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DOI: 10.4230/LIPIcs.ITCS.2020.31
URN: urn:nbn:de:0030-drops-117165
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11716/
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Jung, Christopher ; Ligett, Katrina ; Neel, Seth ; Roth, Aaron ; Sharifi-Malvajerdi, Saeed ; Shenfeld, Moshe

A New Analysis of Differential Privacy’s Generalization Guarantees

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LIPIcs-ITCS-2020-31.pdf (0.5 MB)


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.

BibTeX - Entry

@InProceedings{jung_et_al:LIPIcs:2020:11716,
  author =	{Christopher Jung and Katrina Ligett and Seth Neel and Aaron Roth and Saeed Sharifi-Malvajerdi and Moshe Shenfeld},
  title =	{{A New Analysis of Differential Privacy’s Generalization Guarantees}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11716},
  URN =		{urn:nbn:de:0030-drops-117165},
  doi =		{10.4230/LIPIcs.ITCS.2020.31},
  annote =	{Keywords: Differential Privacy, Adaptive Data Analysis, Transfer Theorem}
}

Keywords: Differential Privacy, Adaptive Data Analysis, Transfer Theorem
Seminar: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 10.01.2020


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