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
We explore the use of parameterized monads for ensuring additional properties of distributions constructed by probabilistic programs. As a specific example we demonstrate how to statically ensure that conditioning in probabilistic programs does not depend on random choices made during execution. This allows us to ensure safety of application of inference algorithms such as Sequential Monte Carlo. We believe there are more potential uses of parameterized monads for probabilistic programming, such as restricting the latent space or keeping track of data types used for conditioning.
Adam Scibior and Andrew D. Gordon