# One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation

arXiv: https://arxiv.org/abs/2202.07194 · HTML: https://mlsanity.com/paper/2202.07194/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Discrete Distribution Estimation under Local Privacy](https://mlsanity.com/paper/1602.07387/) (2016)
- [Collecting and Analyzing Multidimensional Data with Local Differential Privacy](https://mlsanity.com/paper/1907.00782/) (2019)
- [Local, Private, Efficient Protocols for Succinct Histograms](https://mlsanity.com/paper/1504.04686/) (2015)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Empirical Risk Minimization in Non-interactive Local Differential Privacy: Efficiency and High Dimensional Case](https://mlsanity.com/paper/1802.04085/) (2018)
- [Privacy-preserving parametric inference: a case for robust statistics](https://mlsanity.com/paper/1911.10167/) (2019)
- [Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries](https://mlsanity.com/paper/1503.01214/) (2015)
- [Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible](https://mlsanity.com/paper/1706.03316/) (2017)
- [Local Private Hypothesis Testing: Chi-Square Tests](https://mlsanity.com/paper/1709.07155/) (2017)
- [Noninteractive Locally Private Learning of Linear Models via Polynomial Approximations](https://mlsanity.com/paper/1812.06825/) (2018)
- [Comparing Population Means under Local Differential Privacy: with Significance and Power](https://mlsanity.com/paper/1803.09027/) (2018)

## Built on by (most cited first, 1 of 1)

- [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026)

## Abstract (arXiv)

Local differential privacy~(LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator~(QMLE) has been developed, but the existing method to build LDP QMLE is difficult to implement for a large-scale survey system in the real world due to long waiting time, expensive communication cost, and the boundedness assumption of derivative of a log-likelihood function. We provided an alternative LDP protocol without those issues, which is potentially much easily deployable to a large-scale survey. We also provided sufficient conditions for the consistency and asymptotic normality and limitations of our protocol. Our protocol is less burdensome for the users, and the theoretical guarantees cover more realistic cases than those for the existing method.