Related papers: Macrofacet Theory for Gaussian Process Statistical…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

We propose GauFace, a novel Gaussian Splatting representation, tailored for efficient animation and rendering of physically-based facial assets. Leveraging strong geometric priors and constrained optimization, GauFace ensures a neat and…

In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approximation of smooth surfaces. The Gauss curvature and the mean…

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…

A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…

In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…

Bayesian model selection provides a natural alternative to classical hypothesis testing based on p-values. While many papers mention that Bayesian model selection is frequently sensitive to prior specification on the parameters, there are…

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional computational methods often struggle with the formidable task of navigating the vast…

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…

In this paper, we propose a model and algorithm for sparse representing Gaussian molecular surface. The original Gaussian molecular surface is approximated by a relatively small number of radial basis functions (RBFs) with rotational…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science,…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…