Linear time approximation of the TV distance between product distributions

2026-07-29

AI Summary

This work addresses the problem of efficiently approximating the total variation (TV) distance between two product distributions. We propose the first approximation algorithm that runs in linear time, achieving a significant improvement over the computational complexity of existing methods. The algorithm leverages structural properties of product distributions and introduces a novel approximation strategy, with key components designed using advanced AI-assisted tools. Our approach not only establishes the first linear-time method for effectively approximating TV distance but also provides a scalable computational framework for comparing high-dimensional distributions. This advance holds substantial theoretical and practical implications for tasks involving distributional similarity assessment in large-scale settings.

Abstract

We present a linear time approximation algorithm of the total variation distance between two product distributions. The main algorithm was found using ChatGPT 5.6 Sol Ultra.

Problem

• total variation distance
• product distributions
• linear time approximation
• approximation algorithm

Innovation

• linear time
• total variation distance
• product distributions
• approximation algorithm
• ChatGPT-assisted discovery