Murray-Smith, Roderick and Pearlmutter, Barak A.
Transformations of Gaussian Process Priors.
Machine Learning Workshop.
Springer-Verlag, pp. 110-125.
Gaussian process prior systems generally consist of noisy measurements of samples of the putatively Gaussian process of interest, where the samples serve to constrain the posterior estimate. Here we consider the case where the
measurements are instead noisy weighted sums of samples. This framework incorporates measurements of derivative information and of filtered versions of the process, thereby allowing GPs to perform sensor fusion and tomography; allows certain group invariances (ie symmetries) to be weakly enforced; and under certain
conditions suitable application allows the dataset to be dramatically reduced in size. The method is applied to a sparsely sampled image, where each sample is
taken using a broad and non-monotonic point spread function. It is also applied to nonlinear dynamic system identification applications where a nonlinear function
is followed by a known linear dynamic system, and where observed data can be a mixture of irregularly sampled higher derivatives of the signal of interest.
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