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In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model…

Copulas provide a modular parameterization of multivariate distributions that decouples the modeling of marginals from the dependencies between them. Gaussian Mixture Copula Model (GMCM) is a highly flexible copula that can model many kinds…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal…

Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…

We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…

In this conceptual work, we present Deep Convolutional Gaussian Mixture Models (DCGMMs): a new formulation of deep hierarchical Gaussian Mixture Models (GMMs) that is particularly suitable for describing and generating images. Vanilla…

We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…

In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is…

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

We present a framework for transfer learning based on modular variational Gaussian processes (GP). We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data.…