Related papers: Improved Laplace Approximation for Marginal Likeli…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…
The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…
This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…
This paper establishes the iteration-complexity of an inner accelerated inexact proximal augmented Lagrangian (IAIPAL) method for solving linearly-constrained smooth nonconvex composite optimization problems that is based on the classical…
Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…
We present a simple and effective method for evaluating double-and single-layer potentials for Laplace's equation in three dimensions close to the boundary. The close evaluation of these layer potentials is challenging because they are…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
This paper presents a new approach for solving the close evaluation problem in three dimensions, commonly encountered while solving linear elliptic partial differential equations via potential theory. The goal is to evaluate layer…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
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…
The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed…
Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai…
We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…
Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification,…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…
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…
We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on…