Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations
This method addresses the challenge of handling complex operations on random variables in probabilistic modeling, particularly for causal inference, but appears incremental as it builds on existing kernel methods.
The paper tackles the problem of performing functional operations on probability distributions by introducing kernel probabilistic programming, which uses reproducing kernel Hilbert space representations, and demonstrates its application to nonparametric structural equation models for causal inference.
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.