An Overview of Causal Inference using Kernel Embeddings

TL;DR

This paper reviews how kernel embeddings in reproducing kernel Hilbert spaces facilitate nonparametric causal inference, enabling better identification of causal effects from observational data.

Contribution

It provides a comprehensive overview of recent methods combining kernel embeddings with causal inference techniques, highlighting their advantages and applications.

Findings

Kernel embeddings enable flexible, nonparametric causal effect estimation.

They facilitate the transformation of observational data distributions into interventional distributions.

Recent research demonstrates improved causal inference using kernel-based methods.

Abstract

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable flexible representations of complex relationships between variables. They serve as a mechanism for efficiently transferring the representation of a distribution downstream to other tasks, such as hypothesis testing or causal effect estimation. In the context of causal inference, the main challenges include identifying causal associations and estimating the average treatment effect from observational data, where confounding variables may obscure direct cause-and-effect relationships. Kernel embeddings provide a robust nonparametric framework for addressing these challenges. They allow for the representations of distributions of observational data and their seamless transformation into representations of interventional distributions to estimate relevant causal quantities. We overview recent research that leverages the expressiveness of kernel embeddings in tandem with causal inference.