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Fast kernel building for Latent Force Models

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Abstract: A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green’s functions associated to the differential operators, and covariance functions associated with latent functions. In the classical formulation of latent force models, the covariance functions are obtained analytically by solving a double integral, leading to expressions that involve numerical solutions of different types of error functions. In consequence, the covariance matrix calculation is considerably expensive, because it requires the evaluation of one or more of these error functions. In this talk, I describe the use of random Fourier features to approximate the solution of these double integrals obtaining simpler analytical expressions for such covariance functions. I show experimental results using ordinary differential operators.

Short-bio: Dr Álvarez received a degree in Electronics Engineering (B. Eng.) with Honours, from Universidad Nacional de Colombia in 2004, a master degree in Electrical Engineering (M. Eng.) from Universidad Tecnológica de Pereira, Colombia in 2006, and a Ph.D. degree in Computer Science from The University of Manchester, UK, in 2011. After finishing his Ph.D., Dr Álvarez joined the Department of Electrical Engineering at Universidad Tecnológica de Pereira, Colombia, where he was appointed as a Faculty member until Dec 2016. From January 2017, Dr Álvarez was appointed as Lecturer in Machine Learning at the Department of Computer Science of the University of Sheffield, UK.

Dr Álvarez is interested in machine learning in general, its interplay with mathematics and statistics, and its applications. In particular, his research interests include probabilistic models, kernel methods, and stochastic processes. He works on the development of new approaches and the application of Machine Learning in areas that include neural engineering, systems biology, and humanoid robotics.

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