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Adaptive Privacy of Sequential Data Releases Under Collusion

Sophie Taylor, Praneeth Kumar Vippathalla, Justin Coon

TL;DR

An adaptive algorithm for data releases that makes use of a modified Blahut-Arimoto algorithm is developed and it is shown that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility.

Abstract

The fundamental trade-off between privacy and utility remains an active area of research. Our contribution is motivated by two observations. First, privacy mechanisms developed for one-time data release cannot straightforwardly be extended to sequential releases. Second, practical databases are likely to be useful to multiple distinct parties. Furthermore, we can not rule out the possibility of data sharing between parties. With utility in mind, we formulate a privacy-utility trade-off problem to adaptively tackle sequential data requests made by different, potentially colluding entities. We consider both expected distortion and mutual information as measures to quantify utility, and use mutual information to measure privacy. We assume an attack model whereby illicit data sharing, which we call collusion, can occur between data receivers. We develop an adaptive algorithm for data releases that makes use of a modified Blahut-Arimoto algorithm. We show that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility. Finally, we discuss how our findings may extend to applications in machine learning.

Adaptive Privacy of Sequential Data Releases Under Collusion

TL;DR

An adaptive algorithm for data releases that makes use of a modified Blahut-Arimoto algorithm is developed and it is shown that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility.

Abstract

The fundamental trade-off between privacy and utility remains an active area of research. Our contribution is motivated by two observations. First, privacy mechanisms developed for one-time data release cannot straightforwardly be extended to sequential releases. Second, practical databases are likely to be useful to multiple distinct parties. Furthermore, we can not rule out the possibility of data sharing between parties. With utility in mind, we formulate a privacy-utility trade-off problem to adaptively tackle sequential data requests made by different, potentially colluding entities. We consider both expected distortion and mutual information as measures to quantify utility, and use mutual information to measure privacy. We assume an attack model whereby illicit data sharing, which we call collusion, can occur between data receivers. We develop an adaptive algorithm for data releases that makes use of a modified Blahut-Arimoto algorithm. We show that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility. Finally, we discuss how our findings may extend to applications in machine learning.
Paper Structure (19 sections, 4 theorems, 34 equations, 5 figures, 2 tables, 3 algorithms)

This paper contains 19 sections, 4 theorems, 34 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Prior Work
  3. Contributions
  4. Problem Setup
  5. Guiding Principles for Data Release
  6. General Optimisation Problem
  7. Solution Overview
  8. The Blahut-Arimoto Algorithm
  9. An Implicit Solution
  10. Self Consistent Variables
  11. Independent Minimisations
  12. An Iterative Algorithm
  13. Blahut-Arimoto for the Mutual Information Problem
  14. Numerical Validation
  15. Expected Distortion Problem
  16. ...and 4 more sections

Key Result

Proposition 1

The following is a sufficient condition on $p^\star(\hat{r} \mid x, z)$: where $\eta = \eta (x, z, \mu_1, \mu_2)$ is a normalisation factor:

Figures (5)

  • Figure 1: Problem setup for a multi-party adaptive scheme
  • Figure 2: Multi-party adaptive privacy scheme: a detailed view of the $k$th party
  • Figure 3: Minimum expected distortion, $\mathrm{D}(\epsilon, \delta)$ against $\epsilon$ and $\delta$.
  • Figure 4: Convergence of Algorithm \ref{['alg: BA distortion']} for different $\mu_1, \mu_2$ pairs.
  • Figure 5: Lower bound on the maximum mutual information $\mathrm{I}(\epsilon, \delta)$ against $\epsilon$ and $\delta$.

Theorems & Definitions (10)

  • Proposition 1
  • Lemma 1
  • proof
  • Theorem 1
  • Lemma 2
  • proof
  • Remark 1
  • Remark 2
  • proof
  • Remark 3