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Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.
Estimates of the proximity of Gaussian measures
S. S. Barsov and V. V. Ul’yanov · 1987
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The Multivariate Normal Distribution
Y. L. Tong · 1990
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Asymptotics in Statistics: Some Basic Concepts
Lucien Le Cam and Grace Lo Yang · 2000
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Introduction to Nonparametric Estimation
Alexandre B. Tsybakov · 2004
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Statistical Inference Based on Divergence Measures
Leandro Pardo · 2006
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Gaussian Processes for Machine Learning
Carl Edward Rasmussen and Christopher K. I. Williams · 2006
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Handbook of Probability
Ionut Florescu and Ciprian A Tudor · 2013
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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 2013
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f f -divergence inequalities
Igal Sason and Sergio Verdú · 2016
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Markov Chains and Mixing Times, second edition, with contributions by Elizabeth L. Wilmer, with a chapter on “coupling from the past” by James G. Propp and David B. Wilson
David A. Levin and Yuval Peres · 2017
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High-Dimensional Probability: An Introduction with Applications in Data Science
Roman Vershynin · 2018
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Polynomial time and private learning of unbounded Gaussian mixture models
Jamil Arbas, Hassan Ashtiani, and Christopher Liaw · 2023
Closest in time.
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