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An Iconic Heavy Hitter Algorithm Made Private
arXiv:2512.17295v1 Announce Type: new
Abstract: Identifying heavy hitters in data streams is a fundamental problem with widespread applications in modern analytics systems. These streams are often derived from sensitive user activity, making update-level privacy guarantees necessary. While recent work has adapted the classical heavy hitter algorithm Misra-Gries to satisfy differential privacy in the streaming model, the privatization of other heavy hitter algorithms with better empirical utility is absent.
Under this observation, we present the first differentially private variant of the SpaceSaving algorithm, which, in the non-private setting, is regarded as the state-of-the-art in practice. Our construction post-processes a non-private SpaceSaving summary by injecting asymptotically optimal noise and applying a carefully calibrated selection rule that suppresses unstable labels. This yields strong privacy guarantees while preserving the empirical advantages of SpaceSaving.
Second, we introduce a generic method for extracting heavy hitters from any differentially private frequency oracle in the data stream model. The method requires only O(k) additional memory, where k is the number of heavy items, and provides a mechanism for safely releasing item identities from noisy frequency estimates. This yields an efficient, plug-and-play approach for private heavy hitter recovery from linear sketches.
Finally, we conduct an experimental evaluation on synthetic and real-world datasets. Across a wide range of privacy parameters and space budgets, our method provides superior utility to the existing differentially private Misra-Gries algorithm. Our results demonstrate that the empirical superiority of SpaceSaving survives privatization and that efficient, practical heavy hitter identification is achievable under strong differential privacy guarantees.
Abstract: Identifying heavy hitters in data streams is a fundamental problem with widespread applications in modern analytics systems. These streams are often derived from sensitive user activity, making update-level privacy guarantees necessary. While recent work has adapted the classical heavy hitter algorithm Misra-Gries to satisfy differential privacy in the streaming model, the privatization of other heavy hitter algorithms with better empirical utility is absent.
Under this observation, we present the first differentially private variant of the SpaceSaving algorithm, which, in the non-private setting, is regarded as the state-of-the-art in practice. Our construction post-processes a non-private SpaceSaving summary by injecting asymptotically optimal noise and applying a carefully calibrated selection rule that suppresses unstable labels. This yields strong privacy guarantees while preserving the empirical advantages of SpaceSaving.
Second, we introduce a generic method for extracting heavy hitters from any differentially private frequency oracle in the data stream model. The method requires only O(k) additional memory, where k is the number of heavy items, and provides a mechanism for safely releasing item identities from noisy frequency estimates. This yields an efficient, plug-and-play approach for private heavy hitter recovery from linear sketches.
Finally, we conduct an experimental evaluation on synthetic and real-world datasets. Across a wide range of privacy parameters and space budgets, our method provides superior utility to the existing differentially private Misra-Gries algorithm. Our results demonstrate that the empirical superiority of SpaceSaving survives privatization and that efficient, practical heavy hitter identification is achievable under strong differential privacy guarantees.
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