Relaxed Triangle Inequality for Kullback-Leibler Divergence Between Multivariate Gaussian Distributions
arXiv:2602.02577v1 Announce Type: new
Abstract: The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between multivariate Gaussian distributions follows a relaxed triangle inequality. Given any three multivariate Gaussian distributions $mathcal{N}_1, mathcal{N}_2$, and $mathcal{N}_3$, if $KL(mathcal{N}_1, mathcal{N}_2)leq epsilon_1$ and $KL(mathcal{N}_2, mathcal{N}_3)leq epsilon_2$, then $KL(mathcal{N}_1, mathcal{N}_3)
Abstract: The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between multivariate Gaussian distributions follows a relaxed triangle inequality. Given any three multivariate Gaussian distributions $mathcal{N}_1, mathcal{N}_2$, and $mathcal{N}_3$, if $KL(mathcal{N}_1, mathcal{N}_2)leq epsilon_1$ and $KL(mathcal{N}_2, mathcal{N}_3)leq epsilon_2$, then $KL(mathcal{N}_1, mathcal{N}_3)
Shiji Xiao, Yufeng Zhang, Chubo Liu, Yan Ding, Keqin Li, Kenli Li
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