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Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…

We make the case for incorporating a notion of time into causal directed acyclic graphs (DAGs). We demonstrate that nontemporal causal DAGs are ambiguous and obstruct justification of the acyclicity assumption. Assuming that causes precede…

Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring…

Recently continuous relaxations have been proposed in order to learn Directed Acyclic Graphs (DAGs) from data by backpropagation, instead of using combinatorial optimization. However, a number of techniques for fully discrete…

Graph based entropy, an index of the diversity of events in their distribution to parts of a co-occurrence graph, is proposed for detecting signs of structural changes in the data that are informative in explaining latent dynamics of…

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.…

Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…

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…

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…

Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…

In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which…

Inferring the structure of directed acyclic graphs (DAGs) from data is a central challenge in causal discovery, particularly in modern high-dimensional settings where large-scale interventional data are increasingly available. While…

Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic…

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…

Standard diffusion models are flexible estimators of complex distributions, but they do not encode causal structures and therefore do not by themselves support causal analysis. We propose a causality-encoded diffusion framework that…

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,…

Learning graphical structures based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous…

The causal dependence in data is often characterized by Directed Acyclic Graphical (DAG) models, widely used in many areas. Causal discovery aims to recover the DAG structure using observational data. This paper focuses on causal discovery…