Related papers: Causal models have no complete axiomatic character…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…
To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present a factorization criterion for…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…
We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is…
A directed acyclic graph (DAG) partially represents the conditional independence structure among observations of a system if the local Markov condition holds, that is, if every variable is independent of its non-descendants given its…
Bayesian networks (BN) are directed acyclic graphical (DAG) models that have been adopted into many fields for their strengths in transparency, interpretability, probabilistic reasoning, and causal modeling. Given a set of data, one hurdle…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider…
In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…
Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…
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…
The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do-calculus is required has been…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical)…