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Directed acyclic graph (DAG) has been widely employed to represent directional relationships among a set of collected nodes. Yet, the available data in one single study is often limited for accurate DAG reconstruction, whereas heterogeneous…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
A directed acyclic graph (DAG) partially represents the conditional independence structure among observations of a system if the local Markov condition holds, that is, if every variable is independent of its non-descendants given its…
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
Directed acyclic graph (DAG) models are widely used to represent causal relationships among random variables in many application domains. This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no…
Directed acyclic graphical models, or DAG models, are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed…
We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a…
Mainly motivated by the problem of modelling directional dependence relationships for multivariate count data in high-dimensional settings, we present a new algorithm, called learnDAG, for learning the structure of directed acyclic graphs…
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…
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…
Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference,…
The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed…
Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…
In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this…
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…