Related papers: Laplace based approximate posterior inference for …

Given a finite set of sample points, meta-learning algorithms aim to learn an optimal adaptation strategy for new, unseen tasks. Often, this data can be ambiguous as it might belong to different tasks concurrently. This is particularly the…

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence,…

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…

The hierarchical prior used in Latent Gaussian models (LGMs) induces a posterior geometry prone to frustrate inference algorithms. Marginalizing out the latent Gaussian variable using an integrated Laplace approximation removes the…

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…

We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…

This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…

The key operation in Bayesian inference, is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre- Simon Laplace (1774). This simple idea approximates the…

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework. We consider a slight reparameterization of the Multivariate Asymmetric…

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…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…

In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…