# Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery

## TL;DR

This paper introduces RCIT and RCoT, two scalable, approximate kernel-based conditional independence tests that enable faster non-parametric causal discovery without sacrificing accuracy in large datasets.

## Contribution

The authors propose two novel relaxations, RCIT and RCoT, which approximate KCIT using random Fourier features, significantly improving scalability for large datasets in causal discovery.

## Key findings

- RCIT and RCoT scale linearly with sample size.
- Both tests produce accurate p-values faster than KCIT.
- Causal discovery algorithms using RCIT or RCoT are as accurate as those using KCIT.

## Abstract

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales cubicly with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.