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The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has…
A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
In this paper we consider a Bayesian analysis of contingency tables allowing for the possibility that cells may have probability zero. In this sense we depart from standard log-linear modeling that implicitly assumes a positivity…
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…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
A credal network under epistemic irrelevance is a generalised type of Bayesian network that relaxes its two main building blocks. On the one hand, the local probabilities are allowed to be partially specified. On the other hand, the…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…