Related papers: Advances in Probabilistic Reasoning
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…
Bayesian Networks (BN) provide robust probabilistic methods of reasoning under uncertainty, but despite their formal grounds are strictly based on the notion of conditional dependence, not much attention has been paid so far to their use in…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent ``bias events,''…
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 uncover a strong correspondence between Bayesian Networks and (Multiplicative) Linear Logic Proof-Nets, relating the two as a representation of a joint probability distribution and at the level of computation, so yielding a…
Various AI models are increasingly being considered as part of clinical decision-support tools. However, the trustworthiness of such models is rarely considered. Clinicians are more likely to use a model if they can understand and trust its…
Artificial Intelligence (AI), and in particular, the explainability thereof, has gained phenomenal attention over the last few years. Whilst we usually do not question the decision-making process of these systems in situations where only…
Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…
We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…
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…
Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports…
This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…