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Privacy Preserving Semi-Decentralized Mean Estimation over Intermittently-Connected Networks

Rajarshi Saha, Mohamed Seif, Michal Yemini, Andrea J. Goldsmith, H. Vincent Poor

TL;DR

This work addresses privately estimating the mean of distributed vectors over intermittently connected networks. It introduces PriCER, a two-stage Private Collaborative Estimation via Relaying scheme that uses neighbor relaying and Gaussian perturbations to achieve differential privacy while mitigating link outages. The paper develops a detailed error analysis separating topology-induced variance and privacy-induced variance, and it optimizes relaying weights and noise variances under peer-to-peer privacy constraints, including closed-form solutions for Erdős-Rényi topologies. It also provides comprehensive privacy analyses at local, relay, and server levels, and demonstrates the approach via numerical experiments on distributed K-means and mean estimation scenarios. The results show PriCER can achieve favorable utility-privacy Tradeoffs in intermittently connected networks and is compatible with over-the-air aggregation techniques, offering practical improvements for privacy-preserving distributed estimation.

Abstract

We consider the problem of privately estimating the mean of vectors distributed across different nodes of an unreliable wireless network, where communications between nodes can fail intermittently. We adopt a semi-decentralized setup, wherein to mitigate the impact of intermittently connected links, nodes can collaborate with their neighbors to compute a local consensus, which they relay to a central server. In such a setting, the communications between any pair of nodes must ensure that the privacy of the nodes is rigorously maintained to prevent unauthorized information leakage. We study the tradeoff between collaborative relaying and privacy leakage due to the data sharing among nodes and, subsequently, propose PriCER: Private Collaborative Estimation via Relaying -- a differentially private collaborative algorithm for mean estimation to optimize this tradeoff. The privacy guarantees of PriCER arise (i) implicitly, by exploiting the inherent stochasticity of the flaky network connections, and (ii) explicitly, by adding Gaussian perturbations to the estimates exchanged by the nodes. Local and central privacy guarantees are provided against eavesdroppers who can observe different signals, such as the communications amongst nodes during local consensus and (possibly multiple) transmissions from the relays to the central server. We substantiate our theoretical findings with numerical simulations. Our implementation is available at https://github.com/rajarshisaha95/private-collaborative-relaying.

Privacy Preserving Semi-Decentralized Mean Estimation over Intermittently-Connected Networks

TL;DR

This work addresses privately estimating the mean of distributed vectors over intermittently connected networks. It introduces PriCER, a two-stage Private Collaborative Estimation via Relaying scheme that uses neighbor relaying and Gaussian perturbations to achieve differential privacy while mitigating link outages. The paper develops a detailed error analysis separating topology-induced variance and privacy-induced variance, and it optimizes relaying weights and noise variances under peer-to-peer privacy constraints, including closed-form solutions for Erdős-Rényi topologies. It also provides comprehensive privacy analyses at local, relay, and server levels, and demonstrates the approach via numerical experiments on distributed K-means and mean estimation scenarios. The results show PriCER can achieve favorable utility-privacy Tradeoffs in intermittently connected networks and is compatible with over-the-air aggregation techniques, offering practical improvements for privacy-preserving distributed estimation.

Abstract

We consider the problem of privately estimating the mean of vectors distributed across different nodes of an unreliable wireless network, where communications between nodes can fail intermittently. We adopt a semi-decentralized setup, wherein to mitigate the impact of intermittently connected links, nodes can collaborate with their neighbors to compute a local consensus, which they relay to a central server. In such a setting, the communications between any pair of nodes must ensure that the privacy of the nodes is rigorously maintained to prevent unauthorized information leakage. We study the tradeoff between collaborative relaying and privacy leakage due to the data sharing among nodes and, subsequently, propose PriCER: Private Collaborative Estimation via Relaying -- a differentially private collaborative algorithm for mean estimation to optimize this tradeoff. The privacy guarantees of PriCER arise (i) implicitly, by exploiting the inherent stochasticity of the flaky network connections, and (ii) explicitly, by adding Gaussian perturbations to the estimates exchanged by the nodes. Local and central privacy guarantees are provided against eavesdroppers who can observe different signals, such as the communications amongst nodes during local consensus and (possibly multiple) transmissions from the relays to the central server. We substantiate our theoretical findings with numerical simulations. Our implementation is available at https://github.com/rajarshisaha95/private-collaborative-relaying.
Paper Structure (26 sections, 7 theorems, 85 equations, 7 figures, 2 tables, 3 algorithms)

This paper contains 26 sections, 7 theorems, 85 equations, 7 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Main Contributions
  3. Paper Organization
  4. System model for private collaboration
  5. Communication model
  6. Privacy model
  7. Private collaborative relaying for mean estimation
  8. Estimation error analysis
  9. Privacy analysis
  10. Local privacy guarantee for node-node communications
  11. Central privacy guarantees at a relay
  12. Central privacy at parameter server
  13. Privacy-constrained weight and variance optimization
  14. Projected gradient descent for MSE minimization
  15. Optimal collaboration over an Erdös-Rényi Topology
  16. ...and 11 more sections

Key Result

Theorem 3.1

Suppose for some $\mathrm{R} > 0$, $\mathbf{x}_i \in \mathbb{B}_d(\mathrm{R})$ for all $i \in [n]$. Given $\mathbf{p}, \mathbf{P}$, $\mathbf{A}$, and $\boldsymbol{\Sigma}$, the MSE of PriCER is upper bounded as: where the expectation is over the stochasticity of intermittent connections and the randomness due to privacy noise. Here, $\sigma_{\rm tiv}^2(\mathbf{p}, \mathbf{P}, \mathbf{A})$ is the

Figures (7)

  • Figure 1: Intermittently connected network. Dotted lines indicate intermittent node-PS and node-node connections. Communication between any two nodes must satisfy DP constraints.
  • Figure 2: Variation of MSE with number of trustworthy neighbors
  • Figure 3: Variation of PIV with number of trustworthy neighbors
  • Figure 4: Topology for $\rm K$-means clustering. $p_i$ and $p_{ij}$ are determined according to akdeniz_mmWave.
  • Figure 5: Projected gradient descent with $2$ trustworthy neighbors
  • ...and 2 more figures

Theorems & Definitions (10)

  • Theorem 3.1
  • Theorem 4.1
  • Theorem 4.2
  • Theorem 4.3
  • Corollary 4.4
  • Theorem 4.5
  • Definition G.1
  • Definition G.2
  • Definition G.3
  • Lemma G.4