Related papers: Method for generating two coupled Gaussian stochas…

The goal of this paper is to establish a relation between characteristic polynomials of $N\times N$ GUE random matrices $\mathcal{H}$ as $N\to\infty$, and Gaussian processes with logarithmic correlations. We introduce a regularized version…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…

In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…

In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…

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…

Gaussian processes (GPs) offer a flexible, uncertainty-aware framework for modeling complex signals, but scale cubically with data, assume static targets, and are brittle to outliers, limiting their applicability in large-scale problems…

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

We show how two-point correlation functions derived within non-isotropic random wave models are in fact quantum results that are obtained in the appropriate limit in terms of the exact Green function of the quantum system. Since no…

We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive…

This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer…

This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…

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…

In a two-state free probability space $(A, \phi, \psi)$, we define an algebraic two-state free Brownian motion to be a process with two-state freely independent increments whose two-state free cumulant generating function is quadratic. Note…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated…

In [1] a new bosonization procedure has been illustrated, which allows to express a fermionic gaussian system in terms of commuting variables at the price of introducing an extra dimension. The Fermi-Bose duality principle established in…

This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes…

This paper develops a generalization of Brownian motion with stationary, autocorrelated increments as a tractable model for problems in business and finance. We show that any real continuous Gaussian Markov process with stationary…

Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…