Related papers: Higher-Order Bayesian Networks, Exactly (Extended …

Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be…

This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…

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 neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural…

Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…

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 emergence and development of cancer is a consequence of the accumulation over time of genomic mutations involving a specific set of genes, which provides the cancer clones with a functional selective advantage. In this work, we model…

Bayesian network classifiers provide a feasible solution to tabular data classification, with a number of merits like high time and memory efficiency, and great explainability. However, due to the parameter explosion and data sparsity…

Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…

Quantifying uncertainty in neural networks is a highly relevant problem which is essential to many applications. The two predominant paradigms to tackle this task are Bayesian neural networks (BNNs) and deep ensembles. Despite some…

A novel method for estimating Bayesian network (BN) parameters from data is presented which provides improved performance on test data. Previous research has shown the value of representing conditional probability distributions (CPDs) via…

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…

We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…

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…

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…

A neural network computes a function. A central property of neural networks is that they are "universal approximators:" for a given continuous function, there exists a neural network that can approximate it arbitrarily well, given enough…

Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…

We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…