Related papers: Asymmetric separation for local independence graph…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…
In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
We study time-dependent mediators in survival analysis using a treatment separation approach due to Didelez [2019] and based on earlier work by Robins and Richardson [2011]. This approach avoids nested counterfactuals and crossworld…
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.…
Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…
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…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…