# Uncertainty quantification by block bootstrap for differentially private stochastic gradient descent

arXiv: https://arxiv.org/abs/2405.12553 · HTML: https://mlsanity.com/paper/2405.12553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 21 May 2024.

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

- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias](https://mlsanity.com/paper/2006.07904/) (2020)
- [Local Differential Privacy and Its Applications: A Comprehensive Survey](https://mlsanity.com/paper/2008.03686/) (2020)
- [Online Covariance Matrix Estimation in Stochastic Gradient Descent](https://mlsanity.com/paper/2002.03979/) (2020)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [A Comprehensive Survey on Local Differential Privacy Toward Data Statistics and Analysis](https://mlsanity.com/paper/2010.05253/) (2020)
- [Statistical inference using SGD](https://mlsanity.com/paper/1705.07477/) (2017)
- [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020)
- [Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator](https://mlsanity.com/paper/2306.02205/) (2023)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [A likelihood ratio approach to sequential change point detection for a general class of parameters](https://mlsanity.com/paper/1802.07696/) (2018)
- [Online Local Differential Private Quantile Inference via Self-normalization](https://mlsanity.com/paper/2306.10260/) (2023)
- [Differentially Private Confidence Interval for Extrema of Parameters](https://mlsanity.com/paper/2303.02892/) (2023)

## 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)

Stochastic Gradient Descent (SGD) is a widely used tool in machine learning. In the context of Differential Privacy (DP), SGD has been well studied in the last years in which the focus is mainly on convergence rates and privacy guarantees. While in the non private case, uncertainty quantification (UQ) for SGD by bootstrap has been addressed by several authors, these procedures cannot be transferred to differential privacy due to multiple queries to the private data. In this paper, we propose a novel block bootstrap for SGD under local differential privacy that is computationally tractable and does not require an adjustment of the privacy budget. The method can be easily implemented and is applicable to a broad class of estimation problems. We prove the validity of our approach and illustrate its finite sample properties by means of a simulation study. As a by-product, the new method also provides a simple alternative numerical tool for UQ for non-private SGD.