arXiv subjects

Tianhao Wang

Publications and source records attributed to Tianhao Wang.

131 records · Page 8Linked to original sources

arXiv2020

Locally Differentially Private Frequency Estimation with Consistency

Local Differential Privacy (LDP) protects user privacy from the data collector. LDP protocols have been increasingly deployed in the industry. A basic building block is frequency oracle (FO) protocols, which estimate frequencies of values. While several FO protocols have been proposed, the design goal does not lead to optimal results for answering many queries. In this paper, we show that adding post-processing steps to FO protocols by exploiting the knowledge that all individual frequencies should be non-negative and they sum up to one can lead to significantly better accuracy for a wide range of tasks, including frequencies of individual values, frequencies of the most frequent values, and frequencies of subsets of values. We consider 10 different methods that exploit this knowledge differently. We establish theoretical relationships between some of them and conducted extensive experimental evaluations to understand which methods should be used for different query tasks.

cs.CR↗

arXiv2019

Estimating Numerical Distributions under Local Differential Privacy

When collecting information, local differential privacy (LDP) relieves the concern of privacy leakage from users' perspective, as user's private information is randomized before sent to the aggregator. We study the problem of recovering the distribution over a numerical domain while satisfying LDP. While one can discretize a numerical domain and then apply the protocols developed for categorical domains, we show that taking advantage of the numerical nature of the domain results in better trade-off of privacy and utility. We introduce a new reporting mechanism, called the square wave SW mechanism, which exploits the numerical nature in reporting. We also develop an Expectation Maximization with Smoothing (EMS) algorithm, which is applied to aggregated histograms from the SW mechanism to estimate the original distributions. Extensive experiments demonstrate that our proposed approach, SW with EMS, consistently outperforms other methods in a variety of utility metrics.

cs.CR↗

arXiv2019

Explicit Description of Centralizers for a Matrix

Let $k$ be a field and $A\in M_n(k)$ be an $n\times n$ matrix. We denote $C_{M_n(k)}(A) = \{B\in M_n(k) : BA = AB\}$ be its centralizers in $M_n(k)$. The dimension of the space of centralizer was already known by Frobenius. This paper will give the explicit $k$-basis for $C_{M_n(k)}(A)$ and also an algorithm (with polynomial complexity respect to multiplication in the field $k$) to construct the explicit basis. Lastly, the result can be used to solve a weaker version of the Wild Problem.

math.RA↗

arXiv2017

Locally Differentially Private Heavy Hitter Identification

The notion of Local Differential Privacy (LDP) enables users to answer sensitive questions while preserving their privacy. The basic LDP frequent oracle protocol enables the aggregator to estimate the frequency of any value. But when the domain of input values is large, finding the most frequent values, also known as the heavy hitters, by estimating the frequencies of all possible values, is computationally infeasible. In this paper, we propose an LDP protocol for identifying heavy hitters. In our proposed protocol, which we call Prefix Extending Method (PEM), users are divided into groups, with each group reporting a prefix of her value. We analyze how to choose optimal parameters for the protocol and identify two design principles for designing LDP protocols with high utility. Experiments on both synthetic and real-world datasets demonstrate the advantage of our proposed protocol.

cs.CR↗

arXiv2017

Optimizing Locally Differentially Private Protocols

Protocols satisfying Local Differential Privacy (LDP) enable parties to collect aggregate information about a population while protecting each user's privacy, without relying on a trusted third party. LDP protocols (such as Google's RAPPOR) have been deployed in real-world scenarios. In these protocols, a user encodes his private information and perturbs the encoded value locally before sending it to an aggregator, who combines values that users contribute to infer statistics about the population. In this paper, we introduce a framework that generalizes several LDP protocols proposed in the literature. Our framework yields a simple and fast aggregation algorithm, whose accuracy can be precisely analyzed. Our in-depth analysis enables us to choose optimal parameters, resulting in two new protocols (i.e., Optimized Unary Encoding and Optimized Local Hashing) that provide better utility than protocols previously proposed. We present precise conditions for when each proposed protocol should be used, and perform experiments that demonstrate the advantage of our proposed protocols.

cs.CR↗