Related papers: Two-step wavelet-based estimation for mixed Gaussi…
In this article we introduce and study oscillating Gaussian processes defined by $X_t = \alpha_+ Y_t {\bf 1}_{Y_t >0} + \alpha_- Y_t{\bf 1}_{Y_t<0}$, where $\alpha_+,\alpha_->0$ are free parameters and $Y$ is either stationary or…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize…
Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual…
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
We propose a novel estimation framework for path-dependent functionals of Levy processes from discretely observed data. Traditional approaches rely on Monte Carlo simulation of full paths, which requires complete model specification and…
A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…