A fundamental problem in differential privacy is to release privatized answers to a class of linear queries with small error. This problem has been well studied in the static case. In this paper, we consider the fully dynamic setting where items may be inserted into or deleted from the dataset over time, and we need to continually release query answers at every time instance. We present efficient black-box constructions of such dynamic differentially private mechanisms from static ones with only a polylogarithmic degradation in the utility.

People have diverse privacy requirements. This is best modeled using a personalized local differential privacy model where each user privatizes their data using a possibly different privacy parameter. While the model of personalized local differential privacy is a natural and important one, prior work has failed to give meaningful error bounds. In this paper, we study the foundational sum/mean estimation problem under this model. We present two novel protocols that achieve strong error guarantees. The first gives a guarantee based on the radius of the data, suiting inputs that are centered around zero. The second extends the guarantee to the diameter of the data, capturing the case when the points are situated arbitrarily. Experimental results on both synthetic and real data show that our protocols significantly outperform existing methods in terms of accuracy while providing a strong level of privacy.

This paper revisits the DBSCAN problem under differential privacy (DP). Existing DP-DBSCAN algorithms aim at publishing the cluster labels of the input points. However, we show that both empirically and theoretically, this approach cannot offer any utility in the published results. We therefore propose an alternative definition of DP-DBSCAN based on the notion of spans. We argue that publishing the spans actually better serves the purposes of visualization and classification of DBSCAN. Then we present a linear-time DP-DBSCAN algorithm achieving the sandwich quality guarantee in any constant dimensions, as well as matching lower bounds on the approximation ratio. A key building block in our algorithm is a linear-time algorithm for constructing a histogram under pure-DP, which is of independent interest. Finally, we conducted experiments on both synthetic and real-world datasets to verify the practical performance of our DP-DBSCAN algorithm.

In the standard model of differential privacy (DP), every user's privacy is treated equally, which is captured by a single privacy parameter \varepsilon. However, in many real-world situations, users may have diverse privacy concerns and requirements, some conservative while others liberal. This is formalized by the model of personalized differential privacy (PDP), where each user may have a different privacy parameter \varepsilon. However, existing techniques for PDP cannot provide good utility for many fundamental problems such as basic counting and sum estimation. In this paper, we present the personalized truncation mechanism for these problems under PDP. We first show that, theoretically, it is never worse than previous mechanisms (up to polylogarithmic factors) on any instance, while can be much better in certain cases. Then we use extensive experiments on both real and synthetic data to demonstrate its empirical advantages. Our mechanism also works for user-level DP, thus supporting a large class of SJA queries over relational databases under foreign-key constraints.

Prior work on private data release has only studied counting queries or linear queries, where each tuple in the dataset contributes a value in [0,1] and a query returns the sum of the values. However, many data analytical tasks involve numerical values that are arbitrary real numbers. In this paper, we present a new mechanism to privatize a dataset D for a given set Q of numerical queries, achieving an error of Õ (√n • Δw(D)) for each query w ∈ Q, where Δw(D) is the maximum contribution of any tuple in D queried by w. This instance- and query-specific error bound not only is theoretically appealing, but also leads to excellent practical performance.

We study the fundamental problem of frequency estimation under both privacy and communication constraints, where the data is distributed among k parties. We consider two application scenarios: (1) one-shot, where the data is static and the aggregator conducts a one-time computation; and (2) streaming, where each party receives a stream of items over time and the aggregator continuously monitors the frequencies. We adopt the model of multiparty differential privacy (MDP), which is more general than local differential privacy (LDP) and (centralized) differential privacy. Our protocols achieve optimality (up to logarithmic factors) permissible by the more stringent of the two constraints. In particular, when specialized to the ε-LDP model, our protocol achieves an error of √ k /(ε Θ(ε) − 1) using O ( k max{ε, log 1/ε}) bits of communication and O ( k log u ) bits of public randomness, where u is the size of the domain.

SPJ (select-project-join) queries form the backbone of many SQL queries used in practice. Accurate cardinality estimation of these queries is thus an important problem, with applications in query optimization, approximate query processing, and data analytics. However, this problem has not been rigorously addressed in the literature, despite the fact that cardinality estimation techniques of the three relational operators, selection, projection, and join, have each been extensively studied (but not when used in combination) in the past 30+ years. The major technical difficulty is that (distinct) projection seems to be difficult to combine with the other two operators when it comes to cardinality estimation.