Related papers: Half-Spectral Space-Time Covariance Models
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
We consider quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present…
For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…
Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…
Functional covariates arise in many scientific and engineering applications when model inputs take the form of time-dependent or spatially distributed profiles, such as varying boundary conditions or changing material behaviours. In…
We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Several stochastic processes with virtual particles in two dimensional space-time are presented whose mean field equations coincide with Schr\"odinger, Dirac, Klein-Gordon and the quantum mechanic equation for a photon. These processes…
Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…
Renewable energy sources provide a constantly increasing contribution to the total energy production worldwide. However, the power generation from these sources is highly variable due to their dependence on meteorological conditions.…