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.

Parametric generalized Gaussian density estimation

Abstract: The primary objective of this paper is to compare the large‐sample as well as the small‐sample properties of different methods for estimating the parameters of a three‐parameter generalized Gaussian distribution. Three estimators, namely, the moment method (MM), the maximum‐likelihood (ML), and the moment/Newton‐step (MNS) estimators, are considered. The applicability of general asymptotic optimality results of the efficient ML and MNS estimation techniques is studied in the generalized Gaussian context. The asymptotic normal distributions of the estimators are obtained. The asymptotic relative superiority of the ML estimator or its variant, the MNS estimator, over the moment method is studied in terms of asymptotic relative efficiency. Based on this study, it is concluded that deviations from normality in the underlying distribution of the data necessitate the use of the efficient ML or MNS methods. In the small‐sample case, a detailed comparative study of the estimators is made possible by extensive Monte Carlo simulations. From this study, it is concluded that the maximum‐likelihood method is found to be significantly superior for heavy‐tailed distributions. In a region of the parameter space corresponding to the vicinity of the Gaussian distribution, the moment method compares well with the other methods. Further, the MNS estimator is shown to perform best for light‐tailed distributions. The simulation results are shown to lend support to analytically derived asymptotic results for each of the methods.

Regression with Input-dependent Noise: A Gaussian Process Treatment

Abstract: Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.

The quadratic Gaussian CEO problem

Abstract: A firm's CEO employs a team of L agents who observe independently corrupted versions of a data sequence {X(t)}/sub t=1//sup /spl infin//. Let R be the total data rate at which the agents may communicate information about their observations to the CEO. The agents are not allowed to convene. Berger, Zhang and Viswanathan (see ibid., vol.42, no.5, p.887-902, 1996) determined the asymptotic behavior of the minimal error frequency in the limit as L and R tend to infinity for the case in which the source and observations are discrete and memoryless. We consider the same multiterminal source coding problem when {X(t)}/sub t=1//sup /spl infin// is independent and identically distributed (i.i.d.) Gaussian random variable corrupted by independent Gaussian noise. We study, under quadratic distortion, the rate-distortion tradeoff in the limit as L and R tend to infinity. As in the discrete case, there is a significant loss between the cases when the agents are allowed to convene and when they are not. As L/spl rarr//spl infin/, if the agents may pool their data before communicating with the CEO, the distortion decays exponentially with the total rate R; this corresponds to the distortion-rate function for an i.i.d. Gaussian source. However, for the case in which they are not permitted to convene, we establish that the distortion decays asymptotically only as R-l.

Derivative Observations in Gaussian Process Models of Dynamic Systems

Abstract: Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1) It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training set size - traditionally a problem for Gaussian process models.

Theoretical analysis and performance of OFDM signals in nonlinear AWGN channels

Abstract: Orthogonal frequency-division multiplexing (OFDM) baseband signals may be modeled by complex Gaussian processes with Rayleigh envelope distribution and uniform phase distribution, if the number of carriers is sufficiently large. The output correlation function of instantaneous nonlinear amplifiers and the signal-to-distortion ratio can be derived and expressed in an easy way. As a consequence, the output spectrum and the bit-error rate (BER) performance of OFDM systems in nonlinear additive white Gaussian noise channels are predictable both for uncompensated amplitude modulation/amplitude modulation (AM/AM) and amplitude modulation/pulse modulation (AM/PM) distortions and for ideal predistortion. The aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the BER performance. The results in closed-form solutions are derived for AM/AM and AM/PM curves approximated by Bessel series expansion and for the ideal predistortion case.