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Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

Machine Learning · Computer Science 2026-03-12 Hanlin Yu , Marcelo Hartmann , Bernardo Williams , Mark Girolami , Arto Klami

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.…

Machine Learning · Statistics 2022-03-02 Nikolaos Gianniotis

Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…

Methodology · Statistics 2025-04-29 Xiahui Li , Fergus Chadwick , Ben Swallow

While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…

Machine Learning · Computer Science 2012-07-02 Max Welling , Sridevi Parise

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…

Computation · Statistics 2012-09-04 Björn Bornkamp

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

Numerical Analysis · Mathematics 2019-09-04 Chen Zhang , Simon Arridge , Bangti Jin

We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model…

Computation · Statistics 2021-10-07 David Rossell , Oriol Abril , Anirban Bhattacharya

In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a…

Probability · Mathematics 2017-04-12 Philipp Wacker

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Machine Learning · Statistics 2020-12-29 Simón Rodríguez Santana , Daniel Hernández-Lobato

This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the…

We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace…

Machine Learning · Computer Science 2015-05-19 David Maxwell Chickering , David Heckerman

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…

Machine Learning · Statistics 2019-09-12 Tomasz Kuśmierczyk , Joseph Sakaya , Arto Klami

In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms…

Machine Learning · Computer Science 2025-09-23 Yinsong Chen , Samson S. Yu , Zhong Li , Chee Peng Lim

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…

Machine Learning · Statistics 2020-07-24 Alexander Immer

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

Artificial Intelligence · Computer Science 2013-04-05 Richard E. Neapolitan , James Kenevan

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…

Machine Learning · Statistics 2018-11-22 Conor Durkan , George Papamakarios , Iain Murray

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

Machine Learning · Computer Science 2024-11-01 Tristan Cinquin , Marvin Pförtner , Vincent Fortuin , Philipp Hennig , Robert Bamler

Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In…

Methodology · Statistics 2025-10-02 Janet van Niekerk , Haavard Rue

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…

Machine Learning · Computer Science 2021-11-08 Runa Eschenhagen , Erik Daxberger , Philipp Hennig , Agustinus Kristiadi

We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the…

Computation · Statistics 2017-06-14 Johan Dahlin , Mattias Villani , Thomas B. Schön