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.

Gaussian Process Bandit Optimisation with Multi-fidelity Evaluations

Abstract: In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $\func$. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $\func$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $\func$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop \mfgpucb, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. \mfgpucbs outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

Nonlinear and non-Gaussian ocean noise

Abstract: Bispectral analysis is a statistical tool for detecting and identifying a nonlinear stochastic signal generating mechanism from data containing its output. Bispectral analysis can also be employed to investigate whether the observed data record is consistent with the hypothesis that the underlying stochastic process has Gaussian distribution. From estimates of bispectra of several records of ambient acoustic ocean noise, a newly developed statistical method for testing whether the noise had a Gaussian distribution, and whether it contains evidence of nonlinearity in the underlying mechanisms generating the observed noise is applied. Seven acoustic records from three environments are examined: the Atlantic south of Bermuda, the northeast Pacific, and the Indian Ocean. The collection of time series represents both ambient acoustic noise (no local shipping) and noise dominated by local shipping. The three ambient records appeared to be both linear and Gaussian processes when examined over a period on the ord...

Gaussian Process modeling of large scale terrain

Abstract: This paper addresses the problem of large scale terrain modeling for a mobile robot. Building a model of large scale terrain data that can adequately handle uncertainty and incompleteness in a statistically sound way is a very challenging problem. This work proposes the use of Gaussian Processes as models of large scale terrain. The proposed model naturally provides a multi-resolution representation of space, incorporates and handles uncertainties aptly and copes with incompleteness of sensory information. Gaussian Process Regression techniques are applied to estimate and interpolate (to fill gaps in unknown areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single Non-Stationary (Neural Network) Gaussian Process is shown to be powerful enough to model large and complex terrain, handling issues relating to discontinuous data effectively. A local approximation methodology based on KD-Trees is also proposed in order to ensure local smoothness and yet preserve the characteristic features of rich and complex terrain data. The use of the local approximation technique based on KD-Trees further addresses concerns relating to the scalability of the proposed approach for large data sets. Experiments performed on sparse GPS based survey data as well as dense laser scanner data taken at different mine-sites are reported in support of these claims.