Related papers: Fractional Gaussian noise: Prior specification and…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been…

Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused…

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

We consider a statistical model of a n-mode quantum Gaussian state which is shift invariant and also gauge invariant. Such models can be considered analogs of classical Gaussian stationary time series, parametrized by their spectral…

Modeling financial time series by stochastic processes is a challenging task and a central area of research in financial mathematics. As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

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…

Hyperbolic decay time series such as, fractional Gaussian noise (FGN) or fractional autoregressive moving-average (FARMA) process, each exhibit two distinct types of behaviour: strong persistence or antipersistence. Beran (1994)…

Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…

A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic…

Implicit neural representations have shown potential in various applications. However, accurately reconstructing the image or providing clear details via image super-resolution remains challenging. This paper introduces Quantum Fourier…

This paper investigates the signal detection problem in colored Gaussian noise with an unknown covariance matrix. To be specific, we consider a sample deficient scenario in which the number of signal bearing samples ($n$) is strictly…

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

Time series forecasting is one of the challenging problems for humankind. Traditional forecasting methods using mean regression models have severe shortcomings in reflecting real-world fluctuations. While new probabilistic methods rush to…

Bayesian optimization (BO) with Gaussian process (GP) surrogate models is a powerful black-box optimization method. Acquisition functions are a critical part of a BO algorithm as they determine how the new samples are selected. Some of the…

The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…