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Anomaly analytics is a popular and vital task in various research contexts, which has been studied for several decades. At the same time, deep learning has shown its capacity in solving many graph-based tasks like, node classification, link…
We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or…
Explainable artificial intelligence (XAI) is an important area in the AI community, and interpretability is crucial for building robust and trustworthy AI models. While previous work has explored model-level and instance-level explainable…
We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modeling of such different data-types, based on global parameters consisting of a directed acyclic…
In causal graphical models based on directed acyclic graphs (DAGs), directed paths represent causal pathways between the corresponding variables. The variable at the beginning of such a path is referred to as an ancestor of the variable at…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
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…
The problem of learning a directed acyclic graph (DAG) up to Markov equivalence is equivalent to the problem of finding a permutation of the variables that induces the sparsest graph. Without additional assumptions, this task is known to be…
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Markov Chain Monte Carlo (MCMC) has been the de facto technique for sampling and inference of large graphs such as online social networks. At the heart of MCMC lies the ability to construct an ergodic Markov chain that attains any given…
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…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model…