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We propose an empirical Bayes formulation of the structure learning problem, where the prior specification assumes that all node variables have the same error variance, an assumption known to ensure the identifiability of the underlying…
The dicycle transversal number t(D) of a digraph D is the minimum size of a dicycle transversal of D, i. e. a set T of vertices of D such that D-T is acyclic. We study the following problem: Given a digraph D, decide if there is a dicycle B…
We focus on the extension of bivariate causal learning methods into multivariate problem settings in a systematic manner via a novel framework. It is purposive to augment the scale to which bivariate causal discovery approaches can be…
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…
This paper explores the conditions for determining fixed nodes in structured networks, specifically focusing on directed acyclic graphs (DAGs). We introduce several necessary and sufficient conditions for determining fixed nodes in…
Causal structures for observational survival data provide crucial information regarding the relationships between covariates and time-to-event. We derive motivation from the information theoretic source coding argument, and show that…
We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation…
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…
We consider the problem of learning a set of direct causes of a target variable from an observational joint distribution. Learning directed acyclic graphs (DAGs) that represent the causal structure is a fundamental problem in science.…
Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on…
Transformer models have recently gained popularity in graph representation learning as they have the potential to learn complex relationships beyond the ones captured by regular graph neural networks. The main research question is how to…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…
Bayesian networks represent relations between variables using a directed acyclic graph (DAG). Learning the DAG is an NP-hard problem and exact learning algorithms are feasible only for small sets of variables. We propose two scalable…
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…
Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization…
Given a connected undirected graph G = [V; E] where |E| =2(|V| -1), we present two algorithms to check if G can be decomposed into two edge disjoint spanning trees, and provide such a decomposition when it exists. Unlike previous algorithms…
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices…
In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most $k$, when an effective…
Directed Acyclic Graphical (DAG) models efficiently formulate causal relationships in complex systems. Traditional DAGs assume nodes to be scalar variables, characterizing complex systems under a facile and oversimplified form. This paper…
Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have…