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.
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48 results for “Directed Acyclic Graphical Models”
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
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…
Unifying DAGs and UGsstat.ML
We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed between any pair of nodes. Specifically, we present local, pairwise and global Marko…
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.
Develops methods for constructing parameter priors in DAG models.
problem Constructing parameter priors for model choice among DAG models.
method Introduces assumptions and methods for parameter priors construction and marginal likelihood computation.
result The only parameter prior for complete Gaussian DAG models that satisfies assumptions is the normal-Wishart distribution.
We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identifica…
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.
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
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.
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.
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…
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.
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed procedure i…
Identifies causal effects in partially directed acyclic graphs with observed variables.
problem Identifying conditional causal effects in graphs with background knowledge and observed variables.
method Three results: identification formula, do calculus generalization, and algorithm completeness.
result Complete algorithm for identifying conditional effects in MPDAGs.
Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG) models. In many applications, feedback naturally arises and directed graphical models …
Study identifies parameters in causal models with latent confounding.
problem Parameter identification in linear non-Gaussian causal models with latent confounding.
method Graphical criterion for necessary and sufficient identifiability of direct causal effects, with polynomial-time algorithm.
result Developed a graphical criterion for identifying direct causal effects in latent variable models with arbitrary non-linear confounding.
Scalable method learns context-specific models for hundreds of variables.
problem Learning context-specific models for large numbers of variables.
method Order-based Markov chain Monte-Carlo search with context-specific sparsity assumption.
result Method scales to hundreds of variables and learns accurate models.
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with curren…
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…
Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large parameter space and the difficulty in searching for a sparse structure. In this article,…
Identifies causal effects in LiNGAM models with latent variables.
problem Identifying causal effects in LiNGAM models with latent confounders.
method Complete graphical characterization and efficient algorithms for certification. RICA adaptation for estimation.
result Efficient algorithms and RICA adaptation for estimating causal effects.
Polynomial-time methods count and sample DAGs from Markov classes.
problem Counting and sampling Markov equivalent DAGs.
method Polynomial-time algorithms for DAGs from Markov classes.
result Long-standing open problem solved, making practical infeasible strategies feasible.
With the growth of deep learning, how to describe deep neural networks unifiedly is becoming an important issue. We first formalize neural networks mathematically with their directed graph representations, and prove a generation theorem about the induced networks of connected directed acyclic graphs. Then, we set up a …
Optimal sample complexity for learning Gaussian DAG models established.
problem Learning the structure of Gaussian DAG models from observational data.
method Established minimax optimal sample complexity for two settings: equal variances without ordering knowledge and general linear models with ordering knowledge.
result Optimal sample complexity for both settings, matching undirected graphical models under equal variances.
Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphsstat.ML
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other.…
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
The paper shows cross-validation fails in learning Gaussian graphical model structures.
problem Cross-validation's failure in learning Gaussian graphical model structures.
method Finite-sample bounds on misidentification probability of Lasso estimator.
result Cross-validation is inconsistent for learning Gaussian graphical model structures.
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhoo…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional…
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). T…
Paper proves global optimality of a simple optimization scheme for learning DAG models.
problem Learning acyclic directed graphical models from data.
method Path-following optimization scheme for bivariate setting.
result Simple optimization scheme globally converges to global minimum.
We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and introduce a feasible approach in which parameter and structure sea…
In Peña (2007), MCMC sampling is applied to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend that work from 20 to 31 nodes. We also extend that work by computing the approximate ratio of connected EGs to connected DAGs, of …
We develop a method to summarize causal models with cycles in cubic time.
problem Cycles in high-dimensional causal models limit applicability of existing methods.
method We relax the acyclicity assumption in LiNG models and develop a low-dimensional DAG summary.
result Our method allows recovery of a low-dimensional DAG from high-dimensional data with cycles.
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and e…
GES algorithm improves consistency for nonparametric DAG models.
problem Consistent estimation of nonparametric DAG models.
method Greedy equivalence search with new consistency proof for nonparametric families.
result Consistency of GES for general nonparametric DAG models with smooth factorization.
Algorithm learns Bayesian network structure efficiently from data.
problem Learning directed acyclic graphical models from observational data.
method Local Markov boundary search procedure to recursively construct ancestral sets.
result Simple greedy search algorithm learns Markov boundary of each node efficiently.
The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs). SPNs are d…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which …
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with . Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estima…
Coarsening Causal DAG Modelsstat.ML
We develop a method to learn abstract causal graphs from interventional data.
problem Estimating causal models at fine granularity is impractical or undesirable.
method Novel graphical identifiability results and an efficient algorithm.
result Directly learns abstract causal graphs from interventional data.
The paper introduces tests for missing data models based on graph assumptions.
problem Verification of assumptions in missing data models is insufficiently addressed.
method The paper explores three classes of missing data models and designs goodness-of-fit tests.
result The paper provides new insights and tests for missing data graphical models.
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 algorithm speeds up learning of graphical models.
problem Learning graphical models with sparse structure efficiently.
method Vertex-greedy score-based algorithm for learning DAGs.
result Polynomial runtime for learning DAG models.
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible…