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The problem of maximizing the information flow through a sensor network tasked with an inference objective at the fusion center is considered. The sensor nodes take observations, compress and send them to the fusion center through a network…
In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally…
We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows,…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of…
This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex arguments and Hodge…
We present a new cycle flow based method for finding fuzzy partitions of weighted directed networks coming from time series data. We show that this method overcomes essential problems of most existing clustering approaches, which tend to…
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a…
The following problem, which stems from the ``flux phase'' problem in condensed matter physics, is analyzed and extended here: One is given a planar graph (or lattice) with prescribed vertices, edges and a weight $\vert t_{xy}\vert$ on each…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This…
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained…
We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns…