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A latent force model is a Gaussian process with a covariance functioninspired by a differential operator. Such covariance function is obtained byperforming convolution integrals between Green's functions associated to thedifferential operators, and covariance functions associated to latentfunctions. In the classical formulation of latent force models, the covariancefunctions are obtained analytically by solving a double integral, leading toexpressions that involve numerical solutions of different types of errorfunctions. In consequence, the covariance matrix calculation is considerablyexpensive, because it requires the evaluation of one or more of these errorfunctions. In this paper, we use random Fourier features to approximate thesolution of these double integrals obtaining simpler analytical expressions forsuch covariance functions. We show experimental results using ordinarydifferential operators and provide an extension to build general kernelfunctions for convolved multiple output Gaussian processes.

Fast Kernel Approximations for Latent Force Models and Convolved Multiple-Output Gaussian processes