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Precision achieved by stochastic sampling algorithms for Bayesian networks typically deteriorates in face of extremely unlikely evidence. To address this problem, we propose the Evidence Pre-propagation Importance Sampling algorithm…
In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…
Bayesian networks are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. They have been employed extensively in areas such as…
Bayesian network structures are usually built using only the data and starting from an empty network or from a naive Bayes structure. Very often, in some domains, like medicine, a prior structure knowledge is already known. This structure…
We provide a method for approximating Bayesian inference using rejection sampling. We not only make the process efficient, but also dramatically reduce the memory required relative to conventional methods by combining rejection sampling…
In this paper we present a new algorithm for online (sequential) inference in Bayesian neural networks, and show its suitability for tackling contextual bandit problems. The key idea is to combine the extended Kalman filter (which locally…
Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because…
We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure…
Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an…
We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…
Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node.…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically…
The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
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…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian…