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This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
Segmentation of Multiple Sclerosis (MS) lesions in longitudinal brain MR scans is performed for monitoring the progression of MS lesions. We hypothesize that the spatio-temporal cues in longitudinal data can aid the segmentation algorithm.…
Most brain disorders are very heterogeneous in terms of their underlying biology and developing analysis methods to model such heterogeneity is a major challenge. A promising approach is to use probabilistic regression methods to estimate…
Recent advances in neuroscience data acquisition allow for the simultaneous recording of large populations of neurons across multiple brain areas while subjects perform complex cognitive tasks. Interpreting these data requires us to index…
Identifying objective neuroimaging biomarkers to forecast Alzheimer's disease (AD) progression is crucial for timely intervention. However, this task remains challenging due to the complex dysfunctions in the spatio-temporal characteristics…
Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this…
Much of the genome is expressed in the vertebrate brain, with individual genes exhibiting different spatially-varying patterns of expression. These variations are not independent, with pairs of genes exhibiting complex patterns of…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian…
The characterisation of the brain as a "connectome", in which the connections are represented by correlational values across timeseries and as summary measures derived from graph theory analyses, has been very popular in the last years.…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
Cross-subject electroencephalography (EEG) decoding remains a fundamental challenge in brain-computer interface (BCI) research due to substantial inter-subject variability and the scarcity of subject-invariant representations. This paper…
In "The Organization of Behavior" (Hebb, 1949), Hebb suggested that the propagation of activity between transiently grouped neurons plays an important role in behavior. Since then, multiple studies have provided evidence supporting Hebb's…
The tensor-structured parametric analysis (TPA) has been recently developed for simulating and analysing stochastic behaviours of gene regulatory networks [Liao et. al., 2015]. The method employs the Fokker-Planck approximation of the…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Neural decoding is still a challenge and hot topic in neurocomputing science. Recently, many studies have shown that brain network patterns containing rich spatial and temporal structure information, which represents the activation…
Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies non-invasively. The structural connectome is initially shaped by genetics and subsequently refined by the environment.…
Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is…