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Achieving Privacy Utility Balance for Multivariate Time Series Data

Gaurab Hore, Tucker McElroy, Anindya Roy

TL;DR

A multivariate all-pass (MAP) filtering method is proposed, employing an optimization algorithm to achieve the best balance between data utility and privacy protection, and is applied to the U.S. Census Bureau's Quarterly Workforce Indicator dataset.

Abstract

Utility-preserving data privatization is of utmost importance for data-producing agencies. The popular noise-addition privacy mechanism distorts autocorrelation patterns in time series data, thereby marring utility; in response, McElroy et al. (2023) introduced all-pass filtering (FLIP) as a utility-preserving time series data privatization method. Adapting this concept to multivariate data is more complex, and in this paper we propose a multivariate all-pass (MAP) filtering method, employing an optimization algorithm to achieve the best balance between data utility and privacy protection. To test the effectiveness of our approach, we apply MAP filtering to both simulated and real data, sourced from the U.S. Census Bureau's Quarterly Workforce Indicator (QWI) dataset.

Achieving Privacy Utility Balance for Multivariate Time Series Data

TL;DR

A multivariate all-pass (MAP) filtering method is proposed, employing an optimization algorithm to achieve the best balance between data utility and privacy protection, and is applied to the U.S. Census Bureau's Quarterly Workforce Indicator dataset.

Abstract

Utility-preserving data privatization is of utmost importance for data-producing agencies. The popular noise-addition privacy mechanism distorts autocorrelation patterns in time series data, thereby marring utility; in response, McElroy et al. (2023) introduced all-pass filtering (FLIP) as a utility-preserving time series data privatization method. Adapting this concept to multivariate data is more complex, and in this paper we propose a multivariate all-pass (MAP) filtering method, employing an optimization algorithm to achieve the best balance between data utility and privacy protection. To test the effectiveness of our approach, we apply MAP filtering to both simulated and real data, sourced from the U.S. Census Bureau's Quarterly Workforce Indicator (QWI) dataset.

Paper Structure

This paper contains 24 sections, 1 theorem, 53 equations, 7 figures, 2 tables.

Table of Contents

  1. Disclaimer
  2. Introduction
  3. Multivariate All-pass Filters
  4. Multivariate All-Pass Filtering
  5. A Class of Multivariate All-pass Filters
  6. Privacy vs Utility for Multiple Time Series
  7. Second-Order Utility
  8. Multivariate Linear Incremental Privacy (m-LIP)
  9. Privacy-Utility Optimization
  10. Feasible Implementation of m-LIP
  11. Positive Definite Estimation of Spectral Densities
  12. Spectral Factorization
  13. Parameterization of the $S\textsf{-MAP}$ Class
  14. Optimal All-pass Filter Selection
  15. Estimation of Trend and Forecast Extension
  16. ...and 9 more sections

Key Result

Proposition 1

Let $\{\mathbf{X}_t\}$, $\{ \mathbf{Y}_t \}$, and $\{ \mathbf{Z}_t\}$ be weakly stationary multivariate time series that are also jointly weakly stationary, where the cross-spectral densities are $S_{\mathbf{X} \mathbf{Y} }$, $S_{\mathbf{X} \mathbf{Z} }$, and $S_{\mathbf{Y} \mathbf{Z} }$. Further, d Then the following formulas for conditional variances and covariances hold: Moreover, the scalar q

Figures (7)

  • Figure 1: Comparison of sample autocorrelation function (ACF) and the cross-correlation function (CCF) of the original and the filtered copies for the first and second series for the case $r=1$ (VAR(1)). The top row shows the two ACF plots while the bottom plot shows the CCF between the two series.
  • Figure 2: Histograms of $m\textsf{-LIP}$ values for VAR(1) (left) and VARMA(1,1) (right), $r=0$ case.
  • Figure 3: Comparison of sample autocorrelation and the cross-correlation functions of the original and the filtered copies for the first and second series for the case $r=1$ (VARMA(1,1)). The top row shows the two ACF plots while the bottom plot shows the CCF between the two series.
  • Figure 4: Comparison of sample autocorrelation and the cross-correlation functions of the original and the filtered copies for the first and second series for the case $r=1$ (VAR(1), ARCH(1) error). The top row shows the two ACF plots while the bottom plot shows the CCF between the two series.
  • Figure 5: QWI employment count for Maryland counties.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Definition 1
  • Definition 2: $S$-Multivariate All-Pass or $S\textsf{-MAP}$
  • Proposition 1
  • proof
  • Definition 3: $m\textsf{-LIP}$