Related papers: Laplacian Constrained Precision Matrix Estimation:…
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed by solving global optimization problems, which could be…
For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix…
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC),…
In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be…
The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of…
This paper considers a resilient high-dimensional constrained consensus problem and studies a resilient distributed algorithm for complete graphs. For convex constrained sets with a singleton intersection, a sufficient condition on…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the…
We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…
We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…
We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…
In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our…
Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and…
Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs.…
Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…