ARGEW improves node embeddings for weighted homophilous graphs by emphasizing strong edge weights.
problem Lack of accurate node embeddings for weighted homophilous graphs.
method ARGEW (Augmentation of Random walks by Graph Edge Weights) augments random walks by emphasizing nodes with larger edge weights.
result ARGEW produces embeddings where node pairs with strong edge weights have closer embeddings.
Paper uses GNN and conformal prediction for accurate edge weight prediction.
problem Predicting edge weights on graphs for various applications.
method Graph Neural Network (GNN) with conformal prediction and error reweighting.
result Our method provides better coverage and efficiency than baselines.
Paper tackles dense subgraph discovery with noisy feedback.
problem Discover dense subgraphs in edge-weighted graphs with noisy feedback.
method Proposes polynomial-time and scalable algorithms for dense subgraph discovery.
result Polynomial-time algorithm obtains nearly-optimal solution with high probability.
The (torsion) complexity of a finite edge-weighted graph is defined to be the order of the torsion subgroup of the abelian group presented by its Laplacian matrix. When G is d-periodic (i.e., G has a free action of the rank-d free abelian group by graph automorphisms, with finite quotient) the Mahler measure of its Lap…
This paper tackles matching two complete graphs with correlated edge weights in geometric models.
problem Matching two complete graphs with edge weights correlated through latent geometries.
method Derives an approximate maximum likelihood estimator for recovering hidden vertex correspondence.
result The estimator provably achieves perfect recovery under certain noise conditions.
Graph Neural Networks (GNNs) have been widely studied for graph data representation and learning. However, existing GNNs generally conduct context-aware learning on node feature representation only which usually ignores the learning of edge (weight) representation. In this paper, we propose a novel unified GNN model, n…
The paper proves ML estimators are strongly consistent for identifying edge weights in BAR models.
problem Identifying edge weights in Bernoulli Autoregressive (BAR) models.
method Maximum Likelihood (ML) estimation for two variants of BAR models.
result ML estimators are strongly consistent for edge weight identification.
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of dif…
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph cluste…
The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.
New algorithm for online learning with noisy side observations.
problem Online learning with noisy side feedback and graph-structured dependencies.
method Proposes an algorithm using a weighted directed graph to model dependencies and guarantees a regret bound of O(√α* T).
result Guarantees a regret of O(√α* T) after T rounds, where α* is the effective independence number.
Optimal Euclidean structure minimizes energy in weighted toroidal graphs.
problem Finding the optimal Euclidean structure for weighted toroidal graphs.
method Minimizing Dirichlet energy over all possible Euclidean structures and realizations within a fixed homotopy class.
result The optimal Euclidean structure induces a weighted Delaunay decomposition.
Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.
problem Finding optimal discrete harmonic maps between hyperbolic surfaces.
method Minimizing Dirichlet energy over all possible hyperbolic structures and realizations within a fixed homotopy class.
result At the optimal hyperbolic structure, the discrete harmonic map and edge weights are induced from a weighted Delaunay decomposition.
Gradient flows on graphons converge to curves on graphon space.
problem Optimizing functions on large, exchangeable graphs.
method Euclidean gradient flow on edge weights converges to a curve on graphon space.
result Gradient flows on graphons can be described as curves of maximal slope on graphon space.
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that …
This work improves graph inference using the degree-4 sum-of-squares hierarchy.
problem Recovering ground-truth binary labelings from corrupted edge observations.
method Apply the degree-4 sum-of-squares hierarchy to a quadratic combinatorial optimization problem.
result The solution of the dual problem is related to edge weights of Johnson and Kneser graphs.
Unified model combines GCN and LPA for better node classification.
problem Combining GCN and LPA for improved node classification.
method Unified model that unifies GCN and LPA, learns edge weights and attention weights.
result Unified model outperforms state-of-the-art GCN-based methods in node classification accuracy.
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motiv…
Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA)…
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…
We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most nγ for some γ<1 and each edge has a random edge weight in [−1,1]. Our algorithm learns {\em …
We address the problem of computing a single linkage dendrogram. A possible approach is to: (i) Form an edge weighted graph G over the data, with edge weights reflecting dissimilarities. (ii) Calculate the MST T of G. (iii) Break the longest edge of T thereby splitting it into subtrees TL, TR. (iv) Apply …
Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditi…
Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biolog…
We study graph matching with correlated Gaussian features and find thresholds for exact recovery.
problem Graph matching with correlated Gaussian features.
method Information-theoretic thresholds and conditions for exact and almost exact recovery.
result Contextual information introduces a richer structure, with thresholds for exact and almost exact recovery no longer coinciding.
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a general model of cascades, including the voter model and the independent cascad…
Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding …
BetaExplainer improves GNN interpretability by masking unimportant edges.
problem Interpreting GNNs' predictions is difficult due to black-box behavior and lack of uncertainty quantification.
method BetaExplainer uses a sparsity-inducing prior to mask unimportant edges during training.
result BetaExplainer provides uncertainty in edge importance and improves predictive accuracy on challenging datasets.
In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's CD(K,n) condition for linear graphs and prove the triviality of edge w…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership information. In particular, we introduce a edge weight distribution matrix to the s…
Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.
problem Improving retrieval-augmented generation rerankers for query-answer tasks.
method Discrete Ricci flow on graphs to evaluate structural importance of chunks.
result Ricci-Filtration outperforms baseline methods in accuracy, precision, recall, and F1 scores.
New method estimates Nishimori temperature for node classification in weighted graphs.
problem Estimating Nishimori temperature for Bayesian inference.
method Spectral method using eigenvalues of Bethe Hessian matrix.
result Spectral method outperforms existing approaches in node classification.
EWS-GCN improves credit scoring by analyzing money transfer connections.
problem Improving credit scoring in transactional banking data.
method Edge Weight-Shared Graph Convolutional Network (EWS-GCN) combining graph and recurrent neural networks.
result EWS-GCN outperforms state-of-the-art models in credit scoring.
We propose a framework that learns the graph structure underlying a set of smooth signals. Given X∈Rm×n whose rows reside on the vertices of an unknown graph, we learn the edge weights w∈R+m(m−1)/2 under the smoothness assumption that trX⊤LX is small. We show that …
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
The Ollivier Ricci flow with prescribed curvature on infinite graphs.
problem Ricci flow with prescribed curvature on infinite graphs.
method Existence and uniqueness of the solution to the Ricci flow.
result Convergence of the Ricci flow for graphs with girth at least 6.
This paper explains GNNs using graph signal denoising.
problem Understanding how GNNs work for node representation learning.
method Spectral graph convolutional networks and graph attention networks are analyzed from the perspective of graph signal denoising.
result GNNs implicitly solve graph signal denoising problems.
This paper optimizes portfolio compression by reducing excess notional in market contracts.
problem Reduction of excess notional in market contracts to decrease systemic risk.
method Examines and solves portfolio compression problems using graph theory and algorithms.
result Developed a clearing algorithm and method to compute maximum volume conservative compression.
New Ricci flow method for directed graphs with balancing factor.
problem Analyzing asymmetry in directed networks.
method Rigorous formulation of Ricci flow on directed weighted graphs with balancing factor.
result Existence and uniqueness of discrete Ricci flow solutions.
For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The measure is intuitive given the abnormal samples are usually rare and they are dissi…
In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for populations of individuals. Current approaches to hypothesis testing for weighted n…
End-to-end graph-based SSL learns all graph factors dynamically.
problem Learning quality of graph in SSL is crucial but difficult.
method Proposes an end-to-end approach to optimize all graph factors.
result Demonstrates effectiveness on benchmark datasets.
Paper studies vertex correspondence recovery in correlated graphs with node features.
problem Recovering hidden vertex correspondence between two correlated graphs with observed edge weights and node features.
method Introduced featured correlated Gaussian Wigner model and proposed QPAlign algorithm for quadratic programming relaxation.
result Characterized optimal information-theoretic thresholds for exact and partial recovery of latent mapping.
Paper introduces HGSL for heterogeneous graphs, improving edge type and weight recovery.
problem Learning structure in heterogeneous graphs with multiple node and edge types.
method Proposes H2MN model for DGPs and derives alternating optimization method.
result Demonstrates superior performance on synthetic and real-world datasets.
Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As real-world graphs are often incomplete and noisy, treating them as ground-truth inform…
New algorithms cluster nodes in SBM graphs faster and more accurately.
problem Efficiently clustering nodes in graphs generated from SBM models.
method Inspired by Lloyd's algorithm, proposes model-free clustering methods for SBM graphs.
result Consistent estimation of node clusters and parameters in SBM graphs.
Paper determines Assouad-Nagata dimension for all minor-closed metrics.
problem Understanding the Assouad-Nagata dimension of minor-closed metrics.
method Using edge-weighted graphs and edge-deletion/contraction to model minor-closed metrics, determining their Assouad-Nagata dimension.
result Determined the Assouad-Nagata dimension for every minor-closed metric.