Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

Abstract: We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as 1/f γ. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the mid-transit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for mid-transit times and truer estimates of their uncertainties.

Hierarchical Gaussian process latent variable models

Abstract: The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets.

Reconstruction of dark energy and expansion dynamics using Gaussian processes

Abstract: An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter space, as the errors found depend strongly on the parameterisation considered. We present a new non-parametric approach to reconstructing the history of the expansion rate and dark energy using Gaussian Processes, which is a fully Bayesian approach for smoothing data. We present a pedagogical introduction to Gaussian Processes, and discuss how it can be used to robustly differentiate data in a suitable way. Using this method we show that the Dark Energy Survey - Supernova Survey (DES) can accurately recover a slowly evolving equation of state to sigma_w = +-0.04 (95% CL) at z=0 and +-0.2 at z=0.7, with a minimum error of +-0.015 at the sweet-spot at z~0.14, provided the other parameters of the model are known. Errors on the expansion history are an order of magnitude smaller, yet make no assumptions about dark energy whatsoever. A code for calculating functions and their first three derivatives using Gaussian processes has been developed and is available for download at this http URL .

A New Approach for Mutual Information Analysis of Large Dimensional Multi-Antenna Channels

Abstract: This paper adresses the behavior of the mutual information of correlated multiple-input multiple-output (MIMO) Rayleigh channels when the numbers of transmit and receive antennas converge to +infin at the same rate. Using a new and simple approach based on Poincare-Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information when properly centered and rescaled converges to a standard Gaussian random variable. Simple expressions for the centering and scaling parameters are provided. These results confirm previous evaluations based on the powerful but nonrigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.