# Gaussian Approximation of Quantization Error for Estimation from Compressed Data

arXiv: https://arxiv.org/abs/2001.03243 · HTML: https://mlsanity.com/paper/2001.03243/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [Optimal Quantization for Matrix Multiplication](https://mlsanity.com/paper/2410.13780/) (2024)
- [Denoising Noisy Neural Networks: A Bayesian Approach with Compensation](https://mlsanity.com/paper/2105.10699/) (2021)
- [Rotation Invariant Quantization for Model Compression](https://mlsanity.com/paper/2303.03106/) (2023)
- [Deep Reinforcement Learning-Empowered Wireless Sensor Networking for 6G Closed-Loop Controls](https://mlsanity.com/paper/2607.08272/) (2026)

## Abstract (arXiv)

We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that the Wasserstein distance between a bitrate-R compressed version of X and its observation under an AWGN-channel of signal-to-noise ratio 22R-1 is sub-linear in the problem dimension. We utilize this fact to connect the risk of an estimator based on an AWGN-corrupted version of X to the risk attained by the same estimator when fed with its bitrate-R quantized version. We demonstrate the usefulness of this connection by deriving various novel results for inference problems under compression constraints, including minimax estimation, sparse regression, compressed sensing, and the universality of linear estimation in remote source coding.