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…
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48 results for “acyclic directed mixed graphs”
New method learns graph structure with hidden causes from observational data.
problem Learning the structure of linear non-Gaussian models with hidden causes.
method Augments hidden variable structure by learning multidirected edges and uses higher order cumulants.
result Correct structure recovery for bow-free acyclic mixed graphs with multi-directed edges.
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.
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.
We solve structure learning for cyclic linear causal models using observational data.
problem Learning the structure of cyclic linear causal models from observational data.
method Assuming simple graphs, we use a criterion for distributional equivalence and implement a greedy search method.
result We show that simple cyclic models are of expected dimension and justify score-based methods for structure learning.
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.
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence…
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 -separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
New graph model handles cycles and latent variables.
problem Models for cycles and latent variables.
method Directed graphs with hyperedges (HEDGes), Markov properties.
result Markov properties for HEDGes are not equivalent.
NOTMAD estimates context-specific Bayesian networks without breaking datasets.
problem Non-convexity of acyclic graphs limits sharing information between context-specific estimators.
method NOTMAD models context-specific Bayesian networks as mixtures of archetypal DAGs, estimating structures and parameters jointly.
result NOTMAD shares information between context-specific acyclic graphs, enabling single-sample resolution.
In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclas…
New method recovers causal DAGs from general environments without strict assumptions.
problem Recovering causal DAGs from real-world data with varying distributions.
method Formalizes desiderata for causal representation learning in general environments, leveraging sufficient change conditions up to third-order derivatives.
result Fully recovers latent DAG and identifies latent variables up to minor indeterminacies under nonparametric mixing.
New method learns DAGs from data without acyclicity constraint.
problem Learning DAGs from data without imposing acyclicity.
method Sparse matrix factorization and -penalized optimization.
result Empirical success in recovering true graphs and almost-DAG graphs.
"Mixed Data" comprising a large number of heterogeneous variables (e.g. count, binary, continuous, skewed continuous, among other data types) are prevalent in varied areas such as genomics and proteomics, imaging genetics, national security, social networking, and Internet advertising. There have been limited efforts a…
Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Modelsstat.ME
New method learns DAGs from noisy data without identifiability assumptions.
problem Learning DAGs from non-identifiable Gaussian models with heteroscedastic noise.
method Mixed-integer programming framework for medium-sized problems.
result Asymptotically optimal solution with early stopping criterion.
An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Modelscs.LG
Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization …
This paper extends stable blanket theory to models with hidden variables and causal cycles.
problem Identifying stable predictors in models with hidden variables and causal cycles.
method Use acyclic directed mixed graphs (ADMGs) and directed graphs (DGs) with -separation and -separation to characterize and construct intervention-stable predictor sets.
result Graphical characterizations of Markov blankets, stable frontiers, and stable blankets in models with hidden variables and cycles.
PAG2ADMG algorithm enumerates all causal graphs consistent with a Markov equivalence class.
problem Lack of methods to enumerate all causal graphs consistent with a Markov equivalence class.
method PAG2ADMG algorithm converts a given PAG into the complete set of ADGMs consistent with the Markov equivalence class.
result First algorithm for enumerating all causal graphs consistent with a Markov equivalence class.
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.
Unifying DAGs and UGsstat.ML
New graph model relaxes acyclic constraint for better flexibility.
problem Graphical model constraints limit flexibility.
method Introduces new graphical models with relaxed constraints.
result New models allow directed cycles and up to two edges between nodes.
Supplement to "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs"stat.ML
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.
New algorithm identifies missing data models using directed acyclic graphs.
problem Identifying missing data distributions represented by DAGs.
method Proposed a new algorithm that generalizes ID algorithm for causal inference.
result Significantly generalizes types of manipulations for identification.
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.
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…
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.
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.
A new sampler improves the inference of causal structures from observational data.
problem Inferring causal relationships from observational data when DAGs are Markov equivalent.
method Developed a non-reversible Markov chain, Causal Zig-Zag sampler, targeting Markov Equivalence Classes of DAGs.
result The sampler improves mixing and offers efficient algorithms for DAG inference.
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.
Paper solves DAG learning from continuous data using integer programming.
problem Learning optimal DAGs from continuous observational data.
method Formulated as mixed-integer quadratic optimization (MIQO) model with penalties and regularizations.
result LN formulation outperforms existing methods in computational time and optimality.
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.
Betti Numbers of Prodsimplicial Complexes for Directed Graphs with Applications to Word Reductionsmath.CO
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.
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 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.
We embed directed acyclic graphs using hyperbolic spaces and geodesic cones.
problem Learning graph representations that preserve hierarchical structure.
method Use hyperbolic spaces and geodesic cones to define embeddings of directed acyclic graphs.
result Our method significantly outperforms existing approaches in graph representation learning.
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.
Front-door Reducibility: Reducing ADMGs to the Standard Front-door Setting via a Graphical Criterionstat.ML
FDR criterion simplifies complex causal graphs to a standard front-door setting.
problem Complex causal graphs make identification of causal effects difficult and computationally infeasible.
method Front-door reducibility (FDR) criterion and FDR-TID algorithm.
result Many graphs can be simplified to a standard front-door setting, making causal effect identification simpler and more interpretable.
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.
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.
Introduces m-connecting imset and factorization for ADMG models.
problem Handling latent confounding in DAG models.
method Introduces m-connecting imset and m-connecting factorization criterion for ADMG models.
result Equivalence of m-connecting factorization criterion to global Markov property.
Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.
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.
Stable mixed graphsstat.OT
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the -separation criterion. These include MC, summary, and ancestral grap…
ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulationscs.LG
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
Unified framework for clustering and learning causal graphs across subjects.
problem Bias and obscured subpopulation-specific dependencies in multivariate systems.
method Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM) integrated with Structural Equation Modeling (SEM).
result Unified framework recovers cluster-specific causal dependency structures with high true positive rate and low false discovery rate.
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.
Proposes an approach to ensure acyclic graphs in Bayesian structure learning.
problem Ensuring acyclic graphs in Bayesian structure learning.
method Integration of knowledge from topological orderings to constrain acyclicty.
result Outperforms related Bayesian score-based approaches in experiments.
New MIP model and algorithms for Bayesian network learning.
problem Optimization problems with acyclic constraints on directed graphs.
method Mixed integer programming model and iterative algorithms based on topological orders.
result Significantly lower number of constraints and efficient search of topological orders.