Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share an edge with high probability, they must be relatively close in all dimensions. …
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48 results for “Edge Probability”
Study detects edge correlation between unlabeled random graphs.
problem Detect edge correlation between unlabeled random graphs.
method Hypothesis testing, conditional second-moment method, pseudoforest structure, enumeration of subpseudoforests.
result Sharp threshold for phase transition in testing error probability.
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…
Paper provides statistical guarantees for GNNs in link prediction.
problem Link prediction accuracy in graph neural networks.
method Proposes a linear GNN architecture (LG-GNN) and derives statistical guarantees.
result LG-GNN produces consistent estimators for edge probabilities and has better detection of high-probability edges.
We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact marginal posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n-1) potential edges in O(n2n…
GISST interprets GNNs by combining attention and sparsity for graph structure and node feature importance.
problem Lack of joint consideration of graph structure and node features in GNN interpretation.
method Model-agnostic framework using attention mechanism and sparsity regularization.
result GISST achieves superior node feature and edge explanation precision in synthetic and real-world datasets.
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the complex Stiefel manifold of 2-frames in n-space to the space of closed n-gons in 3-space of total length 2. Our probability measure on polygon s…
UniNet efficiently learns network representations from large graphs.
problem Efficiently learning network representations from large graphs.
method Metropolis-Hastings sampling for efficient edge sampling and random walk model abstraction.
result UniNet outperforms existing NRL models on billion-edge networks.
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…
We consider the densest -subgraph problem, which seeks to identify the -node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest -subgraph problem, based on a nucle…
We propose {graphical sure screening}, or GRASS, a very simple and computationally-efficient screening procedure for recovering the structure of a Gaussian graphical model in the high-dimensional setting. The GRASS estimate of the conditional dependence graph is obtained by thresholding the elements of the sample covar…
Detects dense subhypergraphs in heterogeneous random hypergraphs.
problem Testing for the existence of a dense subhypergraph in heterogeneous random hypergraphs.
method Established detection boundaries and constructed asymptotically powerful and adaptive tests.
result Developed tests for distinguishing between null and alternative hypotheses.
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes. While learning arbitrary graphs with nodes and edges is known to be hard in the sense of requiring $Ω( \min\{ k^2 \log n, …
Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least and the minimal correlation is at least .
Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means selecting a subset of nodes and recording all of their edges. This sampling mech…
BWFlow improves graph generation by smoothly interpolating graph components.
problem Disjoint modeling of graph nodes and edges leads to irregular and non-smooth probability paths.
method Modeling graphs as MRFs and using optimal transport displacement for a smooth probability path.
result BWFlow achieves better training convergence and efficient sampling in graph generation.
Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groupsmath.PR
Square percolation determines threshold for group divergence in random graphs.
problem Threshold for quadratic divergence in random right-angled Coxeter groups.
method Square-graph analysis of random graphs to determine connectivity and divergence.
result Threshold probability for quadratic divergence is \( p_c(n) = \sqrt{\sqrt{6}-2}/\sqrt{n} \).
We consider the problem of selecting a seed set to maximize the expected number of influenced nodes in the social network, referred to as the \textit{influence maximization} (IM) problem. We assume that the topology of the social network is prescribed while the influence probabilities among edges are unknown. In order …
New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.
problem Community detection in hypergraphs with large hyperedges.
method Extending Ricci flow to hypergraphs by defining edge probability measures and transporting them on the line expansion.
result Enhanced sensitivity to hypergraph structure, especially in large hyperedges.
Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such discoveries, including directing further investigation, it is important that thos…
Method certifies edge predictions with cloud-level reliability.
problem Ensuring reliability of edge intelligence models.
method Conformal alignment-based cascading mechanism.
result Certifies conditional coverage with user control over risk level.
This work estimates edge weights of edge-reinforced random walks using observed data.
problem Statistical estimation of edge weights in edge-reinforced random walks.
method Proposes an estimator based on the generalized method of moments using the magic formula and hyperbolic Gaussian structure.
result Analyzes the sample complexity of the proposed estimator.
Sharp boundaries for detecting dense subhypergraphs established.
problem Detecting dense subhypergraphs in random hypergraphs.
method Established sharp detection boundaries for known and unknown edge probabilities.
result Sharp detectable regions differ significantly from graph counterparts.
Study sets limits for detecting a subhypergraph in uniform hypergraphs.
problem Recovering a subhypergraph from a uniform hypergraph with different edge probabilities.
method Information-theoretic analysis for weak and exact recovery.
result Sharp conditions for weak or exact recovery of the subhypergraph.
Fairness constraints improve exact recovery in structured prediction models.
problem Exact recovery of fair binary node labels from noisy observations.
method Analyzed Globerson et al. (2015) model with fairness constraints and improved exact recovery for graphs with poor expansion properties.
result Fairness constraints improve the probability of exact recovery from noisy observations.
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.
New method for online learning IC models with node-level feedback.
problem Learning IC models with node-level feedback in social networks.
method Detailed analysis and online algorithm with cumulative regret.
result First confidence-region result and online algorithm for IC models with node-level feedback.
Understanding how users navigate in a network is of high interest in many applications. We consider a setting where only aggregate node-level traffic is observed and tackle the task of learning edge transition probabilities. We cast it as a preference learning problem, and we study a model where choices follow Luce's a…
Study on signed graphs with random signs, focusing on community detection.
problem Community detection in signed stochastic block models.
method Strong concentration inequalities for adjacency and Laplacian matrices, applied to signed Laplacian matrix.
result The sign of the first eigenvector of the Laplacian matrix defines a weakly consistent estimator for balanced community detection.
Study on matching nodes between graphs to preserve edges, focusing on limits and algorithms.
problem Matching nodes between graphs to preserve most edges, especially in random graphs.
method Investigates fundamental limits and designs algorithms to recover alignments in planted graphs.
result High probability guarantees on the success or failure of graph alignment algorithms.
Study financial contagion and risk in sparse networks with directed edges.
problem Analyzing systemic risk in sparse financial networks with balance-sheet interactions.
method Linear fraction of institutions with zero out-degree, sender-truncated subgraph G_sh, adversarial and random systemic events, explicit fan-in accumulation bound.
result Maximal forward reachability in G_sh is O(log n) with high probability in the subcritical regime, and multi-hit defaults are negligible in the supercritical regime.
The paper controls false discovery rate in link prediction using conformal inference.
problem Identifying true edges in a graph while controlling false discoveries.
method Proposes a novel method based on conformal inference to control false discovery rate (FDR) in link prediction.
result Empirically demonstrates FDR control for both simulated and real data.
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…
New algorithm for competing influence spread in unknown networks.
problem Maximizing influence spread in a social network with unknown probabilities.
method Combinatorial multi-armed bandit (CMAB) framework, Triggering Probability Modulated (TPM) condition, OCIM-TS, OCIM-OFU, OCIM-ETC.
result Sublinear Bayesian and frequentist regret for OCIM-TS and OCIM-OFU, respectively.
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We prese…
Seeded graph matching for the correlated Gaussian Wigner model via the projected power methodmath.ST
PPM improves graph matching for correlated Gaussian Wigner models with high probability.
problem Graph matching in the Correlated Gaussian Wigner model with edge correlations.
method Seeded projected power method (PPM) for iterative improvement of initial partial matches.
result PPM recovers ground-truth matching with high probability in O(log n) iterations if seed is close enough.
A new test statistic counts tree co-occurrences to detect edge correlation between networks.
problem Detecting edge correlation between networks using latent vertex correspondence.
method The test statistic is based on counting co-occurrences of signed trees for a family of non-isomorphic trees.
result The test runs in time and succeeds with high probability for large .
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…
A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local "richness" of the cyclic structure. In this paper, we introduce renewal non-backtrac…
We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time, where n is the number of attributes; the number of parents per attribute is bound…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a realization from a random graph model, and estimate the underlying edge probability ma…
Dropout neural networks can approximate any function with high probability.
problem Approximating functions with dropout neural networks.
method Two universal approximation theorems for dropout neural networks in random and deterministic modes.
result Dropout neural networks can approximate any function in probability and in .
Real-time anomaly detection for edge streams using MIDAS and MIDAS-F.
problem Detecting unusual behavior in dynamic graph edge streams.
method MIDAS-F focuses on microcluster anomalies, incorporating anomalies into internal states to reduce poisoning effect.
result MIDAS-F outperforms MIDAS in accuracy, with up to 62% higher ROC-AUC.
New method calibrates probabilistic linear solver for online coverage guarantees.
problem Uncertainty in probabilistic linear solver solutions without coverage guarantees.
method Online conformal prediction-PLS (OCP-PLS) method to calibrate uncertainty thresholds.
result Validates online calibration of uncertainty thresholds via online conformal prediction.
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucia…
Node Embedding for Homophilous Graphs with ARGEW: Augmentation of Random walks by Graph Edge Weightscs.SI
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.