MOTIVATION: Hi-C technology has been developed to profile genome-wide chromosome conformation. So far Hi-C data have been generated from a large compendium of different cell types and different tissue types. Among different chromatin conformation units, chromatin loops were found to play a key role in gene regulation across different cell types. While many different loop calling algorithms have been developed, most loop callers identified shared loops as opposed to cell-type-specific loops. RESULTS: We propose SSSHiC, a new loop calling algorithm based on significance in scale space, which can be used to understand data at different levels of resolution. By applying SSSHiC to neuronal and glial Hi-C data, we detected more loops that are potentially engaged in cell-type-specific gene regulation. Compared with other loop callers, such as Mustache, these loops were more frequently anchored to gene promoters of cellular marker genes and had better APA scores. Therefore, our results suggest that SSSHiC can effectively capture loops that contain more gene regulatory information. AVAILABILITY AND IMPLEMENTATION: The Hi-C data used in this study can be accessed through the PsychENCODE Knowledge Portal at https://www.synapse.org/#! Synapse: syn21760712. The code utilized for Curvature SSS cited in this study is available at https://github.com/jsmarron/MarronMatlabSoftware/blob/master/Matlab9/Matlab9Combined.zip. All custom code used in this research can be found in the GitHub repository: https://github.com/jerryliu01998/HiC. The code has also been submitted to Code Ocean with the doi: 10.24433/CO.1912913.v1.

Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good forecasting performance. However, in many data applications, such as those in neuroscience, the Granger causality graph estimates from existing vector autoregression methods tend to be quite dense and difficult to interpret, unless one compromises on the goodness-of-fit. To address this issue, this paper proposes to incorporate a commonly used structural assumption --- that the ground-truth graph should be largely connected, in the sense that it should only contain at most a few components. We take a Bayesian approach and develop a novel tree-rank prior distribution for the regression coefficients. Specifically, this prior distribution forces the non-zero coefficients to appear only on the union of a few spanning trees. Since each spanning tree connects $p$ nodes with only $(p-1)$ edges, it effectively achieves both high connectivity and high sparsity. We develop a computationally efficient Gibbs sampler that is scalable to large sample size and high dimension. In analyzing test-retest functional magnetic resonance imaging data, our model produces a much more interpretable graph estimate, compared to popular existing approaches. In addition, we show appealing properties of this new method, such as efficient computation, mild stability conditions and posterior consistency.

MOTIVATION: It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between a pair of brain regions. There is an emerging statistical literature describing methods for the analysis of such multi-network data in which nodes are common across networks but the edges vary. However, there has been essentially no consideration of the important problem of outlier detection. In particular, for certain subjects, the neuroimaging data are so poor quality that the network cannot be reliably reconstructed. For such subjects, the resulting adjacency matrix may be mostly zero or exhibit a bizarre pattern not consistent with a functioning brain. These outlying networks may serve as influential points, contaminating subsequent statistical analyses. We propose a simple Outlier DetectIon for Networks (ODIN) method relying on an influence measure under a hierarchical generalized linear model for the adjacency matrices. An efficient computational algorithm is described, and ODIN is illustrated through simulations and an application to data from the UK Biobank. RESULTS: ODIN was successful in identifying moderate to extreme outliers. Removing such outliers can significantly change inferences in downstream applications. AVAILABILITY AND IMPLEMENTATION: ODIN has been implemented in both Python and R and these implementations along with other code are publicly available at github.com/pritamdey/ODIN-python and github.com/pritamdey/ODIN-r, respectively. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

High angular resolution diffusion imaging (HARDI) is a type of diffusion magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere in q-space. It has been widely used in data acquisition for human brain structural connectome analysis. To more accurately estimate the structural connectome, dense samples in q-space are often acquired, potentially resulting in long scanning times and logistical challenges. This paper proposes a statistical method to select q-space directions optimally and estimate the local diffusion function from sparse observations. The proposed approach leverages relevant historical dMRI data to calculate a prior distribution to characterize local diffusion variability in each voxel in a template space. For a new subject to be scanned, the priors are mapped into the subject-specific coordinate and used to help select the best q-space samples. Simulation studies demonstrate big advantages over the existing HARDI sampling and analysis framework. We also applied the proposed method to the Human Connectome Project data and a dataset of aging adults with mild cognitive impairment. The results indicate that with very few q-space samples (e.g., 15 or 20), we can recover structural brain networks comparable to the ones estimated from 60 or more diffusion directions with the existing methods.

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor covariate, or use a low dimensional approximation of the coefficient tensor. However, low rank approximations of the coefficient tensor can suffer if the true rank is not small. We propose a tensor regression framework which assumes a soft version of the parallel factors (PARAFAC) approximation. In contrast to classic PARAFAC where each entry of the coefficient tensor is the sum of products of row-specific contributions across the tensor modes, the soft tensor regression (Softer) framework allows the row-specific contributions to vary around an overall mean. We follow a Bayesian approach to inference, and show that softening the PARAFAC increases model flexibility, leads to improved estimation of coefficient tensors, more accurate identification of important predictor entries, and more precise predictions, even for a low approximation rank. From a theoretical perspective, we show that employing Softer leads to a weakly consistent posterior distribution of the coefficient tensor, irrespective of the true or approximation tensor rank, a result that is not true when employing the classic PARAFAC for tensor regression. In the context of our motivating application, we adapt Softer to symmetric and semi-symmetric tensor predictors and analyze the relationship between brain network characteristics and human traits.

In this paper, we propose a supervised graph representation learning method to model the relationship between brain functional connectivity (FC) and structural connectivity (SC) through a graph encoder-decoder system. The graph convolutional network (GCN) model is leveraged in the encoder to learn lower-dimensional node representations (i.e. node embeddings) integrating information from both node attributes and network topology. In doing so, the encoder manages to capture both direct and indirect interactions between brain regions in the node embeddings which later help reconstruct empirical FC networks. From node embeddings, graph representations are learnt to embed the entire graphs into a vector space. Our end-to-end model utilizes a multi-objective loss function to simultaneously learn node representations for FC network reconstruction and graph representations for subject classification. The experiment on a large population of non-drinkers and heavy drinkers shows that our model can provide a characterization of the population pattern in the SC-FC relationship, while also learning features that capture individual uniqueness for subject classification. The identified key brain subnetworks show significant between-group difference and support the promising prospect of GCN-based graph representation learning on brain networks to model human brain activity and function.

Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a recently developed metric on the space of SPDMs for quantifying differences across FC observations, and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with task classification rates that match or outperform state-of-the-art techniques.

We present a Riemannian framework for analyzing signals and images in a manner that is invariant to their level of blurriness, under Gaussian blurring. Using a well known relation between Gaussian blurring and the heat equation, we establish an action of the blurring group on image space and define an orthogonal section of this action to represent and compare images at the same blur level. This comparison is based on geodesic distances on the section manifold which, in turn, are computed using a path-straightening algorithm. The actual implementations use coefficients of images under a truncated orthonormal basis and the blurring action corresponds to exponential decays of these coefficients. We demonstrate this framework using a number of experimental results, involving 1D signals and 2D images. As a specific application, we study the effect of blurring on the recognition performance when 2D facial images are used for recognizing people.

We propose a novel Riemannian framework for comparing signals and images in a manner that is invariant to their levels of blur. This framework uses a log-Fourier representation of signals/images in which the set of all possible Gaussian blurs of a signal, i.e. its orbits under semigroup action of Gaussian blur functions, is a straight line. Using a set of Riemannian metrics under which the group actions are by isometries, the orbits are compared via distances between orbits. We demonstrate this framework using a number of experimental results involving 1D signals and 2D images.

In this paper, we present a novel concept named semantic component for 3D object search which describes a key component that semantically defines a 3D object. In most cases, the semantic component is intra-category stable and therefore can be used to construct an efficient 3D object retrieval scheme. By segmenting an object into segments and learning the similar segments shared by all the objects in the same category, we can summarise what human uses for object recognition, from the analysis of which we develop a method to find the semantic component of an object. In our experiments, the proposed method is justified and the effectiveness of our algorithm is also demonstrated.