This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property…
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48 results for “graph property testing”
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
The paper tests properties of trees in graphical models using covariance queries.
problem Testing properties of trees in graphical models.
method Covariance queries model, randomized tests for tree properties.
result Efficient testing of global tree properties using sub-quadratic number of queries.
Polynomial delay algorithm tests causal models with hidden variables.
problem Testing causal models with hidden variables in polynomial delay.
method c-component local Markov property (C-LMP) and polynomial delay algorithm.
result First algorithm for poly-delay testing of CIs in causal graphs with hidden variables.
We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics a…
k-hop Graph Neural Networksstat.ML
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot…
This paper evaluates LLMs on large graph property estimation tasks.
problem Limited context length of LLMs limits their evaluation on large graphs.
method Developed EstGraph dataset and introduced four tasks for LLMs to estimate large graph properties.
result LLMs perform better on graph property estimation tasks when provided with context-rich prompts based on random walks.
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented,…
With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to traditional graph techniques, they are still perceived as techniques with limite…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We find that none of the classical numerical graph invariants by itself allows to s…
DeepGG generates graph distributions for drug discovery and molecular design.
problem Learning graph distributions for various applications.
method Improved deep graph generator based on deep state machines with graph and node embeddings.
result The state machine design favors specific graph distributions.
Efficient algorithms learn causal graphs with minimal interventions.
problem Learning causal relationships between observed variables in the presence of latents.
method Bi-criteria approximation goal combining intervention design and graph property testing.
result Achieve intervention cost within a small constant factor of the optimal.
A new test assesses how well observed networks fit a specified ERGM model.
problem Testing the goodness of fit for ERGMs with a single network observation.
method Kernel Stein discrepancy combined with a discrete Stein operator for ERGMs, Monte Carlo simulation.
result The test provides theoretical and practical support for assessing ERGM fit.
Rotationally equivariant convolutions improve molecular property prediction.
problem Predicting molecular properties using graph neural networks.
method Ablation study with rotationally equivariant and invariant convolutions on QM9 data set.
result Rotationally equivariant layers decrease test error by an average of 23%.
The study evaluates GRL approaches and finds limitations in their applicability.
problem Challenges in applying GRL approaches to real-world graphs with varying structural differences.
method Empirical data-driven framework and theoretical analysis of GRL approaches.
result Existing GRL approaches are insufficient for real-world graphs with diverse structural patterns.
Develops methods to analyze manifold singularities using graph Laplacian.
problem Analyzing geometric properties of singularities in datasets.
method Theory and methods using the graph Laplacian to provide explicit bounds on manifold singularities.
result Explicit bounds on the graph Laplacian for functions near manifold singularities.
A new readout layer improves graph property prediction.
problem Graph property prediction challenges due to information loss.
method Introduces a novel generalized global pooling layer for Message-Passing Neural Networks.
result New state-of-the-art results in graph property prediction.
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph in the low dimensional space. However, real world graphs have a combination of s…
Extends graph similarity theory to improve MPNNs' generalization abilities.
problem Understanding MPNNs' generalization beyond training data.
method Extends graph similarity theory, assesses graph structure, aggregation, and loss functions.
result Improves understanding of MPNNs' generalization properties.
Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph models have been proposed to explain the macroscopic properties of these systems and to provide a foundation for statistical inferences and predictions. It is of interest to…
Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphsmath.ST
Paper studies minimax optimal regression using Laplacian smoothing over graphs.
problem Minimax optimal regression over Sobolev spaces.
method Laplacian smoothing on neighborhood graphs.
result Upper bounds match minimax optimal rates for first-order Sobolev class.
This work investigates how GCNs should handle local structure discrepancies in testing nodes.
problem GCNs assume homophily but real graphs often have discrepancies in local structure.
method Using causal graph analysis, the study intervenes the graph structure to assess the local structure's impact on predictions.
result The method effectively enhances GCN predictions by eliminating local structure discrepancies.
Improved symbolic regression finds optimal formulas robust to noise.
problem Finding accurate formulas for noisy data.
method Exploits graph modularity, uses normalizing flows, and statistical hypothesis testing.
result Discoveres many formulas previously unattainable.
A new test detects noise in graph data, useful for forecasting.
problem Detecting uncorrelated noise in graph data.
method Spatio-temporal extension of traditional tests, using graph signals.
result Asymptotic distribution known, no assumption of identically distributed data.
In graph instance representation learning, both the diverse graph instance sizes and the graph node orderless property have been the major obstacles that render existing representation learning models fail to work. In this paper, we will examine the effectiveness of GRAPH-BERT on graph instance representation learning,…
The paper explores statistical limits for detecting correlation in tree structures.
problem Detecting correlation between two tree structures.
method Investigates conditions for existence of one-sided tests in the limit of large tree depth.
result Identifies a phase transition at correlation parameter , where tests exist for .
This work evaluates graph models' robustness to structural distributional shifts.
problem Evaluating graph models' robustness to structural distributional shifts.
method Proposes a general approach for inducing diverse distributional shifts based on graph structure.
result Simple models often outperform more sophisticated methods on structural distributional shifts.
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory fl…
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.
Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good graph representation must satisfy the preservation of structural information, w…
A new algorithm reduces CI tests for causal graph recovery.
problem Exponential CI tests limit causal discovery algorithms.
method CCPG (Causal Consistent Partition Graph) with polynomial CI tests.
result CCPG efficiently recovers causal graph with polynomial tests.
Study evaluates RKHS choices for assessing graph models using KSD tests.
problem Effect of RKHS choice on KSD tests for graph model assessment.
method Investigated power performance and computational runtime of KSD tests for ERGMs and synthetic graph generators.
result Different RKHS choices affect KSD test performance and computational runtime.
Graph Substructure Networks (GSN) improves GNN expressivity by counting subgraph isomorphisms.
problem Limited expressivity of GNNs in detecting and counting graph substructures.
method Topologically-aware message passing scheme based on substructure encoding.
result GSN is strictly more expressive than the Weisfeiler-Leman (WL) test and can disambiguate even hard graph isomorphism instances.
Study shows it's impossible to count communities without finding them.
problem Determining the number and sizes of communities in random graph models.
method Hypothesis testing between models with different community structures, using low-degree polynomial framework.
result Testing between two different planted distributions is as hard as finding the communities.
Study shows gMPNNs struggle with OOD link prediction in larger test graphs.
problem Inductive out-of-distribution link prediction in larger test graphs.
method Theoretical analysis and development of a gMPNN with structural pairwise embeddings.
result Structural node embeddings from gMPNNs converge to random guessing as test graphs grow.
Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies in statistics and learning theory have provided some theoretical insights about …
A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancystat.ML
A new test for IRG models using KSD for small networks.
problem Testing goodness-of-fit for inhomogeneous random graph models.
method Kernelised Stein Discrepancy (KSD) test for IRG models.
result The test is effective for small networks and provides theoretical guarantees.
Novel graph network learns hierarchical network structure.
problem Lack of information in hierarchical network topology.
method Hierarchical clustering for multiscale decomposition, graph convolutional layers.
result Competitive performance on citation network benchmark.
Explains differences between WL and folklore-WL formulations in graph neural networks.
problem Understanding the differences between WL and folklore-WL formulations in graph neural networks.
method Visual explanation of differences between WL and folklore-WL formulations.
result Clarifies the differences between WL and folklore-WL formulations.
A scalable method to learn causal graphs from large data.
problem Learning causal graphs from large scale data is challenging.
method Differentiable Adjacency Test (DAT) to evaluate adjacency in causal graphs.
result DAT-Graph can learn graphs of 1000 variables with state-of-the-art accuracy.
DYMAG uses dynamic waveforms to improve graph neural networks.
problem Improving graph neural networks for better graph understanding.
method DYMAG employs dynamical system-based waveforms for message aggregation in graph neural networks.
result DYMAG outperforms baseline models in graph recovery, property prediction, and random graph generation.
Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However, most of the existing graph neural networks suffer from the following limitations…
New method for testing directed graphs using surrogate data.
problem No established method for statistical testing on directed graphs.
method Define directed graph wide-sense stationary signals, generate surrogates preserving covariance, construct null distributions.
result Feasibility and superiority of new approach over existing methods.
OmniMatch algorithm perfectly matches graphs without edge correlation.
problem Graph matching in the absence of edge correlation.
method OmniMatch algorithm for seeded multiple graph matching.
result OmniMatch aligns unseeded vertices across multiple networks efficiently and perfectly.
Polynomial-time test for detecting dense subgraphs in heterogeneous networks.
problem Detecting a planted community in heterogeneous networks.
method Proposes a polynomial-time test with a standard normal distribution null limiting distribution.
result The test is efficient and performs well in both simulations and real data.
Tests if vertices in graphs have the same latent positions.
problem Testing equality of latent positions in random graphs.
method Empirical Mahalanobis distances from spectral embeddings.
result Test statistics follow chi-square distributions under null and local alternatives.
Materials property prediction using symmetry-labeled graphs as atomic-position independent descriptorscond-mat.mtrl-sci
Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning …