The total variation distance between high-dimensional Gaussians
By Luc Devroye, Abbas Mehrabian, Tommy Reddad. 2018
259 citations recorded by the source corpus.
We prove a lower bound and an upper bound for the total variation distance between two high-dimensional Gaussians, which are within a constant factor of one another.
View Paper: https://www.semanticscholar.org/paper/b1048213518de9b7dba8225cfc5fe350c1557759
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Citations in the corpus
- No Subclass Left Behind: Fine-Grained Robustness in Coarse-Grained Classification Problems (2020, methodology): “Before we prove Lemma 3, we first provide a simple lemma bounding the total variation distance of two Gaussians in terms of the Euclidean distance between their parameters, directly based on the results from [14].”
- DSTAGNN: Dynamic Spatial-Temporal Aware Graph Neural Network for Traffic Flow Forecasting (2022, methodology): “There are many methods for measuring the di ff erence in probability distributions, such as Kullback-Leibler (KL) divergence (Goldberger et al., 2003), Hellinger Distance (Kailath, 1967), and Total Variation Distance (Devroye et al., 2018).”
- Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss (2021, background): “For two Gaussian distributions with variance σ2 · Id×d and centers at most σ6 far from each other, their TV-distance is at most 16 (see the first equation on Page 5 of (Devroye et al., 2018)), hence for any x ∈ N(R), we have P (Si|x) ≥ 2 3 − 1 6 = 1 2 .”