Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

Bernhard Schölkopf; Krikamol Muandet; Kenji Fukumizu; Jonas Peters

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arXiv · 1501.06794

Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

Bernhard Schölkopf·Krikamol Muandet·Kenji Fukumizu·Jonas Peters

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Abstract

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as {\em kernel probabilistic programming}. We illustrate it on synthetic data, and show how it can be used for nonparametric structural equation models, with an application to causal inference.

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Bernhard Schölkopf, Krikamol Muandet, Kenji Fukumizu, Jonas Peters. 2015-01-27. Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations. https://arxiv.org/abs/1501.06794

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