Related papers: Optimal estimation of Gaussian DAG models

Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved…

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…

Parallel real-time systems (e.g., autonomous driving systems) often contain functionalities with complex dependencies and execution uncertainties, leading to significant timing variability which can be represented as a probabilistic…

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To…

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose…

Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper…

A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables.…

We prove that the true underlying directed acyclic graph (DAG) in Gaussian linear structural equation models is identifiable as the minimum-trace DAG when the error variances are weakly increasing with respect to the true causal ordering.…

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…

Counting and uniform sampling of directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we show that these tasks can be performed in polynomial time, solving a…

We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum…

We consider the problem of learning a Bayesian network or directed acyclic graph (DAG) model from observational data. A number of constraint-based, score-based and hybrid algorithms have been developed for this purpose. For constraint-based…

We consider the problem of learning a directed graph $G^\star$ from observational data. We assume that the distribution which gives rise to the samples is Markov and faithful to the graph $G^\star$ and that there are no unobserved…

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…

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.…

Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…

Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a…

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only…