Related papers: Tight Bounds on the Laplace Approximation Accuracy…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

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,…

Tensor decompositions have been successfully applied to compress neural networks. The compression algorithms using tensor decompositions commonly minimize the approximation error on the weights. Recent work assumes the approximation error…

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…

We examine the behaviour of the Laplace and saddlepoint approximations in the high-dimensional setting, where the dimension of the model is allowed to increase with the number of observations. Approximations to the joint density, the…

From the classical and influential works of Neal (1996), it is known that the infinite width scaling limit of a Bayesian neural network with one hidden layer is a Gaussian process, when the network weights have bounded prior variance.…

The Laplace approximation provides a closed-form model selection objective for neural networks (NN). Online variants, which optimise NN parameters jointly with hyperparameters, like weight decay strength, have seen renewed interest in the…

Posterior inference for Dirichlet process mixture models is analytically intractable and typically relies on Markov chain Monte Carlo methods, which can become computationally prohibitive at moderate to large sample sizes. In this work, we…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…

This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP)…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a $d$-dimensional image ($d = 2, 3, \ldots$), the boundary can often be described by a closed smooth $(d -…

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and…

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral…

Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…