Related papers: Every LWF and AMP chain graph originates from a se…
In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models…
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 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 use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
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 address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with…
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maximal independent set. 2. Every locally countable connected…
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.…
Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with…
Every directed acyclic graph (DAG) over a finite non-empty set of variables (= nodes) N induces an independence model over N, which is a list of conditional independence statements over N.The inclusion problem is how to characterize (in…
In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the…
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…
An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
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…
Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…
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…
We develop a category-theoretic criterion for determining the equivalence of causal models having different but homomorphic directed acyclic graphs over discrete variables. Following Jacobs et al. (2019), we define a causal model as a…
LWF chain graphs combine directed acyclic graphs and undirected graphs. We present a PC-like algorithm that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed…