---
title: "Private Generative Bootstrap via Blocking: Privacy-Preserving Uncertainty Quantification"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2608.02480v1"
permalink: "https://feed.astralor.com/items/itm_5aea94f098bec48f4d9cc5a7"
published: "2026-08-03T16:47:14.000Z"
score: 81
channel: "ai"
tags: ["PGBB","Uncertainty Quantification","Differential Privacy","Amortized Inference","Bayesian Bootstrap","Privacy Protection"]
---

# Private Generative Bootstrap via Blocking: Privacy-Preserving Uncertainty Quantification

## AI commentary

> What makes this paper noteworthy is its fusion of differential privacy with Bayesian bootstrap without requiring a data-generating model, which is highly practical. For engineers working on privacy-preserving computation, statistical release, or AI decision-making with confidence intervals, PGBB offers a plug-and-play new approach that deserves a close read.

## At a glance

As AI systems gain more access to personal data, protecting the privacy of statistical answers and their uncertainty is crucial. This paper proposes a new Private Generative Bayesian Bootstrap (PGBB) that randomly groups individuals and assigns a single weight to each group, concealing individual contributions to strengthen differential privacy. Amortized inference decouples private learning from posterior sampling, with calibrated noise added during training; subsequent posterior draws require no extra privacy or computation. Theoretical guarantees for differential privacy, convergence, and posterior discrepancy are established. Simulations and applications to U.S. Census returns and birthweight quantiles show PGBB yields competitive private uncertainty quantification, outperforming private Bayesian alternatives that require a specified data-generating model.

## Key points

- Introduces PGBB, a privacy-preserving Bayesian bootstrap using blocking and group-level weights instead of individual random weights.
- Combines amortized inference with differential privacy: calibrated noise is added during training, enabling subsequent posterior sampling at no extra privacy cost.
- Provides theoretical guarantees on differential privacy, convergence, and discrepancy from the non-private blocked bootstrap, plus a data-free tuning strategy.
- Demonstrates competitive private uncertainty quantification in simulations and U.S. Census/natality data, outperforming model-based private Bayesian alternatives.

## Full text

With AI systems gaining more access to individuals' information, it is important to protect privacy when reporting statistical answers. Equally important is to privatize the reporting of uncertainty in such answers. To this end, we adopt a Bayesian likelihood-free framework and make simulation from the posterior private. In particular, we propose a new private instantiation of the Bayesian bootstrap using a blocking strategy. Rather than assigning idiosyncratic random weights to each individual, we randomly group individuals and assign a single weight to each group. By concealing individuals' contributions within a group, we fortify differential privacy gates. We harness amortized inference that decouples private learning from posterior sampling. A push-forward map from observation weights to posterior samples is learned privately by adding calibrated noise during training. Subsequent posterior draws require no additional privacy and computation budget. We call the resulting method the Private Generative Bayesian Bootstrap (PGBB). We establish a differential privacy guarantee, analyze convergence to the non-private blocked-bootstrap target, and quantify the discrepancy between the ordinary and blocked Bayesian-bootstrap posteriors. In addition, we derive data-free tuning of the block Dirichlet concentration parameter that restores posterior dispersion asymptotically. We also show a single fit of PGBB can support a family of loss-based decision rules simultaneously without additional privacy cost. In simulations and in applications to U.S. Census returns to schooling and U.S. natality birthweight quantiles, PGBB gives competitive private uncertainty quantification and improves over private Bayesian alternatives that require a specified data-generating model in common settings.

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