Related papers: A Characterization of the Dirichlet Distribution w…

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new…

In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known.…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from…

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental…

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

We examine Bayesian methods for learning Bayesian networks from a combination of prior knowledge and statistical data. In particular, we unify the approaches we presented at last year's conference for discrete and Gaussian domains. We…

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,…

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…

We present a framework for online inference in the presence of a nonexhaustively defined set of classes that incorporates supervised classification with class discovery and modeling. A Dirichlet process prior (DPP) model defined over class…

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

This paper addresses the task of set prediction using deep learning. This is important because the output of many computer vision tasks, including image tagging and object detection, are naturally expressed as sets of entities rather than…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…