# Lower Bounds for the Total Variation Distance Given Means and Variances of Distributions

arXiv: https://arxiv.org/abs/2212.05820 · HTML: https://mlsanity.com/paper/2212.05820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 17 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 1 of 1)

- [Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians](https://mlsanity.com/paper/2109.01064/) (2021)

## Built on by (most cited first, 3 of 3)

- [Fundamental Limitations of Alignment in Large Language Models](https://mlsanity.com/paper/2304.11082/) (2023)
- [Towards Explaining Deep Neural Network Compression Through a Probabilistic Latent Space](https://mlsanity.com/paper/2403.00155/) (2024)
- [Restricted Spectral Gap Decomposition for Simulated Tempering Targeting Mixture Distributions](https://mlsanity.com/paper/2505.15059/) (2025)

## Abstract (arXiv)

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.