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We develop both theory and algorithms to analyze privatized data in unbounded differential privacy (DP), where even the sample size is considered a sensitive quantity that requires privacy protection. We show that the distance between the…

Statistics Theory · Mathematics 2026-04-24 Jordan Awan , Andres Felipe Barrientos , Nianqiao Ju

Implementations of the exponential mechanism in differential privacy often require sampling from intractable distributions. When approximate procedures like Markov chain Monte Carlo (MCMC) are used, the end result incurs costs to both…

Cryptography and Security · Computer Science 2022-04-05 Jeremy Seeman , Matthew Reimherr , Aleksandra Slavkovic

The verification of differential privacy algorithms that employ Gaussian distributions is little understood. This paper tackles the challenge of verifying such programs by introducing a novel approach to approximating probability…

Cryptography and Security · Computer Science 2025-09-11 Bishnu Bhusal , Rohit Chadha , A. Prasad Sistla , Mahesh Viswanathan

Many algorithms have been developed to estimate probability distributions subject to differential privacy (DP): such an algorithm takes as input independent samples from a distribution and estimates the density function in a way that is…

Cryptography and Security · Computer Science 2024-12-17 Albert Cheu , Debanuj Nayak

Given a dataset of $n$ i.i.d. samples from an unknown distribution $P$, we consider the problem of generating a sample from a distribution that is close to $P$ in total variation distance, under the constraint of differential privacy (DP).…

Data Structures and Algorithms · Computer Science 2023-06-23 Badih Ghazi , Xiao Hu , Ravi Kumar , Pasin Manurangsi

We develop a novel approximate Bayesian computation (ABC) framework, ABCDP, that produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the Sparse Vector Technique (SVT), widely studied in…

Machine Learning · Statistics 2021-02-10 Mijung Park , Margarita Vinaroz , Wittawat Jitkrittum

We design a class of additive noise mechanisms that satisfy \((\varepsilon, \delta)\)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes.…

Cryptography and Security · Computer Science 2026-05-28 Huikang Liu , Aras Selvi , Wolfram Wiesemann

Estimating the probability density of a population while preserving the privacy of individuals in that population is an important and challenging problem that has received considerable attention in recent years. While the previous…

Computation · Statistics 2024-05-24 Mario Beraha , Stefano Favaro , Vinayak Rao

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP…

Machine Learning · Statistics 2019-06-18 Mikko A. Heikkilä , Joonas Jälkö , Onur Dikmen , Antti Honkela

Significant success has been realized recently on applying machine learning to real-world applications. There have also been corresponding concerns on the privacy of training data, which relates to data security and confidentiality issues.…

Machine Learning · Statistics 2017-12-27 Bai Li , Changyou Chen , Hao Liu , Lawrence Carin

Markov chain Monte Carlo (MCMC) algorithms have long been the main workhorses of Bayesian inference. Among them, Hamiltonian Monte Carlo (HMC) has recently become very popular due to its efficiency resulting from effective use of the…

Computation · Statistics 2021-06-18 Ossi Räisä , Antti Koskela , Antti Honkela

The exponential increase in the amount of available data makes taking advantage of them without violating users' privacy one of the fundamental problems of computer science. This question has been investigated thoroughly under the framework…

Data Structures and Algorithms · Computer Science 2023-07-19 Jakub Tětek

Privacy in AI remains a topic that draws attention from researchers and the general public in recent years. As one way to implement privacy-preserving AI, differentially private learning is a framework that enables AI models to use…

Machine Learning · Computer Science 2023-05-03 Tianyu Xia , Shuheng Shen , Su Yao , Xinyi Fu , Ke Xu , Xiaolong Xu , Xing Fu

In this paper, we present a notion of differential privacy (DP) for data that comes from different classes. Here, the class-membership is private information that needs to be protected. The proposed method is an output perturbation…

Signal Processing · Electrical Eng. & Systems 2023-06-12 Raksha Ramakrishna , Anna Scaglione , Tong Wu , Nikhil Ravi , Sean Peisert

Differential privacy (DP) is widely employed to provide privacy protection for individuals by limiting information leakage from the aggregated data. Two well-known models of DP are the central model and the local model. The former requires…

Cryptography and Security · Computer Science 2024-11-05 Yucheng Fu , Tianhao Wang

We propose a framework to convert $(\varepsilon, \delta)$-approximate Differential Privacy (DP) mechanisms into $(\varepsilon', 0)$-pure DP mechanisms under certain conditions, a process we call ``purification.'' This algorithmic technique…

Cryptography and Security · Computer Science 2025-11-19 Yingyu Lin , Erchi Wang , Yi-An Ma , Yu-Xiang Wang

We present a novel method for accurately auditing the differential privacy (DP) guarantees of DP mechanisms. In particular, our solution is applicable to auditing DP guarantees of machine learning (ML) models. Previous auditing methods…

Machine Learning · Computer Science 2026-01-14 Antti Koskela , Jafar Mohammadi

This paper aims to provide differential privacy (DP) guarantees for Markov chain Monte Carlo (MCMC) algorithms. In a first part, we establish DP guarantees on samples output by MCMC algorithms as well as Monte Carlo estimators associated…

Machine Learning · Statistics 2025-11-04 Andrea Bertazzi , Tim Johnston , Gareth O. Roberts , Alain Durmus

We consider the problem of Bayesian learning on sensitive datasets and present two simple but somewhat surprising results that connect Bayesian learning to "differential privacy:, a cryptographic approach to protect individual-level privacy…

Machine Learning · Statistics 2015-04-14 Yu-Xiang Wang , Stephen E. Fienberg , Alex Smola

Differential privacy (DP) is becoming increasingly important for deployed machine learning applications because it provides strong guarantees for protecting the privacy of individuals whose data is used to train models. However, DP…

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