# Generalized Linear Models with 1-Bit Measurements: Asymptotics of the Maximum Likelihood Estimator

arXiv: https://arxiv.org/abs/2501.04937 · HTML: https://mlsanity.com/paper/2501.04937/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 4 of 4)

- [Mean Estimation from One-Bit Measurements](https://mlsanity.com/paper/1901.03403/) (2019)
- [Deep Signal Recovery with One-Bit Quantization](https://mlsanity.com/paper/1812.00797/) (2018)
- [Estimation in Poisson Noise: Properties of the Conditional Mean Estimator](https://mlsanity.com/paper/1911.03744/) (2019)
- [The Cramer-Rao Bound for Signal Parameter Estimation from Quantized Data](https://mlsanity.com/paper/2209.13182/) (2022)

## Built on by (most cited first, 2 of 2)

- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)

## Abstract (arXiv)

This work establishes regularity conditions for consistency and asymptotic normality of the multiple parameter maximum likelihood estimator(MLE) from censored data, where the censoring mechanism is in the form of 1-bit measurements. The underlying distribution of the uncensored data is assumed to belong to the exponential family, with natural parameters expressed as a linear combination of the predictors, known as generalized linear model (GLM). As part of the analysis, the Fisher information matrix is also derived for both censored and uncensored data, which helps to quantify the impact of censoring and assess the performance of the MLE. The choice of GLM allows one to consider a variety of practical examples where 1-bit estimation is of interest. In particular, it is shown how the derived results can be used to analyze two practically relevant scenarios: the Gaussian model with both unknown mean and variance, and the Poisson model with an unknown mean.