Wave network efficiently propagates long-range information in undirected graphs.
problem Efficiently propagating long-range information in undirected graphs.
method Propagates information in waves of nonlinear computation.
result Wave outperforms graph convolution on three graph-based tasks.
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.
Study on directed graphs using Ricci curvature, extending previous undirected graph results.
problem Generalization of Ricci curvature for directed graphs.
method Introducing a new Ricci curvature for directed graphs using mean transition probability kernel.
result Several geometric and spectral properties of directed graphs under a lower Ricci curvature bound.
Nonparametric undirected graphical model selection using diffusion models
problem Undirected graphical model selection
method Diffusion models
result Model selection consistency
New algorithm reduces regret in multi-agent bandits over undirected graphs.
problem Minimize regret in a multi-agent bandit setting with malicious agents.
method Proposed a new algorithm for undirected graphs, considering the number of malicious neighbors.
result The new algorithm achieves nearly linear regret improvement over existing methods.
Study financial market graphs with Laplacian constraints.
problem Learning undirected graphs in financial markets.
method Proposes algorithms to estimate graphs accounting for financial data properties.
result Guidelines for estimating graphs in financial markets.
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ1 penalization methods. However, current methods assume that the data are independent and identically distributed. If the distribution, and hence the graph, evolves over time t…
Optimizes Thompson Sampling for undirected graphical bandits with optimal regret.
problem Optimizing decision-making in multi-armed bandit problems with varying graph feedback.
method Proposed a variant of Thompson Sampling for undirected and directed graphical bandits.
result Achieved optimal regret bounds for both undirected and directed graphical bandits.
An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to es…
Generalizes k-means to graphs using PageRank.
problem Clustering nodes in directed and undirected graphs.
method Utilizes PageRank to compute node centrality in graphs.
result Robustly computes centrality in graphs and metric spaces.
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define …
New graph operations for stochastic processes improve model flexibility.
problem Limited flexibility in graph convolutional networks for stochastic processes.
method Parameterization of graph-dependent linear operations using functional calculus.
result Improved learning flexibility and richer behaviors in graph models.
Approximates cycles in planar and bounded-genus graphs.
problem Finding many disjoint cycles in planar and bounded-genus graphs.
method Constant-factor approximation algorithms for vertex-disjoint and edge-disjoint cycles.
result First algorithms for vertex-disjoint paths in fully planar and bounded-genus instances.
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…
FastMap-D embeds directed graphs using potential fields.
problem Embedding directed graphs in Euclidean space.
method Generalization of FastMap to handle directed graphs using a potential field and machine learning.
result FastMap-D outperforms other approaches in embedding directed graphs.
In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph b…
New method for testing graph invariants under undirected models.
problem Testing graph invariants under undirected models.
method Skip-down algorithm for monotone graph invariants.
result Optimal and adaptive confidence intervals for graph invariants.
We extend the edge version of the classical Menger's Theorem for undirected graphs to n-dimensional simplicial complexes with chains over the field F2. The classical Menger's Theorem states that two different vertices in an undirected graph can be connected by k pairwise edge-disjoint paths if, and only…
Directed graphs can be intrinsically knotted and 4-linked.
problem Intrinsic linking and knotting in directed graphs.
method Construction of examples and operations (consistent edge contraction, H-cyclic subcontraction).
result Directed graphs can have consistently oriented knotted cycles and intrinsically 3- and 4-linked structures.
The paper defines curvature dimension inequalities on directed graphs and evaluates them.
problem Defining curvature dimension inequalities on directed graphs.
method Defining CD(m, K) on finite directed graphs.
result Evaluates m and K on finite directed graphs.
We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension D to increase with the sample size n. First, we prove lower bounds that show that if we want accurate infe…
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high dimensional inference. Just as additive models extend linear models by replacing linear …
New method clusters directed graphs using Koopman operators.
problem Challenges in clustering directed graphs, especially complex eigenvalues and lack of cluster definition.
method Relate graph Laplacians to transfer operators and metastable sets in stochastic systems, derive clustering algorithms for directed and time-evolving graphs.
result Clusters can be interpreted as coherent sets, useful for analyzing transport and mixing processes.
We solve learning mixtures of graphs from epidemic cascades, establishing conditions and algorithms.
problem Learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades.
method Established necessary and sufficient conditions for polynomial-time solvability, provided efficient algorithms with optimal sample complexity.
result First rigorous conditions and algorithms for learning graph mixtures from epidemic cascades.
Tensor variable elimination for plated factor graphs enables exact inference in models with repeated structure.
problem Efficient inference in models with repeated structure.
method Generalized variable elimination to tensor variable elimination on plated factor graphs.
result Tractable inference for a class of plated factor graphs.
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.
The paper develops formulas to count sizes of Markov equivalence classes of DAGs.
problem Measuring uncertainty and complexity in causal learning from DAGs.
method Introducing core graphs and deriving polynomial size formulas via symbolic computation.
result Efficient formulas for counting sizes of Markov equivalence classes of DAGs.
Study semi-coarse spaces' homotopy and homology, extending coarse geometry.
problem Extend homotopy and homology concepts to semi-coarse spaces.
method Analyze homotopy and construct homology groups invariant under semi-coarse homotopy equivalence.
result Show semi-coarse homology is isomorphic to Vietoris-Rips homology for graphs.
PANDA augments data to regularize graph models, improving parameter estimation and graph construction.
problem Regularizing estimation and construction of undirected graphical models.
method AdaPtive Noise Augmentation (PANDA) iteratively optimizes augmented data loss function.
result Noise-augmented loss function converges to expected penalized loss function, enabling efficient parameter inference.
Graph Gaussian processes use Matérn models for better function learning.
problem Lack of Gaussian process models for graph input spaces.
method Stochastic partial differential equation characterization of Matérn Gaussian processes.
result Graph Matérn Gaussian processes inherit properties of Euclidean and Riemannian models and can be trained efficiently.
Characterizes Bayesian networks up to unconditional equivalence.
problem Characterizing Bayesian networks up to unconditional equivalence.
method Transformational characterization via undirected graphs and specified moves.
result Two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of moves.
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.
R package huge simplifies graph estimation for high-dimensional data.
problem Estimating high-dimensional undirected graphs from data.
method Uses recent results in literature, including recent graph estimation methods.
result Improves on existing package glasso by providing more features and better efficiency.
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text modelling (e.g. conditional random fields). But where Bayesian approaches for d…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers N via a Poisson point process with mean measure Λ on the power set of N. Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected s,t-connectivity problem in graphs.
Deep Q-learning generates directed acyclic graphs.
problem Generating DAGs with specified structures.
method Deep reinforcement learning, specifically deep Q-learning.
result Demonstrated capability of generating DAGs in sparse reward environments.
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ1-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse u…
New models for causal effect identification without directed cycles.
problem Identifying causal effects in complex graphical models.
method Introduces new graphical models with directed, undirected, and bidirected edges, without cycles. Provides algorithms for identification and learning from data.
result Developed algorithms for identifying causal effects in new models and gated models.
Proposes a new model for directed graphs combining deep learning and latent variable models.
problem Graph representation learning for directed graphs.
method Deep Latent Space Model (DLSM) integrating GCN encoder and stochastic decoder with hierarchical variational auto-encoder architecture.
result Achieves state-of-the-art performance on link prediction and community detection tasks.
A new algorithm optimizes multi-way matching problems.
problem Consistent matching of multiple sets of elements.
method Directly optimizes the NP-hard objective using coordinate updates and graph-based initialization.
result Empirically outperforms existing methods on benchmark tasks.
The paper describes the K-theory of C∗-algebras of locally finite graphs.
problem Computing the K-theory of C∗-algebras of locally finite graphs. method Using a directed graph representation and Cuntz-Krieger algebra, the paper computes the K-theory of C∗(Γ). result The K-theory of C∗(Γ) is determined by the graph's genus, number of ends, and dead-ends. In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by m-separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
Convolutional neural networks for graphs improve feature extraction efficiency.
problem Learning from graph data, especially for complex attributes.
method Proposed a framework for learning convolutional neural networks on arbitrary graphs.
result Learned feature representations are competitive with graph kernels and efficient.
New spectral clustering for directed graphs reveals socio-economic patterns.
problem Spectral clustering for directed graphs is unsatisfactory due to edge directionality.
method Proposes a complex-valued matrix representation and analysis for directed graphs.
result Our approach reveals socio-economic patterns in internal migration data.
This paper addresses graph embedding issues and introduces \strap for scalable, non-linear embeddings.
problem Preserving out-degree distributions and conflicting optimization goals on directed graphs.
method Introduces transpose proximity and \strap, a factorization-based algorithm that handles both directed and undirected graphs.
result Proposes \strap, which outperforms state-of-the-art methods in effectiveness and scalability.
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
The covariance graph (aka bi-directed graph) of a probability distribution p is the undirected graph G where two nodes are adjacent iff their corresponding random variables are marginally dependent in p. In this paper, we present a graphical criterion for reading dependencies from G, under the assumption that $…