Local, Private, Efficient Protocols for Succinct Histograms

Abstract

We give efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy. In this model, individual users randomize their data themselves, sending differentially private reports to an untrusted server that aggregates them. We study protocols that produce a succinct histogram representation of the data. A succinct histogram is a list of the most frequent items in the data (often called "heavy hitters") along with estimates of their frequencies; the frequency of all other items is implicitly estimated as 0. If there are $n$ users whose items come from a universe of size $d$, our protocols run in time polynomial in $n$ and $\log (d)$. With high probability, they estimate the accuracy of every item up to error $O\left(\sqrt{\log (d)/({\epsilon }^{2}n)}\right)$ where $\epsilon$ is the privacy parameter. Moreover, we show that this much error is necessary, regardless of computational efficiency, and even for the simple setting where only one item appears with significant frequency in the data set. Previous protocols (Mishra and Sandler, 2006; Hsu, Khanna and Roth, 2012) for this task either ran in time $\Omega (d)$ or had much worse error (about $\sqrt[6]{\log (d)/({\epsilon }^{2}n)}$), and the only known lower bound on error was $\Omega (1/\sqrt{n})$. We also adapt a result of McGregor et al (2010) to the local setting. In a model with public coins, we show that each user need only send 1 bit to the server. For all known local protocols (including ours), the transformation preserves computational efficiency.

References in corpus (1)

• RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response

Cited by in corpus (7)

• Privacy-Aware Recommendation with Private-Attribute Protection using Adversarial Learning
• TIPRDC: Task-Independent Privacy-Respecting Data Crowdsourcing Framework for Deep Learning with Anonymized Intermediate Representations
• Secure Hot Path Crowdsourcing with Local Differential Privacy under Fog Computing Architecture
• Random Sampling Plus Fake Data: Multidimensional Frequency Estimates With Local Differential Privacy
• Data Poisoning Attacks to Locally Differentially Private Frequent Itemset Mining Protocols
• On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms
• Infinite Stream Estimation under Personalized $w$-Event Privacy