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We describe a method to perform functional operations on probabilitydistributions of random variables. The method uses reproducing kernel Hilbertspace representations of probability distributions, and it is applicable to alloperations which can be applied to points drawn from the respectivedistributions. We refer to our approach as {\em kernel probabilisticprogramming}. We illustrate it on synthetic data, and show how it can be usedfor nonparametric structural equation models, with an application to causalinference.

Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations