Differentially private online Bayesian estimation with adaptive truncation

Official URL: https://dx.doi.org/10.55730/1300-0632.4054

In this paper, a novel online and adaptive truncation method is proposed for differentially private Bayesian online estimation of a static parameter regarding a population. A local differential privacy setting is assumed where sensitive information from individuals is collected on an individual level and sequentially. The inferential aim is to estimate, on the fly, a static parameter regarding the population to which those individuals belong. We propose sequential Monte Carlo to perform online Bayesian estimation. When individuals provide sensitive information in response to a query, it is necessary to corrupt it with privacy-preserving noise to ensure the privacy of those individuals. The amount of corruption is proportional to the sensitivity of the query, which is determined usually by the range of the queried information. The proposed truncation technique adapts to the previously collected data to adjust the query range for the next individual. The idea is that, based on previous data, one can carefully arrange the interval into which the next individual’s information is to be truncated before being distorted with privacy-preserving noise. In this way, predictive queries are designed with small sensitivity, hence small privacy-preserving noise, enabling more accurate estimation while maintaining the same level of privacy. To decide on the location and the width of the interval, an exploration-exploitation approach is employed, a la Thompson sampling, with an objective function based on Fisher information. The merits of the methodology are shown with numerical examples.