Related papers: Mixed Laplace approximation for marginal posterior…

Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…

Approximate Bayesian inference based on Laplace approximation and quadrature methods have become increasingly popular for their efficiency at fitting latent Gaussian models (LGM), which encompass popular models such as Bayesian generalized…

Laplace approximations are among the simplest and most practical methods for approximate Bayesian inference in neural networks, yet their Euclidean formulation struggles with the highly anisotropic, curved loss surfaces and large symmetry…

Efficient Bayesian inference remains a computational challenge in hierarchical models. Simulation-based approaches such as Markov Chain Monte Carlo methods are still popular but have a large computational cost. When dealing with the large…

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared…

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually…

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter…

In this thesis, we disentangle the generalized Gauss-Newton and approximate inference for Bayesian deep learning. The generalized Gauss-Newton method is an optimization method that is used in several popular Bayesian deep learning…