Related papers: Causal models have no complete axiomatic character…

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional…

We give a category-theoretic treatment of causal models that formalizes the syntax for causal reasoning over a directed acyclic graph (DAG) by associating a free Markov category with the DAG in a canonical way. This framework enables us to…

Faithfulness is a common assumption in causal inference, often motivated by the fact that the faithful parameters of linear Gaussian and discrete Bayesian networks are typical, and the folklore belief that this should also hold for other…

The very expressiveness of Bayesian networks can introduce fresh challenges due to the large number of relationships they often model. In many domains, it is thus often essential to supplement any available data with elicited expert…

Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant…

Causal inference with observational data critically relies on untestable and extra-statistical assumptions that have (sometimes) testable implications. Well-known sets of assumptions that are sufficient to justify the causal interpretation…

Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic…

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…

We investigate the asymptotic properties of Bayesian bivariate causal discovery for Gaussian Linear Structural Equation Models (SEMs) with heteroscedastic noise. We demonstrate that with purely observational data, the posterior distribution…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

Causal effect identification typically requires a fully specified causal graph, which can be difficult to obtain in practice. We provide a sufficient criterion for identifying causal effects from a candidate set of Markov equivalence…

Graphs are expressive abstractions representing more effectively relationships in data and enabling data science tasks. They are also a widely adopted paradigm in causal inference focusing on causal directed acyclic graphs. Causal DAGs…

Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…

Discrete Bayesian Networks have been very successful as a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called the chain event graph (CEG) models, that…

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…

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…