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A New Analysis of Differential Privacy’s Generalization Guarantees

Authors Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, Moshe Shenfeld

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Author Details

Christopher Jung
  • University of Pennsylvania, Philadelphia, PA, USA
Katrina Ligett
  • The Hebrew University, Jerusalem, Israel
Seth Neel
  • University of Pennsylvania, Philadelphia, PA, USA
Aaron Roth
  • University of Pennsylvania, Philadelphia, PA, USA
Saeed Sharifi-Malvajerdi
  • University of Pennsylvania, Philadelphia, PA, USA
Moshe Shenfeld
  • The Hebrew University, Jerusalem, Israel

Funding

  • Jung, Christopher: Supported in part by NSF grant AF-1763307.
  • Ligett, Katrina: Supported in part by Israel Science Foundation (ISF) grant #1044/16, the United States Air Force and DARPA under contracts FA8750-16-C-0022 and FA8750-19-2-0222, and the Federmann Cyber Security Center in conjunction with the Israel national cyber directorate.
  • Neel, Seth: Supported in part by an NSF Graduate Research Fellowship.
  • Roth, Aaron: Supported in part by NSF grant AF-1763314, the United States Air Force and DARPA under Contract No FA8750-16-C-0022, and a grant from the Sloan Foundation.
  • Shenfeld, Moshe: Supported in part by Israel Science Foundation (ISF) grant #1044/16, the United States Air Force and DARPA under contracts FA8750-16-C-0022 and FA8750-19-2-0222, and the Federmann Cyber Security Center in conjunction with the Israel national cyber directorate. Any opinions,findings and conclusions or recommendations expressed in this materialare those of the author(s) and do not necessarily reflect the views ofthe United States Air Force and DARPA.

Acknowledgements

We thank Adam Smith for helpful conversations at an early stage of this work, and Daniel Roy for helpful feedback on the presentation of the result.

Cite As Get BibTex

Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, and Moshe Shenfeld. A New Analysis of Differential Privacy’s Generalization Guarantees. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ITCS.2020.31

Abstract

We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and gives structural insights that we expect will be useful elsewhere. We show: 1) that differential privacy ensures that the expectation of any query on the conditional distribution on datasets induced by the transcript of the interaction is close to its expectation on the data distribution, and 2) sample accuracy on its own ensures that any query answer produced by the mechanism is close to the expectation of the query on the conditional distribution. This second claim follows from a thought experiment in which we imagine that the dataset is resampled from the conditional distribution after the mechanism has committed to its answers. The transfer theorem then follows by summing these two bounds, and in particular, avoids the "monitor argument" used to derive high probability bounds in prior work.
An upshot of our new proof technique is that the concrete bounds we obtain are substantially better than the best previously known bounds, even though the improvements are in the constants, rather than the asymptotics (which are known to be tight). As we show, our new bounds outperform the naive "sample-splitting" baseline at dramatically smaller dataset sizes compared to the previous state of the art, bringing techniques from this literature closer to practicality.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sample complexity and generalization bounds
Keywords
  • Differential Privacy
  • Adaptive Data Analysis
  • Transfer Theorem

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