Related papers: On construction and analysis of sparse random matr…
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix…
We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
We theoretically study semi-supervised clustering in sparse graphs in the presence of pairwise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs, and study the impact of semi-supervision for varying constraint…
We investigate structural properties of large, sparse random graphs through the lens of "sampling convergence" (Borgs et. al. (2017)). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a…
Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…
Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…