Differential Privacy for Bayesian Inference through Posterior Sampling
Authors: Christos Dimitrakakis, Blaine Nelson, Zuhe Zhang, Aikaterini Mitrokotsa, Benjamin I. P. Rubinstein
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We then prove bounds on the sensitivity of the posterior to the data, which delivers a measure of robustness. We also show how to use posterior sampling to provide differentially private responses to queries, within a decision-theoretic framework. Finally, we provide bounds on the utility of answers to queries and on the ability of an adversary to distinguish between data sets. The latter are complemented by a novel use of Le Cam s method to obtain lower bounds on distinguishability. Our results hold for arbitrary metrics, including those for the common definition of differential privacy. For specific choices of the metric, we give a number of examples satisfying our assumptions. ... Appendix A contains proofs of the main theorems. Finally, Appendix B details proofs of the examples demonstrating our assumptions. |
| Researcher Affiliation | Collaboration | Christos Dimitrakakis EMAIL University of Lille, F-59650 Villeneuve-d Ascq, France SEAS, Harvard University, Cambridge MA-02138, USA DIT, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden Blaine Nelson EMAIL Google, Inc. 1600 Amphitheatre Parkway Mountain View, CA 94043, USA Zuhe Zhang EMAIL School of Mathematics & Statistics The University of Melbourne Parkville, VIC 3010, Australia Aikaterini Mitrokotsa EMAIL Department of Computer Science & Engineering Chalmers University of Technology SE-412 96, Gothenburg, Sweden Benjamin I. P. Rubinstein EMAIL School of Computing & Information Systems The University of Melbourne Parkville, VIC 3010, Australia |
| Pseudocode | Yes | Algorithm 1 BAPS: Bayesian Posterior Sampling ... Algorithm 2 PSAQR: Posterior Sample Query Response |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | For this reason, we provide illustrative examples in the exponential family. However, our setting is wholly general and not limited to specific distribution families, or i.i.d. observations. Any family could be chosen: so long as it either satisfies our assumptions directly, or can be restricted so that it does. For example, our framework applies to families of discrete Bayesian networks with directed-acyclic topologies (e.g., Markov chains; see Lemma 24 on page 21) and multivariate Gaussians (see Lemma 23), where the observations may not satisfy the i.i.d. assumption. ... Section 5. Examples Satisfying our Assumptions. |
| Dataset Splits | No | The paper does not describe any empirical experiments using specific datasets, and therefore no information about dataset splits is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any empirical experiments, therefore no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical and does not describe any empirical experiments, therefore no specific software dependencies with version numbers are mentioned. |
| Experiment Setup | No | The paper is theoretical and does not describe any empirical experiments, therefore no specific experimental setup details such as hyperparameters or training configurations are provided. |