Algorithm reconstructs vertex positions in random geometric graphs with improved accuracy.
problem Reconstructing vertex positions in random geometric graphs with high accuracy.
method Hybrid of graph distances and short-range estimates based on common neighbors.
result Algorithm reconstructs vertex positions with error of O(nβ), improving over previous results. The paper proves properties for random graphs based on geometric submanifolds.
problem Establishing measure-metric properties of random geometric graphs.
method Analyzing ε-neighborhood graphs with specific conditions on submanifold and distribution. result Volume doubling and local Poincaré inequalities hold for random geometric graphs with high probability.
Improved algorithm for causal structure learning in large networks.
problem Estimating high-dimensional directed acyclic graphs from noisy data.
method A modified PC-Algorithm that uses small sets of variables for conditioning.
result Significant gains in computational complexity and estimation accuracy, especially in large networks with hub nodes.
Method finds motifs in knowledge graphs, revealing their structure.
problem Identifying meaningful subunits in knowledge graphs.
method Inspired by simple graphs, the approach uses compression techniques to find motifs.
result Motifs found reflect the basic structure of the graph.
C-RSP embeds multi-view graphs using randomized shortest paths.
problem Combining multiple views of a graph to improve inference quality.
method C-RSP algorithm that generates a common embedding using RSP.
result C-RSP outperforms benchmarks in embedding and clustering tasks.
Extends random dot product graph model to handle multiple graphs.
problem Modeling and analyzing multiple graphs with shared nodes.
method Jointly embed adjacency matrices into a latent space.
result Node representations converge to latent positions with Gaussian error.
Proposes a method to improve graph embedding by removing least frequent nodes.
problem Capturing global graph structure in random walk-based embeddings.
method Extends random walk-based graph embedding by removing least frequent nodes.
result Improves predictive performance slightly, if at all.
A framework for hypothesis testing on attributed graphs using sampling.
problem Statistical testing on graph data, especially large attributed graphs.
method Sampling-based framework with PHASE and PHASEopt for accurate and efficient hypothesis testing.
result PHASE and PHASEopt improve accuracy and efficiency of hypothesis testing in attributed graphs.
Study sharpens threshold for matching correlated graphs without labels.
problem Matching latent vertex correspondences in correlated random graphs.
method Analyzes information-theoretic limits for correct vertex matching in sub-sampled graphs.
result Establishes a sharp information-theoretic threshold for vertex matching recovery.
New method clusters directed and undirected graphs without losing directional information.
problem Clustering directed graphs due to asymmetry in edge connectivity.
method Generalized Dirichlet Energy (GDE) and generalized spectral clustering (GSC).
result GSC outperforms existing methods in clustering accuracy and robustness.
Proposes autoencoding with random forests using spectral graph theory.
problem Learning low-dimensional embeddings of random forest models.
method Combines nonparametric statistics and spectral graph theory for optimization.
result Establishes a universal consistent decoder for random forest models.
GraLSP improves graph neural networks by incorporating local structural patterns.
problem GNNs struggle with identifying common structural patterns in graphs.
method GraLSP uses random anonymous walks to capture local graph structures and incorporates these into feature aggregation mechanisms.
result GraLSP outperforms other models in various prediction tasks on multiple datasets.
Paper compares unsupervised network representation learning methods.
problem Lack of systematic comparison of UNRL methods.
method Unified context-based optimization function.
result No single method is a clear winner, choice depends on graph properties and task.
New method quantifies network cycles to enhance community detection.
problem Challenges in detecting communities in networks, especially in sparse graphs.
method Renewal non-backtracking random walks (RNBRW) to quantify cyclic structure.
result RNBRW improves community detection algorithms, especially in sparse graphs.
A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Rando…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
New framework for neural networks converging to low loss without overparameterization.
problem Training deep neural networks without overparameterization assumptions.
method Construction of random sparse lifts and analysis using algebraic topology and random graph theory.
result Provable convergence to low loss for large sparse neural networks.
Study reveals neural scaling laws in random graphs and natural language models.
problem Understanding the origin of neural scaling laws in complex systems.
method Examined scaling laws in transformers trained on random walks and simplified natural language models.
result Neural scaling laws emerge in the absence of power law structure in data correlations.
COMRECGC finds common recourse for global counterfactual explanations in GNNs.
problem Finding common recourse for global counterfactual explanations in GNNs.
method Formalized the common recourse explanation problem and designed COMRECGC algorithm.
result COMRECGC outperforms strong baselines on four real-world graph datasets.
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…
New method estimates graphons from multiple networks with high accuracy and low complexity.
problem Estimating graphon function from multiple networks with different node sets and sizes.
method Histogram-based estimator that aligns nodes across all networks.
result High accuracy and low computational complexity achieved.
Bayesian learning for forests and trees improves graph detection and structure learning.
problem Learning graph structures in non-decomposable graphs.
method Adapted MCMC and SSS algorithms for forests and trees, using the Chow-Liu algorithm and Matrix Tree Theorem.
result SSS with trees or forests outperforms SSS with decomposable graphs in certain cases.
Paper presents a method to estimate mixed-variable distributions.
problem Estimating joint, conditional, and marginal distributions from mixed data.
method Graph representation of data, eigenvector equations for distribution estimation.
result Method successfully estimates distributions for various machine learning tasks.
ZSL-KG learns class representations from common sense knowledge graphs.
problem Predicting classes without labeled examples using semantic class representations.
method TrGCN, a novel transformer graph convolutional network, embeds nodes from common sense knowledge graphs in a vector space.
result ZSL-KG improves over existing methods on five out of six zero-shot benchmark datasets.
Extract common latent factors from graphs for better representation learning.
problem Graph-level representation learning challenges due to limited labeled data and poor negative sample selection.
method Graph-wise Common Latent Factor Extraction (GCFX) using deepGCFX model.
result Improved graph-level and node-level tasks performance compared to state-of-the-art methods.
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
New method learns DAG structure in clustered data, accounting for local variations.
problem Learning DAG structure in clustered data with varying effects.
method Extends mixed models to structure learning, using a differentiable graph coupling mechanism.
result Asymptotically recovers true structure, detecting dependencies missed by other methods.
Paper tests similarity between networks using a bootstrap method.
problem Determining if two networks are similar or proportional.
method Parametric bootstrap approach and Frobenius norm-based test.
result The method is versatile and consistent under various models.
Bayesian optimization improves performance with common random numbers.
problem Optimizing expensive stochastic functions with common random numbers.
method Proposes a novel Gaussian process model and Knowledge Gradient for Common Random Numbers.
result Significant performance improvements with moderate computational cost.
This work analyzes PPR-based node embeddings and their topological information.
problem Understanding and interpreting PPR-based node embeddings.
method Unified framework and two methods for topology recovery.
result PPR-based embeddings maintain more topological information than random walk-based embeddings.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
A novel graph-regularized CCA approach for datasets with a common source graph.
problem Discovering hidden sources in datasets with common geometry.
method Graph regularizer to encode common sources' geometry in CCA.
result Improved classification performance over competing methods.
Two spectral algorithms detect clusters in directed graphs with cyclic or acyclic patterns.
problem Detecting clusters in directed graphs with cyclic or acyclic patterns.
method Computation of extremal eigenvalues of the transition matrix associated with the directed graph.
result The proposed methods outperform state-of-the-art methods on synthetic datasets and real-world networks.
The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.
problem Lack of a general guideline for evaluating causal discovery algorithms.
method Derive exact distributional results under random guessing for evaluation metrics and propose a pipeline for using negative controls.
result Evaluation metrics can achieve very favorable values under random guessing, highlighting the need for negative control results.
Attention-based GNNs can't prevent oversmoothing, leading to homogeneous node representations.
problem The issue of oversmoothing in attention-based GNNs.
method Viewed attention-based GNNs as nonlinear time-varying dynamical systems and used tools from the theory of products of inhomogeneous matrices and the joint spectral radius.
result Graph attention mechanism cannot prevent oversmoothing and loses expressive power exponentially.
Proposes a model to clean and analyze network data.
problem Noisy and missing connections in network data.
method Generalized linear model with low rank effects.
result Efficient algorithm for fitting the model and demonstrating its effectiveness.
GLSearch uses GNN to learn efficient search strategies for finding large common subgraphs.
problem Finding the Maximum Common Subgraph (MCS) between two graphs is NP-hard and hard to solve efficiently.
method GLSearch combines GNN and DQN to learn optimal node pairs for expansion in a branch and bound algorithm.
result GLSearch finds significantly larger common subgraphs than heuristic search methods given the same computation budget.
Proposes a probabilistic framework for stationary topological signals on simplicial complexes.
problem Complex data structures require new models and tools.
method Generalizes stationarity to topological signals on simplicial complexes.
result Defines topological power spectral density (PSD) for stationary signals.
New method for faster graph parameter inference from large random Kronecker graphs.
problem Efficiently infer graph parameters from large random Kronecker graphs.
method Decompose adjacency matrix into signal and noise components, then use denoising and solving approach.
result Proposed method achieves comparable or better performance than existing methods at lower computational cost.
GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
Improved graph clustering for sparse graphs using non-backtracking random walks.
problem Improving graph clustering performance for sparse graphs.
method VEC-NBT uses a non-backtracking random walk to modify VEC, a graph embedding technique.
result VEC-NBT achieves comparable or greater accuracy with shorter walks than VEC for sparser graphs.
Graph Neural Networks struggle on random graphs without node identifiers.
problem Graph Neural Networks' limitations on random graphs without node identifiers.
method Study of Graph Neural Networks and Structural Graph Neural Networks convergence on large random graphs.
result Structural Graph Neural Networks are more powerful and universal than Graph Neural Networks on random graphs.
Ripple Walk Training tackles graph neural network training issues for large and deep graphs.
problem Neighbors explosion, node dependence, and oversmoothing in large and deep GNNs.
method Subgraph-based training framework with Ripple Walk Sampler for high-quality subgraph sampling.
result RWT improves training efficiency and reduces space complexity for deep and large GNNs.
In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random k-regular graphs. Moreover we show that …
Generalizes Leighton's theorem to cube complexes.
problem Extending graph covering theorem to cube complexes.
method Generalizes Leighton's theorem to a family of cube complexes.
result Cube complexes have common finite covers.
Introduces higher-order clustering coefficients to better understand network structures.
problem Understanding the clustering behavior of higher-order network cliques in complex networks.
method Develops higher-order clustering coefficients as a generalization of traditional clustering coefficients.
result Provides new insights into the structure of real-world networks.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.