We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
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48 results for “chordal graphs”
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses t…
A new machine learning approach for generating high-quality chordal extensions.
problem Defining the definitive relation between chordal extension and optimization algorithm performance.
method On-policy imitation learning scheme mimicking the minimum degree rule to generate high-quality chordal extensions.
result On-policy imitation learning approach effectively learns the minimum degree policy and produces graphs with desirable fill-in characteristics.
We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding bisimplicial edges. It follows that chordal graphs and chordal bipartite graphs belong…
New method simplifies Graphical Lasso for chordal graphs.
problem Sparse covariance estimation for large graphs.
method Closed-form solution for chordal graphs, reducing GL to matrix completion.
result Graphical Lasso and thresholding equivalence holds for chordal structures.
New proof shows extendable shellability for simple complexes.
problem Proving extendable shellability for specific simplicial complexes.
method Considering chordal graph structure and linear quotients.
result All -dimensional complexes with vertices are extendably shellable.
Estimates graph connected components from sampled subgraphs.
problem Estimating the number of connected components in large graphs from subgraph samples.
method Subgraph sampling model, focusing on chordal graphs.
result Optimal sample complexity and linear-time estimators for chordal graphs.
GCNs' performance linked to feature, graph, and ground truth alignment.
problem Improving GCNs' classification performance.
method Subspace alignment measure (SAM) based on Frobenius norm of chordal distances.
result SAM quantifies the alignment between features, graph, and ground truth.
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previou…
Completing correlation matricesq-fin.MF
A method to complete incomplete correlation matrices using maximum entropy.
problem Incomplete correlation matrices in financial applications.
method Maximizing entropy of the distribution described by the matrix, constructing a chordal graph.
result A proper correlation matrix can be constructed for large models involving multiple currencies.
New method simplifies causal inference with tiered background knowledge.
problem Large equivalence classes of DAGs limit causal information.
method Integrates tiered background knowledge to create 'tiered MPDAGs' with simplified structure.
result Tiered MPDAGs are chain graphs with chordal components, simplifying causal effect estimation.
A new invariant captures geometric features of circle embeddings.
problem Capturing geometric features of circle embeddings invariantly.
method Chordal distance transform and persistent homology.
result Persistent homology of chordal distance transform is invariant.
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In ge…
We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with…
Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.
problem Understanding the geometry of the space of positive metrics at infinity.
method Using Monge-Ampère equations and test configurations, algebraic descriptions of geodesic rays and chordal distances are derived.
result The Mabuchi chordal distance between geodesic rays associated with ample test configurations equals the spectral distance between their filtrations.
Counts and samples DAGs equivalent to a ground truth DAG.
problem Identifying the number and structure of DAGs equivalent to a ground truth DAG.
method Clique tree representation of chordal graphs for counting and sampling.
result Polynomial time algorithm for counting and sampling in bounded degree graphs.
A new method scores contextual Markov networks without assuming chordality.
problem Learning structure in contextual Markov networks is hard due to many possible structures.
method Marginal pseudo-likelihood as a consistent structure estimator.
result Marginal pseudo-likelihood yields a consistent structure estimator.
New metric spaces for geodesic rays in cohomology classes.
problem Constructing geodesic rays in cohomology classes with finite energy.
method Introduced a chordal metric and proved geodesic properties.
result Found a characterization of geodesic rays in terms of test curves.
Develops a method to efficiently learn causal DAGs using directed clique trees.
problem Efficiently learning causal DAGs in the presence of large cliques.
method Decomposes DAGs into independently orientable components using directed clique trees and designs a two-phase intervention algorithm.
result Proves that the number of single-node interventions necessary to orient any DAG in an EC is at least the sum of half the size of the largest cliques in each chain component of the essential graph.
In this paper we characterize compact extended Ptolemy metric spaces with many circles up to Möbius equivalence. This characterization yields a Möbius characterization of the -dimensional spheres and hemispheres when endowed with their chordal metrics. In particular, we show that every compact extended…
This paper clarifies vine copula structures using graph and matrix representations.
problem Ambiguity in vine copula representations in literature.
method Graph and matrix representations to clarify vine structures, including cherry and chordal sequences.
result A unique matrix representation of vine structures when given a perfect elimination ordering.
New algorithm computes flag mean and median on flag manifolds.
problem Computing first order flag statistics on flag manifolds.
method Transformed problem to Stiefel manifold for optimization.
result Proved convergence and effectiveness of the flag-mean computation.
New algorithms bound graph structure sampling and learning high-dimensional graphical models.
problem Learning high-dimensional graphical models and efficient graph structure sampling.
method Online learning framework with exponentially weighted average (EWA) or randomized weighted majority (RWM) forecasters using log loss function.
result New sample complexity bounds and efficient algorithms for learning Bayes nets, including trees and chordal skeletons.
Paper detects adversarial attacks in sound classification models.
problem Adversarial attacks threaten data-driven models, especially in sound classification.
method Detects adversarial subspaces in unitary vector domain using chordal distance and generalized Schur decomposition.
result Regularized logistic regression detector outperforms other approaches on benchmark datasets.
Estimates log-concave densities in graphical models using tent functions.
problem Maximum likelihood estimation of log-concave densities in undirected graphs.
method MLE as product of tent functions corresponding to maximal cliques.
result MLE can be found via convex optimization.
Communities in social networks or graphs are sets of well-connected, overlapping vertices. The effectiveness of a community detection algorithm is determined by accuracy in finding the ground-truth communities and ability to scale with the size of the data. In this work, we provide three contributions. First, we show t…
New algorithm learns Markov network structures efficiently.
problem Learning Markov network structures without chordality assumptions.
method Local penalized likelihood ratio tests and two-stage hill-climbing algorithm.
result PLRHC-BIC algorithm compares favorably against state-of-the-art methods.
Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective space; the cubic and projective space are identified in term…
Grassmannian packings improve CNN kernels' diversity and reduce sparsity.
problem Kernel sparsity and lack of diversity in CNNs decrease model capacity.
method Initialize CNN kernels with Grassmannian packings to maximize diversity and minimize sparsity.
result Grassmannian packings lead to diverse features and improved classification accuracy.
Unified approach to shape matching using optimal control.
problem Shape registration of curves and surfaces.
method Unified Riemannian metrics, optimal control, chordal distances.
result Unified framework for shape matching.
Geometric regularisation improves statistical models by avoiding degeneracy loci.
problem Non-identifiability, singular information, and moment indeterminacy in statistical models.
method Develops the geometric regularisation of distribution-kernel pairs using Whitney, Thom, and Mather theorems.
result Finite-dimensional weak transversality theorem for generic kernels, avoiding degeneracy strata of high codimension.
BacHMMachine harmonizes Baroque chorales using theory-driven principles and Hidden Markov Models.
problem Algorithmic harmonization of Baroque chorales.
method Theory-driven approach guided by music composition principles, combined with data-driven learning of key and chord transitions.
result BacHMMachine generates musically coherent harmonizations with reduced computational burden and greater interpretability.
A method to compute divergences between decomposable models, useful in supervised learning.
problem Computing exact divergences between high-dimensional distributions is intractable.
method Proposes an approach to compute exact alpha-beta divergences between marginal and conditional distributions of decomposable models.
result Tractable computation of marginal and conditional alpha-beta divergences.
Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
problem Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
method Analyzing the behavior of memory-efficient optimizers like GaLore, which project gradients onto a rank-r subspace recomputed every T steps.
result Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
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.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
Graphons of Line Graphsstat.ML
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
edGNN improves graph embeddings for directed labeled graphs.
problem Improving node and graph embeddings for directed labeled graphs.
method edGNN is a GNN designed for directed labeled graphs, leveraging both topology and labels.
result edGNN is as powerful as the Weisfeiler-Lehman algorithm for graph isomorphism.
Graph CNNs adapt to varying graph structures for better performance.
problem Fixed graph structures limit the performance of Graph CNNs on real data.
method Adaptive graph learning and distance metric learning for efficient graph construction.
result Adaptive Graph CNNs improve convergence speed and predictive accuracy on various graph datasets.
MxPool learns graph features from diverse graphs using a hierarchical structure.
problem Learning graph features from diverse graphs with varying properties and sizes.
method MxPool uses a multiplex structure with multiple graph convolution/pooling networks in a hierarchical learning structure.
result MxPool outperforms state-of-the-art methods on graph classification benchmarks.
Study the geometry of graph product extension graphs.
problem Properties of graph products.
method Introduce and study the extension graph of graph products of groups.
result Extension graph is isomorphic to crossing graph of a quasi-median graph and exhibits asymptotic dimension similar to quasi-trees.
Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
UGRAPHEMB embeds graphs into vectors preserving their proximity, achieving competitive results.
problem Graph-level representation learning in an unsupervised and inductive manner.
method UGRAPHEMB uses graph-graph proximity to embed graphs into a vector space. MSNA generates multi-scale node attention for graph-level embedding.
result UGRAPHEMB achieves competitive accuracy in graph classification, similarity ranking, and visualization tasks.
Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
problem Quasi-transitive graphs quasi-isometric to planar graphs need to be upgraded to Cayley graphs.
method Upgrading a planar graph to a Cayley graph.
result Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
Deep Divergence Graph Kernels learn graph representations without supervision.
problem Learning graph representations without feature engineering or labeled graphs.
method Unsupervised method using cross-graph attention networks and divergence scores.
result Learned representations achieve competitive results on graph classification tasks.
Paper proposes a new graph embedding framework to improve graph analytics.
problem Graph embedding often fails to capture the distribution of latent codes.
method Adversarial graph autoencoder framework that combines topological structure and node content.
result ARGA and ARVGA outperform baselines in link prediction, clustering, and visualization.
GRAPH-BERT uses only attention for graph representation learning.
problem Graph neural networks over-rely on graph links and suffer from performance issues.
method GRAPH-BERT uses only attention mechanism without graph convolution or aggregation, trained on sampled subgraphs.
result GRAPH-BERT outperforms existing GNNs in learning effectiveness and efficiency.