Extends causal additive models to include higher-order interactions.
problem Inferring causal insights from data with higher-order mechanisms.
method Introduces directed acyclic hypergraphs to represent higher-order interactions in causal structure learning.
result Learning more complex hypergraphs can lead to better empirical results.
A new method for clearing liability networks using sheaves on directed hypergraphs.
problem Clearing in liability networks using a novel mathematical approach.
method Associate a liability sheaf on a directed hypergraph to a liability network, identifying clearing configurations as global sections of this sheaf.
result Clearing configurations are precisely the global sections of the sheaf, and the sheaf construction is functorial under change of coefficient category.
Develops neural network for directed hypergraphs for node classification.
problem Irregular data structure, particularly directed graphs.
method Directed hypergraph neural network and semi-supervised learning method.
result Novel directed hypergraph neural network achieves highest accuracies on node classification tasks.
During the last two decades, we easilly see that the World Wide Web's link structure is modeled as the directed graph. In this paper, we will model the World Wide Web's link structure as the directed hypergraph. Moreover, we will develop the PageRank algorithm for this directed hypergraph. Due to the lack of the World …
Bayesian nonparametric approach for clustering non-exchangeable groups.
problem Clustering grouped data with dependencies among groups.
method Graphical Dirichlet process modeling with Markov property.
result Efficient posterior inference algorithm developed.
Unified LLY Ricci curvature defined for hypergraphs.
problem Defining Ricci curvature for hypergraphs.
method Unified framework for LLY Ricci curvature on hypergraphs, establishing bounds and proving properties.
result Bonnet-Myers-type theorem for hypergraphs, highlighting curvature's potential in hypergraph analysis.
New method learns DAGs from data without acyclicity constraint.
problem Learning DAGs from data without imposing acyclicity.
method Sparse matrix factorization and ℓ1-penalized optimization. result Empirical success in recovering true graphs and almost-DAG graphs.
Paper introduces models to discover complex structures in large hypergraphs.
problem Understanding dependency structures in complex systems represented as hypergraphs.
method Probabilistic models treating classes of similar units as nodes in a latent hypergraph, using low-rank representations.
result Improves link prediction and discovers interpretable structures in diverse real-world systems.
Develops a new method for learning non-parametric DAGs using RKHS.
problem Challenges of learning non-parametric causal models with large combinatorial search space.
method Uses reproducing kernel Hilbert spaces (RKHS) and sparsity-inducing regularization terms based on partial derivatives to enforce acyclicity.
result Shows improved performance through simulations and data analyses.
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".
The paper tackles learning varying DAG structures based on contextual features.
problem Learning a single DAG for the entire population from observational data.
method A neural network that maps contextual features to a weighted adjacency matrix of a DAG, with a projection layer to ensure acyclicity.
result The new approach can recover context-specific DAGs where existing methods fail.
Neural networks with DAGs show linearity as width increases.
problem Understanding linearity in neural networks with arbitrary DAG structures.
method Analyzing the transition to linearity in networks with arbitrary DAGs, characterizing width by minimum in-degree.
result General neural networks with DAGs exhibit linearity as width approaches infinity.
ENCOD learns causal graphs efficiently without acyclicity constraints.
problem Learning causal graphical models from observational and interventional data.
method ENCOD uses optimization of edge likelihoods with separate orientation parameters.
result ENCOD efficiently recovers large graphs (hundreds of nodes) without acyclicity constraints.
ALIAS uses RL to learn DAGs without acyclicity constraints.
problem Efficiently learning DAGs from observational data without acyclicity constraints.
method ALIAS employs RL to generate DAGs in a single step with optimal complexity, bypassing acyclicity constraints.
result ALIAS outperforms state-of-the-art methods in causal discovery.
ProDAG uses variational inference to learn DAGs with uncertainty quantification.
problem Statistical and computational challenges in learning a single DAG from data.
method Bayesian variational inference framework with novel distributions.
result ProDAG outperforms state-of-the-art alternatives in accuracy and uncertainty quantification.
DAGgr aggregates multiple DAGs to stabilize causal structure learning.
problem Stability in learning causal structure from data.
method Model averaging of candidate DAGs weighted by predictive likelihood, with acyclicity enforced.
result DAGgr consistently outperforms individual DAGs and bootstrap-aggregation baselines.
Paper proposes methods to learn DAGs from partial orderings.
problem Learning DAGs from partial orderings is challenging.
method General estimation framework and efficient algorithms for low- and high-dimensional problems.
result Efficient estimation of DAGs from partial orderings is possible.
Paper proposes DAG-DB for learning discrete DAGs via backpropagation.
problem Learning Directed Acyclic Graphs (DAGs) from data.
method DAG-DB uses Discrete Backpropagation with I-MLE and Straight-Through Estimation.
result DAG-DB learns DAGs effectively using probabilistic sampling and backpropagation.
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivi…
CSHT predicts financial returns from news using a novel transformer model on a sphere.
problem Financial forecasting from news and sentiment.
method Granger-causal hypergraph structure, Riemannian geometry, causally masked Transformer attention.
result CSHT outperforms baselines in return prediction, regime classification, and asset ranking.
We explore non-acyclic GFlowNets in discrete settings.
problem Training and understanding non-acyclic GFlowNets in discrete environments.
method Relaxing acyclicity assumption, simpler theoretical framework, novel theoretical insights, experimental validation.
result Theoretical and experimental validation of non-acyclic GFlowNets in discrete environments.
PIVID infers DAG structures from data using variational inference and permutations.
problem Estimating the structure of Bayesian networks from observational data.
method PIVID uses variational inference and continuous relaxations of discrete distributions to infer a distribution over permutations and DAGs.
result PIVID outperforms deterministic and Bayesian approaches in estimating DAG structures from data.
We present a method to generate directed acyclic graphs (DAGs) using deep reinforcement learning, specifically deep Q-learning. Generating graphs with specified structures is an important and challenging task in various application fields, however most current graph generation methods produce graphs with undirected edg…
COSMO learns DAG structure without acyclicity constraints.
problem Learning DAG structure from data efficiently and without constraints.
method Differentiable approximation of smooth orientation matrix.
result COSMO converges to acyclic solutions without evaluating acyclicity.
The Conant-Ashby theorem is verified for hypergraph observers, leading to unique learning rules.
problem Verifying conditions for hypergraph observers to maintain internal models.
method Formalizing persistent observers, applying the Conant-Ashby theorem, and using natural gradient descent.
result Natural gradient descent is the unique admissible learning rule for hypergraph observers.
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
problem Missing structure in pairwise Fisher graphs for multi-observable radiation patterns.
method Higher-order Fisher tensors and natural exponential-family coordinates.
result Exact triality of Fisher tensors, cumulants, and hypergraphs.
The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.
problem Conditions for integral homology 3-spheres to bound acyclic smooth 4-manifolds and their symplectic fillings.
method Structural results and analysis of smooth embeddings of lens spaces in C2. result Smooth embeddings of connected sums of lens spaces in C2 cannot be upgraded to Stein embeddings. New method uses information theory to uncover causal relationships in complex systems.
problem Discovering causal relationships in multivariate systems, especially in Bayesian networks and hypergraphs.
method Partial Information Decomposition (PID) to explicitly model higher-order interactions.
result PID components reveal direct causal neighbors and collider relationships in Bayesian networks and multi-tail hyperedges in causal hypergraphs.
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underl…
In this note we derive enumerative formulas for several types of labelled acyclic directed graphs by slight modifications of the familiar recursive formula for simple acyclic digraphs. These considerations are motivated by, and based upon, recent combinatorial results in geometric topology obtained by S.Choi, who estab…
The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditi…
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.
Study of Betti numbers in prodsimplicial complexes for directed graphs, focusing on DNA recombination.
problem Analyzing Betti numbers in directed graphs for DNA recombination.
method Custom prodsimplicial complexes for acyclic directed graphs, investigating Betti numbers.
result Investigated Betti numbers and cycles in prodsimplicial complexes for DNA recombination.
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions. In this paper, we present a new learning frame…
Study compares hypergraph and graph-level models for higher-order relational learning.
problem Evaluating effectiveness of hypergraph-level vs. graph-level models in relational learning.
method Systematic evaluation of various hypergraph and graph-level architectures.
result Graph-level models applied to hypergraph expansions outperform hypergraph-level models.
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
problem The size of Markov equivalence classes under relaxed assumptions.
method Analytical proofs for three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
result Exponentially large lower bounds for the expected size of Markov equivalence classes.
Develops a Markov Random Field model for hypergraphs to improve machine learning tasks.
problem Modeling data generation processes on hypergraphs for better machine learning.
method Hypergraph Markov Random Field model using multivariate Gaussian distribution.
result Proposed model enhances algorithm design and outperforms existing methods in structure inference and node classification.
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
problem Challenges in capturing hypergraph structure and text attributes in node classification.
method Mixing hypergraph-aware layers with BERT for improved node classification.
result HyperBERT achieves state-of-the-art results on text-attributed hypergraph benchmarks.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
Extends graph theory to hypergraphs with manifold-valued nodes.
problem Representing complex N-ary relationships on manifolds.
method Defined function spaces and symmetric products for manifold-valued nodes and edges.
result Generalized hypergraph Laplacians to manifold-valued hypergraphs.
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs, that does not require that the ver…
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph p-Laplacian. Unlike the …
Study counterfactuals in cyclic systems with shifts and scales.
problem Counterfactual inference in cyclic systems with shifts and scales.
method Shift-scale interventions in cyclic SCMs.
result Valid inference in cyclic systems with shifts and scales.
DAGSurv uses deep neural networks to analyze survival data based on causal graphs.
problem Analyzing survival data with causal relationships between variables.
method Variational inference-based conditional variational autoencoder for causal structured survival prediction.
result DAGSurv outperforms other survival analysis methods in predicting time-to-event.
Paper introduces a noise-robust classification method using hypergraph neural networks.
problem Noisy label learning problem in image datasets.
method PCA for dimensionality reduction, then applies graph-based semi-supervised learning methods including hypergraph neural network.
result Our proposed hypergraph neural network achieves the best performance when noise level increases.
New method detects communities in hypergraphs by embedding them into a vector space.
problem Detecting communities in hypergraphs with multi-way interactions.
method Augmenting non-uniform hypergraphs, embedding into a vector space, using an alternative updating scheme.
result Asymptotic consistencies in community detection and hypergraph estimation established.
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional independencies, and are especially useful in modeling the effects of latent variables im…