Related papers: Learning AMP Chain Graphs under Faithfulness
This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover,…
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…
In this article we consider Bayesian inference for partially observed Andersson-Madigan-Perlman (AMP) Gaussian chain graph (CG) models. Such models are of particular interest in applications such as biological networks and financial time…
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…
We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separates a given nonadjacent pair of nodes such that no proper subset of Z separates that…
A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this…
The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing…
We study identifiability of Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which…
This paper studies faithful explanations for Graph Neural Networks (GNNs). First, we provide a new and general method for formally characterizing the faithfulness of explanations for GNNs. It applies to existing explanation methods,…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated…
In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an…
Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of…
Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph…
Chain graphs (CG) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CGs fall into Markov…
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…
As Graph Neural Networks (GNNs) become more pervasive, it becomes paramount to build reliable tools for explaining their predictions. A core desideratum is that explanations are \textit{faithful}, \ie that they portray an accurate picture…