Related papers: Bayesian inference with finitely wide neural netwo…

Quantifying the uncertainty in the output of a neural network is essential for deployment in scientific or engineering applications where decisions must be made under limited or noisy data. Bayesian neural networks (BNNs) provide a…

We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain…

Recent works on Bayesian neural networks (BNNs) have highlighted the need to better understand the implications of using Gaussian priors in combination with the compositional structure of the network architecture. Similar in spirit to the…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

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…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…

This work proposes $\mu$GUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or MRI signal representation, with exemplar demonstration in…