Rényi Divergence and Sibson Mutual Information as Measures of α-Leakage in Information-Theoretic Privacy

Conceptos Básicos

Rényi divergence and Sibson mutual information are proposed as exact α-leakage measures, quantifying the maximum and average information gain an adversary can obtain on sensitive data through a privacy-preserving channel.

Resumen

This paper introduces a new information gain measure called the ˜f-mean information gain, where ˜f(t) = exp((α-1)/α t). It is shown that the maximum ˜f-mean information gain is attained at Rényi divergence, which is then proposed as the Y-elementary α-leakage. The ˜f-mean of this Y-elementary leakage is measured by Sibson mutual information, which is interpreted as the maximum ˜f-mean information gain over all estimation decisions applied to the channel output.
The existing α-leakage measures, such as Arimoto mutual information, can be expressed as ˜f-mean measures by using a scaled probability distribution. This provides a straightforward way to derive the known leakage upper bound results.
The paper also derives a decomposition of the ˜f-mean information gain, analogous to the Sibson identity for Rényi divergence. This reveals that the generalized Blahut-Arimoto method for computing Rényi capacity (or Gallager's error exponent) is an alternating maximization of the ˜f-mean information gain over estimation decision and channel input. Additionally, it is shown that the ˜f-mean information gain equals the difference between cross entropy and Rényi entropy, generalizing the excess entropy interpretation of Kullback-Leibler divergence.

Estadísticas

The maximum ˜f-mean information gain is attained at Rényi divergence.
Sibson mutual information is the ˜f-mean of the Y-elementary information leakage.
The existing α-leakage measures can be expressed as ˜f-mean measures using a scaled probability distribution.
The ˜f-mean information gain equals the difference between cross entropy and Rényi entropy.

Citas

"Rényi divergence is shown to be the maximum ˜f-mean information gain incurred at each elementary event y of channel output Y and Sibson mutual information is the ˜f-mean of this Y-elementary information gain."
"Both are proposed as α-leakage measures, indicating the most information an adversary can obtain on sensitive data."
"The existing α-leakage by Arimoto mutual information can be expressed as ˜f-mean measures by a scaled probability."

Ideas clave extraídas de

$α$-leakage by Rényi Divergence and Sibson Mutual Information

by Ni Ding a las arxiv.org 05-02-2024

https://arxiv.org/pdf/2405.00423.pdf

Consultas más profundas

How can the proposed α-leakage measures be applied to practical privacy-preserving systems to quantify the information leakage and guide the design of optimal privacy-utility trade-offs

The proposed α-leakage measures, based on Rényi divergence and Sibson mutual information, offer a robust framework for quantifying information leakage in practical privacy-preserving systems. By utilizing these measures, system designers can effectively assess the amount of information that an adversary can obtain about sensitive data. This quantification of information leakage is crucial in guiding the design of optimal privacy-utility trade-offs in such systems.
To apply these α-leakage measures in practice, system designers can first analyze the specific characteristics of the system, including the data types, communication channels, and potential adversaries. By understanding these factors, they can tailor the α-leakage measures to suit the system's requirements accurately.
Once the α-leakage measures are integrated into the system, they can be used to evaluate the effectiveness of existing privacy mechanisms and identify potential vulnerabilities. By quantifying the information leakage, system designers can make informed decisions about enhancing privacy protections while balancing utility considerations. This iterative process allows for the optimization of privacy-preserving systems to achieve the desired level of privacy without compromising utility.

What are the potential limitations or drawbacks of using Rényi divergence and Sibson mutual information as α-leakage measures compared to other information-theoretic privacy metrics

While Rényi divergence and Sibson mutual information offer valuable insights into information leakage in privacy-preserving systems, there are potential limitations and drawbacks compared to other information-theoretic privacy metrics.
One limitation is the complexity of interpreting and implementing these measures in real-world systems. Rényi divergence and Sibson mutual information may require a deep understanding of information theory concepts, making them challenging to apply for practitioners without specialized knowledge. Additionally, the computational complexity of calculating these measures for large datasets or complex systems could be a drawback in practical applications.
Furthermore, the choice of α parameter in the α-leakage measures may introduce subjectivity and uncertainty. Selecting the appropriate α value to quantify information leakage effectively can be a non-trivial task and may impact the accuracy of the results obtained.
Compared to other privacy metrics, such as differential privacy or mutual information, Rényi divergence and Sibson mutual information may offer different perspectives on information leakage but may not capture all aspects of privacy concerns comprehensively. It is essential to consider these limitations and drawbacks when choosing α-leakage measures for privacy analysis in practical systems.

Given the connection between the ˜f-mean information gain and cross entropy, how can this insight be leveraged to develop new privacy-preserving machine learning algorithms or data analysis techniques

The connection between the ˜f-mean information gain and cross entropy provides a valuable insight that can be leveraged to develop new privacy-preserving machine learning algorithms and data analysis techniques. By understanding this relationship, researchers and practitioners can explore innovative approaches to enhance privacy protections while maintaining data utility.
One potential application of this insight is in developing privacy-preserving machine learning models that prioritize data privacy without compromising model performance. By incorporating the principles of ˜f-mean information gain and cross entropy, researchers can design algorithms that optimize privacy-utility trade-offs effectively. This could involve modifying existing machine learning algorithms to incorporate privacy constraints based on the insights gained from the information-theoretic measures.
Additionally, the connection between ˜f-mean information gain and cross entropy can inspire the development of novel privacy-enhancing data analysis techniques. Researchers can explore new methods for data anonymization, secure data sharing, and privacy-preserving data processing by leveraging the principles underlying these measures. This could lead to the creation of more robust and privacy-aware data analysis tools that are better equipped to handle sensitive information while preserving individual privacy rights.