Related papers: Bayesian inference with finitely wide neural netwo…

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is…

We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…

The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…

Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…

We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving…

To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…