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