Related papers: Laplace based approximate posterior inference for …

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…

We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…

The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the…

There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of…

We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…

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…

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically…