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Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions and a proper learning algorithm, it…
We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables…
We study the problem of learning the topology of a directed Gaussian Graphical Model under the equal-variance assumption, where the graph has $n$ nodes and maximum in-degree $d$. Prior work has established that $O(d \log n)$ samples are…
The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of…
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…
Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large…
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG…
We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert…
We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by…
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…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is…
Directed acyclic graphs (DAGs) constitute a central modeling tool to enable principled reasoning about cause-effect interactions in complex systems. However, since the causal structure underlying a group of variables is often unknown and…
Recent advances in differentiable structure learning have framed the combinatorial problem of learning directed acyclic graphs as a continuous optimization problem. Various aspects, including data standardization, have been studied to…
We are interested in the problem of learning the directed acyclic graph (DAG) when data are generated from a linear structural equation model (SEM) and the causal structure can be characterized by a polytree. Under the Gaussian polytree…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…
We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…
We address the issue of recovering the structure of large sparse directed acyclic graphs from noisy observations of the system. We propose a novel procedure based on a specific formulation of the l1-norm regularized maximum likelihood,…