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Enhancing Feature-Specific Data Protection via Bayesian Coordinate Differential Privacy

Maryam Aliakbarpour, Syomantak Chaudhuri, Thomas A. Courtade, Alireza Fallah, Michael I. Jordan

TL;DR

A Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), is proposed that enables feature-specific privacy quantification and obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Abstract

Local Differential Privacy (LDP) offers strong privacy guarantees without requiring users to trust external parties. However, LDP applies uniform protection to all data features, including less sensitive ones, which degrades performance of downstream tasks. To overcome this limitation, we propose a Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), that enables feature-specific privacy quantification. This more nuanced approach complements LDP by adjusting privacy protection according to the sensitivity of each feature, enabling improved performance of downstream tasks without compromising privacy. We characterize the properties of BCDP and articulate its connections with standard non-Bayesian privacy frameworks. We further apply our BCDP framework to the problems of private mean estimation and ordinary least-squares regression. The BCDP-based approach obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Enhancing Feature-Specific Data Protection via Bayesian Coordinate Differential Privacy

TL;DR

A Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), is proposed that enables feature-specific privacy quantification and obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Abstract

Local Differential Privacy (LDP) offers strong privacy guarantees without requiring users to trust external parties. However, LDP applies uniform protection to all data features, including less sensitive ones, which degrades performance of downstream tasks. To overcome this limitation, we propose a Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), that enables feature-specific privacy quantification. This more nuanced approach complements LDP by adjusting privacy protection according to the sensitivity of each feature, enabling improved performance of downstream tasks without compromising privacy. We characterize the properties of BCDP and articulate its connections with standard non-Bayesian privacy frameworks. We further apply our BCDP framework to the problems of private mean estimation and ordinary least-squares regression. The BCDP-based approach obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Paper Structure

This paper contains 34 sections, 19 theorems, 84 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our contributions:
  3. Bayesian Feature-Specific Protection:
  4. Related Work:
  5. Organization:
  6. Problem Formulation
  7. Local differential privacy
  8. Bayesian differential privacy:
  9. Coordinate differential privacy:
  10. Our formulation: Bayesian coordinate differential privacy:
  11. Properties of BCDP
  12. BCDP through the Lens of Hypothesis Testing
  13. For BCDP:
  14. BCDP can be achieved via LDP
  15. BCDP does not imply LDP
  16. ...and 19 more sections

Key Result

Proposition 1

If $M$ is $\varepsilon$-LDP then $(\pi,M)$ is $\varepsilon$-BDP. Conversely, if $(\pi,M)$ is $\varepsilon$-BDP, then (assuming $\cY$ is a Polish space) there exists a mechanism $M'$ which is $\varepsilon$-LDP such that $P\{M(\vecx) = M'(\vecx)\} = 1$.

Figures (3)

  • Figure 1: General relation of LDP (\ref{['definition:LDP']}), BDP (\ref{['def:pi-DP']}), CDP (\ref{['def:coordinate-dp']}) and BCDP (\ref{['def:BCDP']}). The condition $\bm{a} \preceq \vecb$ is to be read as $a_i \leq b_i \ \forall i$. The implication arrows and the described transformation of the parameters are to be interpreted as sufficient condition. For example, an $\varepsilon_L$-DP mechanism is guaranteed to be $\vecc$-CDP for $\vecc \preceq \varepsilon_L \bm1$. The function that translates $\vecc$-CDP under the prior $\pi$ to BCDP is presented in the \ref{['prop:cdp-to-bdp']}.
  • Figure 2: The figure illustrates how the mechanism $M_{\mathsf{mean}}$ in Mechanism \ref{['alg:local-channels']} obtains the estimate $\bm\hat{\nu}$. For example, the vector $Y^k$ is obtained by taking the vector $(x_{k},x_{k+1},\ldots,x_{d})$ and using the LDP channel $M_{\mathsf{LDP}}$ with privacy parameter $c_k - c_{k-1}$. $\hat{\nu}_i$ is obtained by taking a linear combination of the component of $\{Y^k\}_{k \in [d]}$ corresponding to $x_i$, i.e., directly below $x_i$ in the figure.
  • Figure 3: MSE as $q$ is varied keeping $\bm\delta$ and $\varepsilon$ constant for $M_{\mathsf{mean}}$ and $\min\bm\delta$-LDP.

Theorems & Definitions (34)

  • Definition 1: Local DP kasiviswanathan2011can
  • Definition 2: Bayesian DP
  • Proposition 1
  • Definition 3: Coordinate DP
  • Definition 4: Bayesian Coordinate DP
  • Proposition 2
  • Theorem 1
  • Proposition 3
  • Example 1
  • Proposition 4
  • ...and 24 more