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Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…

Bayesian deep learning all too often underfits so that the Bayesian prediction is less accurate than a simple point estimate. Uncertainty quantification then comes at the cost of accuracy. For linearized models, the null space of the…

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…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

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…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…

Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric…

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…

Bayesian inference is a popular method to build learning algorithms but it is hampered by the fact that its key object, the posterior probability distribution, is often uncomputable. Expectation Propagation (EP) (Minka (2001)) is a popular…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…