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.

Nonparametric belief propagation

Abstract: Continuous quantities are ubiquitous in models of real-world phenomena, but are surprisingly difficult to reason about automatically. Probabilistic graphical models such as Bayesian networks and Markov random fields, and algorithms for approximate inference such as belief propagation (BP), have proven to be powerful tools in a wide range of applications in statistics and artificial intelligence. However, applying these methods to models with continuous variables remains a challenging task. In this work we describe an extension of BP to continuous variable models, generalizing particle filtering, and Gaussian mixture filtering techniques for time series to more complex models. We illustrate the power of the resulting nonparametric BP algorithm via two applications: kinematic tracking of visual motion and distributed localization in sensor networks.

An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels

Abstract: Although Gaussian radial basis function (RBF) kernels are one of the most often used kernels in modern machine learning methods such as support vector machines (SVMs), little is known about the structure of their reproducing kernel Hilbert spaces (RKHSs). In this work, two distinct explicit descriptions of the RKHSs corresponding to Gaussian RBF kernels are given and some consequences are discussed. Furthermore, an orthonormal basis for these spaces is presented. Finally, it is discussed how the results can be used for analyzing the learning performance of SVMs

Fault Detection for Non-Gaussian Processes Using Generalized Canonical Correlation Analysis and Randomized Algorithms

Abstract: In this paper, we first study a generalized canonical correlation analysis (CCA)-based fault detection (FD) method aiming at maximizing the fault detectability under an acceptable false alarm rate. More specifically, two residual signals are generated for detecting of faults in input and output subspaces, respectively. The minimum covariances of the two residual signals are achieved by taking the correlation between input and output into account. Considering the limited application scope of the generalized CCA due to the Gaussian assumption on the process noises, an FD technique combining the generalized CCA with the threshold-setting based on the randomized algorithm is proposed and applied to the simulated traction drive control system of high-speed trains. The achieved results show that the proposed method is able to improve the detection performance significantly in comparison with the standard generalized CCA-based FD method.

Phase-locked loop dynamics in the presence of noise by Fokker-Planck techniques

Abstract: Statistical parameters of the phase-error behavior of a phase-locked loop tracking a constant frequency signal in the presence of additive, stationary, Gaussian noise are obtained by treating the problem as a continuous random walk with a sinusoidal restoring force. The Fokker-Planck or diffusion equation is obtained for a general loop and for the case of frequency-modulated received signals. An exact expression for the steady-state phase-error distribution is available only for the first-order loop, but approximate and asymptotic expressions are derived for the second-order loop. Results are obtained also for the expected time to loss of lock and for the frequency of skipping cycles. Some of the results are extended to tracking loops with nonsinusoidal error functions. Validity thresholds of widely accepted approximate models of the phase-locked loop are obtained by comparison with the exact results available for the first-order loop.