Related papers: On the physics of nested Markov models: a generali…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…
Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
In scientific domains -- from biology to the social sciences -- many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is…
Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI)…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
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.…
The perceived advantage of machine learning (ML) models is that they are flexible and can incorporate a large number of features. However, many of these are typically correlated or dependent, and incorporating all of them can hinder model…
Causal discovery and inference from observational data is an essential problem in statistics posing both modeling and computational challenges. These are typically addressed by imposing strict assumptions on the joint distribution such as…
Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
Variable-length Markov chains (VLMCs) are a flexible class of higher-order Markov models that admit a natural representation as context trees. Existing Bayesian methods for specifying prior distributions on tree structures rely on branching…
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially…
Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…