Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

TL;DR

This paper introduces a kernel-based approach for performing functional operations on probability distributions, enabling flexible probabilistic programming applicable to various statistical and causal inference tasks.

Contribution

It presents a novel kernel probabilistic programming framework that leverages reproducing kernel Hilbert space representations for distributions, extending functional operations to probabilistic models.

Findings

Effective on synthetic data

Applicable to nonparametric structural equation models

Useful for causal inference

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.