Differentially Private Filtering (1207.4305v2)

Abstract: Emerging systems such as smart grids or intelligent transportation systems often require end-user applications to continuously send information to external data aggregators performing monitoring or control tasks. This can result in an undesirable loss of privacy for the users in exchange of the benefits provided by the application. Motivated by this trend, this paper introduces privacy concerns in a system theoretic context, and addresses the problem of releasing filtered signals that respect the privacy of the user data streams. Our approach relies on a formal notion of privacy from the database literature, called differential privacy, which provides strong privacy guarantees against adversaries with arbitrary side information. Methods are developed to approximate a given filter by a differentially private version, so that the distortion introduced by the privacy mechanism is minimized. Two specific scenarios are considered. First, the notion of differential privacy is extended to dynamic systems with many participants contributing independent input signals. Kalman filtering is also discussed in this context, when a released output signal must preserve differential privacy for the measured signals or state trajectories of the individual participants. Second, differentially private mechanisms are described to approximate stable filters when participants contribute to a single event stream, extending previous work on differential privacy under continual observation.

• The paper formalizes differential privacy for dynamic systems, extending its application to streaming data in distributed environments.
• It adapts Kalman filters to preserve individual privacy while maintaining high accuracy by minimizing noise-induced distortion.
• Stable filter approximation methods are presented to control mean-squared error when securing multi-participant event streams.

An Expert Review of "Differentially Private Filtering"

The paper "Differentially Private Filtering" by Jerome Le Ny and George J. Pappas explores a critical intersection of privacy protection and signal processing within distributed cyber-physical systems. It employs the concept of differential privacy—originally developed within the field of static databases—to ensure the privacy of dynamic signal streams. Differential privacy has gained attention due to its robustness against adversaries with access to arbitrary side information, presenting a promising approach for securing data in real-time applications.

Problem Context and Approach

The paper's focus is on systems, like smart grids and intelligent transportation networks, where users must supply continuous data for central analytics and control functions. Le Ny and Pappas adeptly address the ensuing privacy concerns by embedding differential privacy within system-theoretic frameworks. By modifying Kalman filters and stable filters to respect differential privacy, the authors provide a methodology to protect private information implicit in dynamic user inputs.

The research extends the definition of differential privacy to accommodate dynamic systems involving multiple participants. This is achieved by developing mechanisms that approximate a given filter such that the distortion resulting from privacy measures is minimized. Two notable scenarios are considered: first, leveraging differential privacy in systems with independent input signals from multiple contributors, and second, applying private filtering techniques to a continuous event stream.

Key Contributions and Results

1. Formulation of Differentially Private Filtering: The authors formalize the concept of differential privacy within dynamic systems. They particularly focus on extending privacy measures so that they are consistent with the nature of dynamic data streams as opposed to static datasets.
2. Kalman Filtering with Differential Privacy: A significant portion of the paper is dedicated to adapting Kalman filtering in a way that preserves privacy. The authors introduce mechanisms to ensure that released signals do not reveal private state trajectories, leveraging additional process information to maintain accuracy.
3. Stable Filter Approximation: Techniques for designing differentially private mechanisms to approximate stable filters are discussed. These methods are extended to handle participants contributing to single event streams, effectively controlling the mean-squared error while maintaining robust privacy guarantees.

The paper claims strong numerical results regarding the negligible impact of added noise on the performance of filters when privacy mechanisms are carefully incorporated. It demonstrates that for systems with small incremental gains regarding individual inputs, accurate outputs can be retained even when privacy is enforced.

Implications and Future Work

The implications of this work are far-reaching, particularly as the demand for privacy-preserving data analytics grows in domains such as smart grids, traffic systems, and healthcare monitoring. The research supports a burgeoning need for methodologies that can balance the trade-off between data utility and privacy within real-time dynamic environments.

In the broader spectrum of AI and machine learning, this research prompts further exploration into privacy-preserving mechanisms that do not compromise model accuracy or real-time processing. Future work could explore more complex dynamic models and integrate machine learning techniques that require differential privacy on large-scale streaming data.

In conclusion, Le Ny and Pappas' work is a foundational step in recognizing and addressing privacy concerns in dynamical systems with connected users. The methods presented can serve as a blueprint for developing secure analytics solutions that respect user privacy while enabling sophisticated data-driven system functions. As reliance on cyber-physical systems grows, such research will prove indispensable in fostering trust and participation in shared data environments.