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In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an…

Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

Now that Bayesian Networks (BNs) have become widely used, an appreciation is developing of just how critical an awareness of the sensitivity and robustness of certain target variables are to changes in the model. When time resources are…

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…

Structural missingness breaks 'just impute and train': values can be undefined by causal or logical constraints, and the mask may depend on observed variables, unobserved variables (MNAR), and other missingness indicators. It simultaneously…

Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…

Bayesian belief network learning algorithms have three basic components: a measure of a network structure and a database, a search heuristic that chooses network structures to be considered, and a method of estimating the probability tables…

Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using…

As one of the classic models that describe the belief dynamics over social networks, a non-Bayesian social learning model assumes that members in the network possess accurate signal knowledge through the process of Bayesian inference. In…

Safe and reliable disclosure of information from confidential data is a challenging statistical problem. A common approach considers the generation of synthetic data, to be disclosed instead of the original data. Efficient approaches ought…

Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse…

The diagnosis of cyber-physical systems aims to detect faulty behaviour, its root cause and a mitigation or even prevention policy. Therefore, diagnosis relies on a representation of the system's functional and faulty behaviour combined…