Lipschitz clustering in metric spaces

Kovalev, Leonid V.

doi:10.48550/arxiv.2108.03535

Cited by 1 publication

(1 citation statement)

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“…While not every clustering method will satisfy a Lipschitz property, there do exist Lipschitz clustering functions that achieve state-of-the-art results, see e.g. [31,56]. Similarly, there is distinct interest in Lipschitz function based classifiers, since they are more robust and less susceptible to adversarial attacks.…”

Section: Uniform Accuracy Over Lipschitz Statisticsmentioning

confidence: 99%

Private measures, random walks, and synthetic data

Boedihardjo,

Strohmer,

Vershynin

2024

Probab. Theory Relat. Fields

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Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex—but very common—machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact metric spaces, for any fixed privacy budget $$\varepsilon $$ ε bounded away from zero. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmically slowly.

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Section: Uniform Accuracy Over Lipschitz Statisticsmentioning

confidence: 99%