Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Correction to Local Information Privacy and Its Applications to Data Aggregation

Bo Jiang, Ming Li, Ravi Tandon

TL;DR

This document provides a correction to the valid range of privacy parameters of the previously proposed LIP mechanism, and proposes efficient algorithms to expand the range of valid privacy parameters.

Abstract

In our previous works, we defined Local Information Privacy (LIP) as a context-aware privacy notion and presented the corresponding privacy-preserving mechanism. Then we claim that the mechanism satisfies epsilon-LIP for any epsilon>0 for arbitrary Px. However, this claim is not completely correct. In this document, we provide a correction to the valid range of privacy parameters of our previously proposed LIP mechanism. Further, we propose efficient algorithms to expand the range of valid privacy parameters. Finally, we discuss the impact of updated results on our original paper's experiments, the rationale of the proposed correction and corrected results.

Correction to Local Information Privacy and Its Applications to Data Aggregation

TL;DR

This document provides a correction to the valid range of privacy parameters of the previously proposed LIP mechanism, and proposes efficient algorithms to expand the range of valid privacy parameters.

Abstract

In our previous works, we defined Local Information Privacy (LIP) as a context-aware privacy notion and presented the corresponding privacy-preserving mechanism. Then we claim that the mechanism satisfies epsilon-LIP for any epsilon>0 for arbitrary Px. However, this claim is not completely correct. In this document, we provide a correction to the valid range of privacy parameters of our previously proposed LIP mechanism. Further, we propose efficient algorithms to expand the range of valid privacy parameters. Finally, we discuss the impact of updated results on our original paper's experiments, the rationale of the proposed correction and corrected results.

Paper Structure

This paper contains 4 sections, 4 theorems, 40 equations, 1 figure, 1 algorithm.

Table of Contents

  1. valid range of privacy parameters
  2. Discussion
  3. Proof of Theorem 1.
  4. Proof of Theorem 2 and Remark 2

Key Result

Theorem 1

For a given probability distribution of $P_X$, with $P_{\min} = \min_x P_{X}(x)$, the mechanism defined in rr-basic satisfies $(\epsilon,0)$- LIP, as long as

Figures (1)

  • Figure 1: When the context-aware randomize response mechanism achieves $(\epsilon,\delta)$-LIP, The relationship between $P_{\min}$ in the prior distribution and $\epsilon,\delta$. Shaded area represents the infeasible region of $\epsilon$ under $\delta$ and $P_{\min}$.

Theorems & Definitions (12)

  • Definition 1: $(\epsilon,\delta)$-Local Information Privacy
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Remark 3
  • Theorem 3
  • Remark 4
  • Example 1
  • Lemma 1
  • ...and 2 more