A simple and practical algorithm for differentially private data release (1012.4763v2)

Abstract: We present new theoretical results on differentially private data release useful with respect to any target class of counting queries, coupled with experimental results on a variety of real world data sets. Specifically, we study a simple combination of the multiplicative weights approach of [Hardt and Rothblum, 2010] with the exponential mechanism of [McSherry and Talwar, 2007]. The multiplicative weights framework allows us to maintain and improve a distribution approximating a given data set with respect to a set of counting queries. We use the exponential mechanism to select those queries most incorrectly tracked by the current distribution. Combing the two, we quickly approach a distribution that agrees with the data set on the given set of queries up to small error. The resulting algorithm and its analysis is simple, but nevertheless improves upon previous work in terms of both error and running time. We also empirically demonstrate the practicality of our approach on several data sets commonly used in the statistical community for contingency table release.

• The paper introduces the MWEM algorithm, a novel integration of the Exponential Mechanism with the Multiplicative Weights update rule to achieve near-optimal differential privacy while preserving data utility.
• It demonstrates significant empirical improvements, outperforming traditional methods in range queries, contingency tables, and data cubes by up to three orders of magnitude.
• The method scales efficiently to high-dimensional datasets by dynamically focusing on the most informative queries, making it a practical tool for privacy-preserving data analysis.

Differentially Private Data Release: The MWEM Algorithm

The paper introduces the MWEM algorithm, a refined and implementable approach to differentially private data release. This framework combines the Exponential Mechanism with the Multiplicative Weights (MW) update rule to produce synthetic datasets that closely approximate true datasets while maintaining privacy guarantees.

Theoretical Innovation

The foundational basis of the MWEM algorithm lies in its ability to effectively balance privacy and utility. By integrating MW, as explored in earlier works like those by Hardt and Rothblum, with the Exponential Mechanism, the algorithm achieves near-optimal theoretical guarantees for differential privacy. This integration permits MWEM to focus its computational resources wisely by selecting only the most informative queries—those that expose the greatest discrepancies between the real and synthetic datasets.

Empirical Results

The paper provides extensive experimental validation across a variety of problem domains. The results consistently demonstrate MWEM’s superior performance compared to prior methods, especially in realistic data scenarios:

1. Range Queries: The algorithm outperforms existing approaches, achieving up to three orders of magnitude improvement in accuracy. This is significant as range queries are fundamental in many real-world applications.
2. Contingency Tables: For datasets commonly used in statistical analyses, MWEM ensures more accurate reproductions of lower dimensional marginals, something critical for valid statistical inference.
3. Data Cubes: MWEM also excels in the context of datacube release. The algorithm reduces the required number of measurements, minimizing average and maximum errors compared to specialized algorithms.

Algorithmic Efficiency

A key contribution of the MWEM algorithm is its scalability. Even when handling data domains with numerous attributes, MWEM can efficiently produce differentially private data while operating under computational constraints. The algorithm's ability to dynamically focus on important data attributes makes it particularly suitable for large datasets, where traditional methods struggle with computational overhead.

Implications and Future Directions

The MWEM algorithm represents a significant step forward in the practical application of differential privacy. Its efficient query management means that it can be adapted for a broad range of applications without extensive domain-specific adjustments. The versatility of MWEM positions it as a foundational tool for data analysts aiming to harness statistical insights while maintaining rigorous privacy standards.

Future research might explore expanding MWEM’s capabilities to more complex data types and queries beyond linear counting. Additionally, considering its modular structure, there is potential for further optimization and integration with emerging technologies in privacy-preserving data analysis.

In conclusion, the MWEM algorithm offers a pragmatic solution to the challenge of differentially private data release, backed by robust theoretical insights and validated through comprehensive empirical evaluation. As such, it stands as a valuable contribution to the field of data privacy, promising significant benefits for both theoretical exploration and practical application.