Biao Cai

Li Xiao, Biao Cai, Gang Qu et al.

Resting-state functional magnetic resonance imaging (rs-fMRI)-derived functional connectivity patterns have been extensively utilized to delineate global functional organization of the human brain in health, development, and neuropsychiatric disorders. In this paper, we investigate how functional connectivity in males and females differs in an age prediction framework. We first estimate functional connectivity between regions-of-interest (ROIs) using distance correlation instead of Pearson's correlation. Distance correlation, as a multivariate statistical method, explores spatial relations of voxel-wise time courses within individual ROIs and measures both linear and nonlinear dependence, capturing more complex information of between-ROI interactions. Then, a novel non-convex multi-task learning (NC-MTL) model is proposed to study age-related gender differences in functional connectivity, where age prediction for each gender group is viewed as one task. Specifically, in the proposed NC-MTL model, we introduce a composite regularizer with a combination of non-convex $\ell_{2,1-2}$ and $\ell_{1-2}$ regularization terms for selecting both common and task-specific features. Finally, we validate the proposed NC-MTL model along with distance correlation based functional connectivity on rs-fMRI of the Philadelphia Neurodevelopmental Cohort for predicting ages of both genders. The experimental results demonstrate that the proposed NC-MTL model outperforms other competing MTL models in age prediction, as well as characterizing developmental gender differences in functional connectivity patterns.

Aiying Zhang, Gemeng Zhang, Biao Cai et al.

Functional connectivity (FC) has become a primary means of understanding brain functions by identifying brain network interactions and, ultimately, how those interactions produce cognitions. A popular definition of FC is by statistical associations between measured brain regions. However, this could be problematic since the associations can only provide spatial connections but not causal interactions among regions of interests. Hence, it is necessary to study their causal relationship. Directed acyclic graph (DAG) models have been applied in recent FC studies but often encountered problems such as limited sample sizes and large number of variables (namely high-dimensional problems), which lead to both computational difficulty and convergence issues. As a result, the use of DAG models is problematic, where the identification of DAG models in general is nondeterministic polynomial time hard (NP-hard). To this end, we propose a $ψ$-learning incorporated linear non-Gaussian acyclic model ($ψ$-LiNGAM). We use the association model ($ψ$-learning) to facilitate causal inferences and the model works well especially for high-dimensional cases. Our simulation results demonstrate that the proposed method is more robust and accurate than several existing ones in detecting graph structure and direction. We then applied it to the resting state fMRI (rsfMRI) data obtained from the publicly available Philadelphia Neurodevelopmental Cohort (PNC) to study the cognitive variance, which includes 855 individuals aged 8-22 years. Therein, we have identified three types of hub structure: the in-hub, out-hub and sum-hub, which correspond to the centers of receiving, sending and relaying information, respectively. We also detected 16 most important pairs of causal flows. Several of the results have been verified to be biologically significant.

Biao Cai, Jingfei Zhang, Yongtao Guan

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional connectivity network based on spiking times recorded from a collection of neurons. To characterize the complex processes underlying the observed data, we propose a new and flexible class of nonstationary Hawkes processes that allow both excitatory and inhibitory effects. We estimate the latent network structure using an efficient sparse least squares estimation approach. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed Hawkes process. Such theoretical results enable us to establish the non-asymptotic error bound and the selection consistency of the estimated parameters. Furthermore, we describe a least squares loss based statistic for testing if the background intensity is constant in time. We demonstrate the efficacy of our proposed method through simulation studies and an application to a neuron spike train data set.