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.

Adaptive detection of range distributed targets

Abstract: A modified generalized likelihood ratio test (MGLRT) for the adaptive detection of a target or targets that are distributed in range is derived. The unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference, which is assumed to be characterized as complex zero-mean correlated Gaussian random variables. The target's or targets' complex amplitudes are assumed to be distributed across the entire input data block (sensor/spl times/range). Results on probabilities of false alarm and detection are derived, and a bounded constant false alarm rate (CFAR) detector is developed. Simulation results are presented. It is shown that the derived MGLRT of range distributed targets is much more effective in detecting targets distributed in range than an M out of K detector, which is cascaded with a single-point target Kelly (1986) detector.

Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies

Abstract: When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task,...

Neural networks vs Gaussian process regression for representing potential energy surfaces: A comparative study of fit quality and vibrational spectrum accuracy

Abstract: For molecules with more than three atoms, it is difficult to fit or interpolate a potential energy surface (PES) from a small number of (usually ab initio) energies at points. Many methods have been proposed in recent decades, each claiming a set of advantages. Unfortunately, there are few comparative studies. In this paper, we compare neural networks (NNs) with Gaussian process (GP) regression. We re-fit an accurate PES of formaldehyde and compare PES errors on the entire point set used to solve the vibrational Schrodinger equation, i.e., the only error that matters in quantum dynamics calculations. We also compare the vibrational spectra computed on the underlying reference PES and the NN and GP potential surfaces. The NN and GP surfaces are constructed with exactly the same points, and the corresponding spectra are computed with the same points and the same basis. The GP fitting error is lower, and the GP spectrum is more accurate. The best NN fits to 625/1250/2500 symmetry unique potential energy poin...

SAR amplitude probability density function estimation based on a generalized Gaussian model

Abstract: In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.

Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes

Abstract: [1] A daily stochastic spatiotemporal precipitation generator that yields spatially consistent gridded quantitative precipitation realizations is described. The methodology relies on a latent Gaussian process to drive precipitation occurrence and a probability integral transformed Gaussian process for intensity. At individual locations, the model reduces to a Markov chain for precipitation occurrence and a gamma distribution for precipitation intensity, allowing statistical parameters to be included in a generalized linear model framework. Statistical parameters are modeled as spatial Gaussian processes, which allows for interpolation to locations where there are no direct observations via kriging. One advantage of such a model for the statistical parameters is that stochastic generator parameters are immediately available at any location, with the ability to adapt to spatially varying precipitation characteristics. A second advantage is that parameter uncertainty, generally unavailable with deterministic interpolators, can be immediately quantified at all locations. The methodology is illustrated on two data sets, the first in Iowa and the second over the Pampas region of Argentina. In both examples, the method is able to capture the local and domain aggregated precipitation behavior fairly well at a wide range of time scales, including daily, monthly, and annually.