An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings

TL;DR

This paper introduces a novel asymptotic test for conditional independence leveraging analytic kernel embeddings, providing a more accurate and reliable method especially in high-dimensional data scenarios.

Contribution

The paper presents a new conditional dependence measure and an asymptotic distribution-based test that outperform existing methods in accuracy and efficiency.

Findings

Outperforms state-of-the-art methods in type-I and type-II errors

Effective in high-dimensional settings

Provides a consistent statistical test for conditional independence

Abstract

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of locations. We obtain its asymptotic distribution under the null hypothesis of conditional independence and design a consistent statistical test from it. We conduct a series of experiments showing that our new test outperforms state-of-the-art methods both in terms of type-I and type-II errors even in the high dimensional setting.