Symmetric KL-divergence by Stein's Method

Liu-Quan Yao; Song-Hao Liu

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arXiv · 2401.11381

Symmetric KL-divergence by Stein's Method

Liu-Quan Yao·Song-Hao Liu

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Abstract

In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rates of order $O\left( \frac{\ln n}{\sqrt{n}}\right)$. The proof is based on Stein's method. The convergence rate of order $O\left( \frac{1}{\sqrt{n}}\right)$ and $O\left( \frac{1}{n}\right) $ are also obtained under higher moment condition.

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Liu-Quan Yao, Song-Hao Liu. 2024-01-21. Symmetric KL-divergence by Stein's Method. https://arxiv.org/abs/2401.11381

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