# Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

arXiv: https://arxiv.org/abs/1501.06794 · HTML: https://mlsanity.com/paper/1501.06794/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2015.

## Built on by (most cited first, 4 of 4)

- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method](https://mlsanity.com/paper/2601.20026/) (2026)
- [Recursive Estimation of Conditional Kernel Mean Embeddings](https://mlsanity.com/paper/2302.05955/) (2023)
- [A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data](https://mlsanity.com/paper/2511.13514/) (2025)

## Abstract (arXiv)

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.