Related papers: Fractional Gaussian noise: Prior specification and…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for…

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst…

We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal,…

In this paper, we propose \texttt{FGPR}: a Federated Gaussian process ($\mathcal{GP}$) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local client computations. Notably, the…

A continuous-time model for the additive white Gaussian noise (AWGN) channel in the presence of white (memoryless) phase noise is proposed and discussed. It is shown that for linear modulation the output of the baud-sampled filter matched…

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…

The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic…

We propose a gradient preconditioning method that makes reward-guided generation with one-step generative models both efficient and reliable. Test-time noise optimization can unlock substantially better reward-guided generations from…

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…

In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…

We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in particular, we obtain recurrence relations for them. We also make…

This work proposes a nonparametric method to compare the underlying mean functions given two noisy datasets. The motivation for the work stems from an application of comparing wind turbine power curves. Comparing wind turbine data presents…

We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

We propose a novel approach to generative adversarial networks (GANs) in which the standard i.i.d. Gaussian latent prior is replaced or hybridized with a quantum-correlated prior derived from measurements of a 16-qubit entangling circuit.…