Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

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Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

EigenGP: Gaussian Process Models with Adaptive Eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements--eigenfunctions of a GP prior--and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements--eigenfunctions--and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machine.Comment: Accepted by IJCAI 201