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Estimating frequencies of certain items among a population is a basic step indata analytics, which enables more advanced data analytics (e.g., heavy hitteridentification, frequent pattern mining), client software optimization, anddetecting unwanted or malicious hijacking of user settings in browsers.Frequency estimation and heavy hitter identification with local differentialprivacy (LDP) protect user privacy as well as the data collector. Existing LDPalgorithms cannot leverage 1) prior knowledge about the noise in the estimateditem frequencies and 2) prior knowledge about the true item frequencies. As aresult, they achieve suboptimal performance in practice.  In this work, we aim to design LDP algorithms that can leverage such priorknowledge. Specifically, we design ${Calibrate}$ to incorporate the priorknowledge via statistical inference. ${Calibrate}$ can be appended to anexisting LDP algorithm to reduce its estimation errors. We model the priorknowledge about the noise and the true item frequencies as two probabilitydistributions, respectively. Given the two probability distributions and anestimated frequency of an item produced by an existing LDP algorithm, our${Calibrate}$ computes the conditional probability distribution of the item'sfrequency and uses the mean of the conditional probability distribution as thecalibrated frequency for the item. It is challenging to estimate the twoprobability distributions due to data sparsity. We address the challenge viaintegrating techniques from statistics and machine learning. Our empiricalresults on two real-world datasets show that ${Calibrate}$ significantlyoutperforms state-of-the-art LDP algorithms for frequency estimation and heavyhitter identification.

Calibrate: Frequency Estimation and Heavy Hitter Identification with Local Differential Privacy via Incorporating Prior Knowledge