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Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input…
Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…
Human brains lie at the core of complex neurobiological systems, where the neurons, circuits, and subsystems interact in enigmatic ways. Understanding the structural and functional mechanisms of the brain has long been an intriguing pursuit…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
Recent studies in neuroscience highlight the significant potential of brain connectivity networks, which are commonly constructed from functional magnetic resonance imaging (fMRI) data for brain disorder diagnosis. Traditional brain…
The Matrix Decomposition techniques have been a vital computational approach to analyzing the hierarchy of functional connectivity in the human brain. However, there are still four shortcomings of these methodologies: 1). Large training…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Analyzing connections between brain regions of interest (ROI) is vital to detect neurological disorders such as autism or schizophrenia. Recent advancements employ graph neural networks (GNNs) to utilize graph structures in brains,…
Typical quantitative MRI (qMRI) methods estimate parameter maps in a two-step pipeline that first reconstructs images from undersampled k-space data and then performs model fitting, which is prone to biases and error propagation. We propose…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
A graphical model is an undirected network representing the conditional independence properties between random variables. Graphical modeling has become part and parcel of systems or network approaches to multivariate data, in particular…
We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…
We prove algorithmic weak and \Szemeredi{} regularity lemmas for several classes of sparse graphs in the literature, for which only weak regularity lemmas were previously known. These include core-dense graphs, low threshold rank graphs,…
This paper analyzes regularization terms proposed recently for improving the adversarial robustness of deep neural networks (DNNs), from a theoretical point of view. Specifically, we study possible connections between several effective…
We propose an algorithm to uncover the intrinsic low-rank component of a high-dimensional, graph-smooth and grossly-corrupted dataset, under the situations that the underlying graph is unknown. Based on a model with a low-rank component…
Cardiac magnetic resonance imaging (MRI) requires reconstructing a real-time video of a beating heart from continuous highly under-sampled measurements. This task is challenging since the object to be reconstructed (the heart) is…
Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain; one of the main outstanding issues is that of inferring from measure data, chiefly functional Magnetic Resonance…
Advances in Large Language Models (LLMs) have led to remarkable capabilities, yet their inner mechanisms remain largely unknown. To understand these models, we need to unravel the functions of individual neurons and their contribution to…
Latent graph inference (LGI) aims to jointly learn the underlying graph structure and node representations from data features. However, existing LGI methods commonly suffer from the issue of supervision starvation, where massive edge…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…