We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data.

For example, census data are usually sampled or collected as aggregated at different administrative divisions, e.g.

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Indoing so, we generalize existing approaches and offer information-theoretic corrections and efficient variational approximations.

While existing approaches only model finite, discrete fidelities, in practice, the feasible fidelity choice is often infinite, which can correspond to a continuous mesh spacing orfinite element length.

Variational inference was employed in prior work to inferz (and w implicitly), and to obtain a point estimate ofθ, as a by-product of optimising the variational lower bound. Critically, in this representation weights are only implicitly parametrized through the use of these latent variables, which transforms inference onweights into inference ofthemuch smaller collection oflatent unit variables.

The approximate posterior distributions of the latent variables are derived with variational inference, and the evidence lower bound is evaluated and optimized by the proposed recursive sampling scheme.

One of the principal assumptions of the GP-LVM is that the prior p(f) regularises the smoothness of all mappings equally, so we only consider onekernel.

Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice.