Local Differential Privacy (LDP) offers strong privacy guarantees without requiring users to trust external parties. However, LDP applies uniform protection to all data features, including less sensitive ones, which degrades performance of downstream tasks. To overcome this limitation, we propose a Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), that enables feature-specific privacy quantification. This more nuanced approach complements LDP by adjusting privacy protection according to the sensitivity of each feature, enabling improved performance of downstream tasks without compromising privacy. We characterize the properties of BCDP and articulate its connections with standard non-Bayesian privacy frameworks. We further apply our BCDP framework to the problems of private mean estimation and ordinary least-squares regression. The BCDP-based approach obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Differential Privacy (DP) is the current gold-standard for measuring privacy. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We consider the problems of empirical mean estimation for univariate data and frequency estimation for categorical data, two pillars of data analysis in the industry, subject to heterogeneous privacy constraints. Each user, contributing a sample to the dataset, is allowed to have a different privacy demand. The dataset itself is assumed to be worst-case and we study both the problems in two different formulations -- the correlated and the uncorrelated setting. In the former setting, the privacy demand and the user data can be arbitrarily correlated while in the latter setting, there is no correlation between the dataset and the privacy demand. We prove some optimality results, under both PAC error and mean-squared error, for our proposed algorithms and demonstrate superior performance over other baseline techniques experimentally.

Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world scenarios in which users dictate their privacy preferences individually. This work considers the problem of mean estimation, where each user can impose their own distinct privacy level. The algorithm we propose is shown to be minimax optimal and has a near-linear run-time. Our results elicit an interesting saturation phenomenon that occurs. Namely, the privacy requirements of the most stringent users dictate the overall error rates. As a consequence, users with less but differing privacy requirements are all given more privacy than they require, in equal amounts. In other words, these privacy-indifferent users are given a nontrivial degree of privacy for free, without any sacrifice in the performance of the estimator.

Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional DP formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world scenarios in which users dictate their privacy preferences individually. This work considers the problem of mean estimation under heterogeneous DP constraints, where each user can impose their own distinct privacy level. The algorithm we propose is shown to be minimax optimal when there are two groups of users with distinct privacy levels. Our results elicit an interesting saturation phenomenon that occurs as one group's privacy level is relaxed, while the other group's privacy level remains constant. Namely, after a certain point, further relaxing the privacy requirement of the former group does not improve the performance of the minimax optimal mean estimator. Thus, the central server can offer a certain degree of privacy without any sacrifice in performance.