Related papers: FSP-Laplace: Function-Space Priors for the Laplace…

The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust…

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

In robotics, deep learning (DL) methods are used more and more widely, but their general inability to provide reliable confidence estimates will ultimately lead to fragile and unreliable systems. This impedes the potential deployments of DL…

Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…

Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of…

Function-space priors in Bayesian Neural Networks (BNNs) provide a more intuitive approach to embedding beliefs directly into the model's output, thereby enhancing regularization, uncertainty quantification, and risk-aware decision-making.…

Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…

Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in…

The meta learning few-shot classification is an emerging problem in machine learning that received enormous attention recently, where the goal is to learn a model that can quickly adapt to a new task with only a few labeled data. We…

Deep neural networks have revolutionized medical image analysis and disease diagnosis. Despite their impressive performance, it is difficult to generate well-calibrated probabilistic outputs for such networks, which makes them…

Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…

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 nonparametric probabilistic models…

Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…

Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables…

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Data augmentation is commonly applied to improve performance of deep learning by enforcing the knowledge that certain transformations on the input preserve the output. Currently, the data augmentation parameters are chosen by human effort…

The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…