Iterative Temporal Learning and Prediction with the Sparse Online Echo State Gaussian Process

Abstract—In this work, we contribute the online echo state gaussian process (OESGP), a novel Bayesian-based online method that is capable of iteratively learning complex temporal dy-namics and producing predictive distributions (instead of point predictions). Our method can be seen as a combination of the echo state network with a sparse approximation of Gaussian processes (GPs). Extensive experiments on the one-step prediction task on well-known benchmark problems show that OESGP produced statistically superior results to current online ESNs and state-of-the-art regression methods. In addition, we characterise the benefits (and drawbacks) associated with the considered online methods, specifically with regards to the trade-off between computational cost and accuracy. For a high-dimensional action recognition task, we demonstrate that OESGP produces high accuracies comparable to a recently published graphical model, while being fast enough for real-time interactive scenarios. I

Intrinsic Gaussian processes on complex constrained domains

We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising as complex subsets of Euclidean space. in-GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the proposed approach is to utilise the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels. This enables in-GPs to be practically applied in great generality, while existing approaches for smoothing on constrained domains are limited to simple special cases. The broad utilities of the in-GP approach is illustrated through simulation studies and data examples

Gaussian Process Modelling for Improved Resolution in Faraday Depth Reconstruction

The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization data are mostly caused by flagging of radio frequency interference and their effects worsen as the percentage of missing data increases. In this paper we present a novel method for inferring missing polarization data based on Gaussian processes (GPs). Gaussian processes are stochastic processes that enable us to encode prior knowledge in our models. They also provide a comprehensive way of incorporating and quantifying uncertainties in regression modelling. In addition to providing non-parametric model estimates for missing values, we also demonstrate that Gaussian process modelling can be used for recovering rotation measure values directly from complex polarization data, and that inferring missing polarization data using this probabilistic method improves the resolution of reconstructed Faraday depth spectra.Comment: 16 pages, 10 figures, submitted to MNRA