Related papers: Approximate Likelihood-Based Inference for Spatial…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to…

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…

Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for…

Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…

Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$…

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…

Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…

We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded…

Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Gaussian processes (GPs) are powerful tools for nonlinear classification in which latent GPs are combined with link functions. But GPs do not scale well to large training data. This is compounded for classification where the latent GPs…