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In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold. We present an extension of the Laplace or K-norm mechanism that utilizes intrinsic distances and volumes…

Statistics Theory · Mathematics 2021-11-09 Matthew Reimherr , Karthik Bharath , Carlos Soto

Differential privacy has become crucial in the real-world deployment of statistical and machine learning algorithms with rigorous privacy guarantees. The earliest statistical queries, for which differential privacy mechanisms have been…

Statistics Theory · Mathematics 2023-02-13 Saiteja Utpala , Praneeth Vepakomma , Nina Miolane

Popular approaches to differential privacy, such as the Laplace and exponential mechanisms, calibrate randomised smoothing through global sensitivity of the target non-private function. Bounding such sensitivity is often a prohibitively…

Machine Learning · Computer Science 2017-06-12 Benjamin I. P. Rubinstein , Francesco Aldà

Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also…

Cryptography and Security · Computer Science 2021-07-27 Natasha Fernandes , Annabelle McIver , Carroll Morgan

Many data applications have certain invariant constraints due to practical needs. Data curators who employ differential privacy need to respect such constraints on the sanitized data product as a primary utility requirement. Invariants…

Cryptography and Security · Computer Science 2022-05-02 Jie Gao , Ruobin Gong , Fang-Yi Yu

In statistical applications it has become increasingly common to encounter data structures that live on non-linear spaces such as manifolds. Classical linear regression, one of the most fundamental methodologies of statistical learning,…

Machine Learning · Statistics 2026-02-10 Aditya Kulkarni , Carlos Soto

The Laplace mechanism is the workhorse of differential privacy, applied to many instances where numerical data is processed. However, the Laplace mechanism can return semantically impossible values, such as negative counts, due to its…

Cryptography and Security · Computer Science 2018-08-31 Naoise Holohan , Spiros Antonatos , Stefano Braghin , Pól Mac Aonghusa

Differential privacy is among the most prominent techniques for preserving privacy of sensitive data, oweing to its robust mathematical guarantees and general applicability to a vast array of computations on data, including statistical…

Cryptography and Security · Computer Science 2021-11-25 Naoise Holohan , Stefano Braghin

Machine learning is increasingly becoming a powerful tool to make decisions in a wide variety of applications, such as medical diagnosis and autonomous driving. Privacy concerns related to the training data and unfair behaviors of some…

Cryptography and Security · Computer Science 2020-03-16 Jiahao Ding , Xinyue Zhang , Xiaohuan Li , Junyi Wang , Rong Yu , Miao Pan

Differential privacy mechanisms such as the Gaussian or Laplace mechanism have been widely used in data analytics for preserving individual privacy. However, they are mostly designed for continuous outputs and are unsuitable for scenarios…

Cryptography and Security · Computer Science 2024-06-06 Zhongteng Cai , Xueru Zhang , Mohammad Mahdi Khalili

In the highly interconnected realm of Internet of Things, exchange of sensitive information raises severe privacy concerns. The Laplace mechanism -- adding Laplace-distributed artificial noise to sensitive data -- is one of the widely used…

Cryptography and Security · Computer Science 2015-04-09 Fragkiskos Koufogiannis , Shuo Han , George J. Pappas

This paper develops a framework for privatizing the spectrum of the graph Laplacian of an undirected graph using differential privacy. We consider two privacy formulations. The first obfuscates the presence of edges in the graph and the…

Optimization and Control · Mathematics 2022-11-29 Calvin Hawkins , Bo Chen , Kasra Yazdani , Matthew Hale

A mechanism for releasing information about a statistical database with sensitive data must resolve a trade-off between utility and privacy. Privacy can be rigorously quantified using the framework of {\em differential privacy}, which…

Databases · Computer Science 2009-03-20 Arpita Ghosh , Tim Roughgarden , Mukund Sundararajan

The Shapley value has been proposed as a solution to many applications in machine learning, including for equitable valuation of data. Shapley values are computationally expensive and involve the entire dataset. The query for a point's…

Machine Learning · Computer Science 2022-06-02 Lauren Watson , Rayna Andreeva , Hao-Tsung Yang , Rik Sarkar

In this paper, we present a comprehensive framework for differential privacy over affine manifolds and validate its usefulness in the contexts of differentially private cloud-based control and average consensus. We consider differential…

Systems and Control · Electrical Eng. & Systems 2026-01-22 Zihao Ren , Lei Wang , Deming Yuan , Guodong Shi

We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without compromising privacy. The method follows an iterative procedure…

Machine Learning · Computer Science 2026-04-02 Jiaqi Wu , Yiqing Sun , Zhigang Yao

Differential Privacy (DP) is being increasingly adopted for non-Euclidean data that lie on complex, high-dimensional manifolds. Existing DP mechanisms for manifold data consider geometric properties when calibrating privacy perturbations,…

Cryptography and Security · Computer Science 2026-05-12 Peilin He , Liou Tang , M. Amin Rahimian , James Joshi

Much of the literature on differential privacy focuses on item-level privacy, where loosely speaking, the goal is to provide privacy per item or training example. However, recently many practical applications such as federated learning…

Machine Learning · Computer Science 2021-01-13 Yuhan Liu , Ananda Theertha Suresh , Felix Yu , Sanjiv Kumar , Michael Riley

Due to the pervasiveness of image capturing devices in every-day life, images of individuals are routinely captured. Although this has enabled many benefits, it also infringes on personal privacy. A promising direction in research on…

Cryptography and Security · Computer Science 2021-02-23 William Croft , Jörg-Rüdiger Sack , Wei Shi

Differential privacy provides strong privacy guarantees simultaneously enabling useful insights from sensitive datasets. However, it provides the same level of protection for all elements (individuals and attributes) in the data. There are…

Machine Learning · Statistics 2019-08-30 Parameswaran Kamalaruban , Victor Perrier , Hassan Jameel Asghar , Mohamed Ali Kaafar
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