Related papers: Bayesian Inference for Gaussian Mixed Graph Models
In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control…
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…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…
Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of…
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…
Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…
Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
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…
Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects…
Directed Acyclic Graphs (DAGs) are solid structures used to describe and infer the dependencies among variables in multivariate scenarios. Having a thorough comprehension of the accurate DAG-generating model is crucial for causal discovery…
This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian…
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…