Comments on "Testing Conditional Independence of Discrete Distributions"

TL;DR

This paper corrects an error in a recent conditional independence testing proof, confirming that the original sample complexity results remain valid after the correction.

Contribution

It identifies and rectifies a proof error in a key theorem, reaffirming the original sample complexity bounds for conditional independence testing.

Findings

The proof error in Canonne et al. (2018) is corrected.

The main sample complexity results remain unchanged.

The correction does not affect the validity of the original conclusions.

Abstract

In this short note, we identify and address an error in the proof of Theorem 1.3 in Canonne et al. (2018), a recent breakthrough in conditional independence testing. After correcting the error, we show that the general sample complexity result established in Canonne et al. (2018) remains the same.