Related papers: GSP-Based MAP Estimation of Graph Signals
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…
Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…
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.…
In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can…
We propose a method by which to recover an underlying graph from a set of multivariate wave signals that is discretely sampled from a solution of the graph wave equation. Herein, the graph wave equation is defined with the graph Laplacian,…
Learning graphical causal structures from time series data presents significant challenges, especially when the measurement frequency does not match the causal timescale of the system. This often leads to a set of equally possible…
Graph Neural Networks (GNNs) require a large number of labeled graph samples to obtain good performance on the graph classification task. The performance of GNNs degrades significantly as the number of labeled graph samples decreases. To…
In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…
Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
We address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the unknown network. Using the…
This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…
We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
Consider the problem of estimating parameters $X^n \in \mathbb{R}^n $, generated by a stationary process, from $m$ response variables $Y^m = AX^n+Z^m$, under the assumption that the distribution of $X^n$ is known. This is the most general…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset. In our problem formulation, we assume that the…
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…