Related papers: General adjoint-differentiated Laplace approximati…
Uncertainty quantification for deep neural networks has recently evolved through many techniques. In this work, we revisit Laplace approximation, a classical approach for posterior approximation that is computationally attractive. However,…
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…
Latent Gaussian Models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and…
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…
The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present…
Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
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…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
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…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…