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.

Light field denoising, light field superresolution and stereo camera based refocussing using a GMM light field patch prior

Abstract: With the recent availability of commercial light field cameras, we can foresee a future in which light field signals will be as common place as images. Hence, there is an imminent need to address the problem of light field processing. We provide a common framework for addressing many of the light field processing tasks, such as denoising, angular and spatial superresolution, etc. (in essence, all processing tasks whose observation models are linear). We propose a patch based approach, where we model the light field patches using a Gaussian mixture model (GMM). We use the ”disparity pattern” of the light field data to design the patch prior. We show that the light field patches with the same disparity value (i.e., at the same depth from the focal plane) lie on a low-dimensional subspace and that the dimensionality of such subspaces varies quadratically with the disparity value. We then model the patches as Gaussian random variables conditioned on its disparity value, thus, effectively leading to a GMM model. During inference, we first find the disparity value of a patch by a fast subspace projection technique and then reconstruct it using the LMMSE algorithm. With this prior and inference algorithm, we show that we can perform many different processing tasks under a common framework.

Analysis of Radio Telemetry Data in Studies of Home Range

Abstract: In home range studies of wild animals and birds, statistical analysis of radio telemetry data poses special problems due to lack of independence of successive observations along the sample path. Assuming that such data are generated by a continuous, stationary, Gaussian process possessing the Markov property, then a multivariate Ornstein-Uhlenbeck diffusion process is necessarily the source and is proposed here to be a workable model. Its characterization is given in terms of typical descriptive properties of home range such as center of activity and confidence regions. Invariance of the model with respect to choice of an observational coordinate system is established, while data for twin deer are used to illustrate the manner in which the model may be used for study of territorial interaction. An approximate maximum likelihood procedure is proposed with results being reported for deer, coyote, and bird tracking data.

Variational Gaussian process classifiers

Abstract: Gaussian processes are a promising nonlinear regression tool, but it is not straightforward to solve classification problems with them. In the paper the variational methods of Jaakkola and Jordan (2000) are applied to Gaussian processes to produce an efficient Bayesian binary classifier.

Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors

Abstract: Limit theorems for functions of stationary mean-zero Gaussian sequences of vectors satisfying long range dependence conditions are considered. Depending on the rate of decay of the coefficients, the limit law can be either Gaussian or the law of a multiple Ito-Wiener integral. We prove the bootstrap of these limit theorems in the case when the limit is normal. A sufficient bracketing condition for these limit theorems to happen uniformly over a class of functions is presented.