning of BNs, which involves one L1-norm penalty term to impose sparsity and another penalty to ensure the learned BN to be a directed acyclic graph - a required property of BNs. We show, through both theoretical analysis and extensive experiments on eleven moderate and large benchmark networks with various sample sizes, that the proposed method has much improved learning accuracy and scalability compared with ten competing algorithms. We apply the proposed method to FDG-PET images of 42 AD and 67 NC subjects, and identify the effective connectivity models for AD and NC, respectively. Our study reveals that the effective connectivity of AD is different from that of NC in many ways, including the global-scale effective connectivity, intra-lobe, interlobe, and inter-hemispheric effective connectivity distributions, as well as the effective connectivity associated with specific brain regions. These findings are consistent with known pathology and clinical progression of AD, and will contribute to AD knowledge discovery.

Diagnosis of Alzheimer's disease (AD) at the early stage of the disease development is of great clinical importance. Current clinical assessment that relies primarily on cognitive measures proves low sensitivity and specificity. The fast growing neuroimaging techniques hold great promise. Research so far has focused on single neuroimaging modalities. However, as different modalities provide complementary measures for the same disease pathology, fusion of multi-modality data may increase the statistical power in identification of disease-related brain regions. This is especially true for early AD, at which stage the disease-related regions are most likely to be weak-effect regions that are difficult to be detected from a single modality alone. We propose a sparse composite linear discriminant analysis model (SCLDA) for identification of disease-related brain regions of early AD from multi-modality data. SCLDA uses a novel formulation that decomposes each LDA parameter into a product of a common parameter shared by all the modalities and a parameter specific to each modality, which enables joint analysis of all the modalities and borrowing strength from one another. We prove that this formulation is equivalent to a penalized likelihood with non-convex regularization, which can be solved by the DC ((difference of convex functions) programming. We show that in using the DC programming, the property of the non-convex regularization in terms of preserving weak-effect features can be nicely revealed. We perform extensive simulations to show that SCLDA outperforms existing competing algorithms on feature selection, especially on the ability for identifying weak-effect features. We apply SCLDA to the Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) images of 49 AD patients and 67 normal controls (NC). Our study identifies disease-related brain regions consistent with findings in the AD literature.

Recent advances in neuroimaging techniques provide great potentials for effective diagnosis of Alzheimer’s disease (AD), the most common form of dementia. Previous studies have shown that AD is closely related to alternation in the functional brain network, i.e., the functional connectivity among different brain regions. In this paper, we consider the problem of learning functional brain connectivity from neuroimaging, which holds great promise for identifying image-based markers used to distinguish Normal Controls (NC), patients with Mild Cognitive Impairment (MCI), and patients with AD. More specifically, we study sparse inverse covariance estimation (SICE), also known as exploratory Gaussian graphical models, for brain connectivity modeling. In particular, we apply SICE to learn and analyze functional brain connectivity patterns from different subject groups, based on a key property of SICE, called the “monotone property” we established in this paper. Our experimental results on neuroimaging PET data of 42 AD, 116 MCI, and 67 NC subjects reveal several interesting connectivity patterns consistent with literature findings, and also some new patterns that can help the knowledge discovery of AD.