# The Generalized Lasso for Sub-gaussian Measurements with Dithered Quantization

arXiv: https://arxiv.org/abs/1807.06976 · HTML: https://mlsanity.com/paper/1807.06976/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2018.

## Built on by (most cited first, 10 of 10)

- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery](https://mlsanity.com/paper/2212.14562/) (2022)
- [A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing](https://mlsanity.com/paper/2310.03758/) (2023)
- [Quantized Low-Rank Multivariate Regression with Random Dithering](https://mlsanity.com/paper/2302.11197/) (2023)
- [Robust Mean Estimation under Quantization](https://mlsanity.com/paper/2601.07074/) (2026)
- [A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate](https://mlsanity.com/paper/2308.16059/) (2023)
- [Matrix Completion from One-Bit Dither Samples](https://mlsanity.com/paper/2310.03224/) (2023)
- [Computationally efficient reductions between some statistical models](https://mlsanity.com/paper/2402.07717/) (2024)
- [One-Bit Clustering for Two Component Sub-Gaussian Mixture Models](https://mlsanity.com/paper/2606.21873/) (2026)

## Abstract (arXiv)

In the problem of structured signal recovery from high-dimensional linear observations, it is commonly assumed that full-precision measurements are available. Under this assumption, the recovery performance of the popular Generalized Lasso (G-Lasso) is by now well-established. In this paper, we extend these types of results to the practically relevant settings with quantized measurements. We study two extremes of the quantization schemes, namely, uniform and one-bit quantization; the former imposes no limit on the number of quantization bits, while the second only allows for one bit. In the presence of a uniform dithering signal and when measurement vectors are sub-gaussian, we show that the same algorithm (i.e., the G-Lasso) has favorable recovery guarantees for both uniform and one-bit quantization schemes. Our theoretical results, shed light on the appropriate choice of the range of values of the dithering signal and accurately capture the error dependence on the problem parameters. For example, our error analysis shows that the G-Lasso with one-bit uniformly dithered measurements leads to only a logarithmic rate loss compared to the full-precision measurements.