Reproducing kernel Hilbert space semantics for probabilistic programs

We propose to write denotational semantics for a probabilistic programming language in terms of reproducing kernel Hilbert spaces for characteristic kernels. This opens up possibilities for providing convergence guarantees for approximate expansions, as well as practical advantages of using kernel methods for machine learning. At the moment we only write semantics for a simple language for probabilistic expressions, but with time we hope to extend it to general probabilistic programs with conditioning.

Adam Ścibior and Bernhard Schölkopf

Extended abstract

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