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Over-the-Air Federated Adaptive Data Analysis: Preserving Accuracy via Opportunistic Differential Privacy

Amir Hossein Hadavi, Mohammad M. Mojahedian, Mohammad Reza Aref

TL;DR

This work tackles preserving accuracy in adaptive data analysis when queries are answered over noisy, distributed channels. It treats AWGN channel noise as a natural Gaussian randomization mechanism and extends ADA to a federated setting with analog MAC transmissions, deriving how transmission amplitude should be tuned to maximize the number of accurately answerable queries. The key contributions include a point-to-point ADA bound under Gaussian channels, a distributed ADA framework with L edge points, and an amplitude-scaling strategy that yields improved query throughput, with quadratic and then exponential growth regimes depending on problem size and federation level. The findings offer a pathway to privacy-preserving, generalizable ADA in distributed systems and point to future work on fading channels and CSI-aware designs for real-world deployments.

Abstract

Adaptive data analysis (ADA) involves a dynamic interaction between an analyst and a dataset owner, where the analyst submits queries sequentially, adapting them based on previous answers. This process can become adversarial, as the analyst may attempt to overfit by targeting non-generalizable patterns in the data. To counteract this, the dataset owner introduces randomization techniques, such as adding noise to the responses. This noise not only helps prevent overfitting, but also enhances data privacy. However, it must be carefully calibrated to ensure that the statistical reliability of the responses is not compromised. In this paper, we extend the ADA problem to the context of distributed datasets. Specifically, we consider a scenario where a potentially adversarial analyst interacts with multiple distributed responders through adaptive queries. We assume the responses are subject to noise, introduced by the channel connecting the responders and the analyst. We demonstrate how this noise can be opportunistically leveraged through a federated mechanism to enhance the generalizability of ADA, thereby increasing the number of query-response interactions between the analyst and the responders. We illustrate that the careful tuning of the transmission amplitude based on the theoretically achievable bounds can significantly impact the number of accurately answerable queries.

Over-the-Air Federated Adaptive Data Analysis: Preserving Accuracy via Opportunistic Differential Privacy

TL;DR

This work tackles preserving accuracy in adaptive data analysis when queries are answered over noisy, distributed channels. It treats AWGN channel noise as a natural Gaussian randomization mechanism and extends ADA to a federated setting with analog MAC transmissions, deriving how transmission amplitude should be tuned to maximize the number of accurately answerable queries. The key contributions include a point-to-point ADA bound under Gaussian channels, a distributed ADA framework with L edge points, and an amplitude-scaling strategy that yields improved query throughput, with quadratic and then exponential growth regimes depending on problem size and federation level. The findings offer a pathway to privacy-preserving, generalizable ADA in distributed systems and point to future work on fading channels and CSI-aware designs for real-world deployments.

Abstract

Adaptive data analysis (ADA) involves a dynamic interaction between an analyst and a dataset owner, where the analyst submits queries sequentially, adapting them based on previous answers. This process can become adversarial, as the analyst may attempt to overfit by targeting non-generalizable patterns in the data. To counteract this, the dataset owner introduces randomization techniques, such as adding noise to the responses. This noise not only helps prevent overfitting, but also enhances data privacy. However, it must be carefully calibrated to ensure that the statistical reliability of the responses is not compromised. In this paper, we extend the ADA problem to the context of distributed datasets. Specifically, we consider a scenario where a potentially adversarial analyst interacts with multiple distributed responders through adaptive queries. We assume the responses are subject to noise, introduced by the channel connecting the responders and the analyst. We demonstrate how this noise can be opportunistically leveraged through a federated mechanism to enhance the generalizability of ADA, thereby increasing the number of query-response interactions between the analyst and the responders. We illustrate that the careful tuning of the transmission amplitude based on the theoretically achievable bounds can significantly impact the number of accurately answerable queries.

Paper Structure

This paper contains 10 sections, 3 theorems, 19 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Adaptive Data Analysis
  3. Federated learning
  4. Contributions and Paper Structure
  5. System Model
  6. Point-to-Point ADA without any communication constraint
  7. Point-to-Point ADA in the Presence of a Gaussian Channel
  8. Distributed ADA in the Presence of a Gaussian Channel
  9. Improving $k$ in $L$
  10. Future Work and Conclusion

Key Result

Theorem 3.1

Fix a Gaussian mechanism parameter $\sigma>0$ and a desired confidence parameter $0<\beta<1$. The Gaussian mechanism can be used to answer $k$ statistical queries while satisfying $(\alpha,\beta)$-distributional accuracy, where $\alpha$ is derived from the following expression: where

Figures (6)

  • Figure 1: We have $L$ responders that respond to analyst queries through an AWGN channel.
  • Figure 2: $g(c)$ versus $c$.
  • Figure 3: Achievable number of accurately answerable queries versus $\sigma/A_{\mathsf{t}}$ for $\alpha=0.1$ and $\beta=0.05$ and different values of $n$.
  • Figure 4: Maximum achievable number of accurately answerable queries versus $n$ for $\alpha=0.1$ and $\beta=0.05$.
  • Figure 5: Maximum number of accurately answered queries versus $\sigma/A_{\mathsf{t}}$ for $\alpha=0.1$ and $\beta=0.05$ and different values of $n$.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Definition 1.1
  • Definition 1.2
  • Theorem 3.1: Theorem 2.1. of rogers2020guaranteed
  • Lemma 3.1
  • proof
  • Corollary 3.1
  • proof