The total variation distance between high-dimensional Gaussians with the same mean
Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel pith:TMOL4WOLrecord.jsonopen to challenge →
read the original abstract
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.
This paper has not been read by Pith yet.
Forward citations
Cited by 11 Pith papers
-
Approximate Minimax Estimation of a Bounded Normal Mean via Stochastic Mirror Ascent
Stochastic mirror ascent provably finds an approximately least-favorable distribution and minimax estimator for the Bounded Normal Mean problem, yielding 6–18% risk improvements over the minimax linear estimator.
-
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
Establishes non-asymptotic Gaussian approximation bounds for federated LSA with explicit communication-heterogeneity trade-offs and introduces an online multiplier bootstrap for last-iterate inference with validity gu...
-
TRAM: Test-Time Risk Adaptation with Mixture of Agents
TRAM is a test-time mixture method that scores and composes risk-neutral source policies using reward and occupancy-based risk to achieve new reward-risk tradeoffs without parameter updates.
-
The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning
NDIS lemma computes closed-form hockey-stick divergence δ(ε) between arbitrary multivariate Gaussians and is applied to obtain tighter privacy for random projection.
-
Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence
Proves global GD convergence on reverse Fisher divergence for GMM score matching to single-Gaussian targets from arbitrary init and to separated GMM targets under random init.
-
Online Conformal Prediction for Non-Exchangeable Panel Data
An online conformal prediction framework for non-exchangeable panel data that forms prediction sets using related units' contemporaneous data with adaptive similarity weights and miscoverage levels to deliver stepwise...
-
On Computing Total Variation Distance Between Mixtures of Product Distributions
A randomized (1±ε)-approximation algorithm for TV distance between k-mixtures of product distributions runs in poly((nq)^k, 1/ε) time, with exact poly(n, 2^{O(k)}) deterministic algorithm for Boolean subcubes and #P-h...
-
Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
New Berry-Esseen bounds for multivariate martingale difference sequences achieve n^{-1/4} rate and polylog(d) dimension dependence in Kolmogorov distance.
-
Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent
Proves the first fully non-asymptotic bound on the accuracy of multiplier bootstrap for constructing confidence sets from Polyak-Ruppert SGD iterates, achieving convex-distance rates up to 1/sqrt(n) under regularity c...
-
Another Look at Bandwidth-free Inference: a Sample Splitting Approach
Sample splitting plus self-normalization (SS-SN) is introduced for bandwidth-free inference on time series parameters, with limiting distributions derived for diverging dimensions.
-
Safety Guarantees in Zero-Shot Reinforcement Learning for Cascade Dynamical Systems
A probabilistic bound is derived showing that safety after zero-shot RL deployment in cascade systems depends on the tracking quality achieved by a low-level controller for the inner states.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.