Xi'an's Og

“the employment of ABC for differentially private data serendipitously eradicates the “approximate” nature of the resulting posterior  samples, which otherwise would be the case if the data were noise-free.”

In parallel or conjunction with the 23w5601 workshop, I was reading some privacy literature and came across this Exact inference with approximate computation for differentially private data via perturbation by Ruobin Gong  that appeared in the Journal of Privacy and Confidentiality last year (2022). When differential privacy is implemented by perturbation, i.e. by replacing the private data with a randomised, usually Gaussian, version, the exact posterior distribution is a convolution which, if unavailable, can be approximated by a standard ABC step. Which, most interestingly does not impact the accuracy of the (public) posterior, i.e. it does not modify this posterior when the probability of acceptance in ABC is the density of the perturbation noise at the public data given the pseudo-data. Which follows from the 1984 introduction of the ABC idea. On the opposite, EM does not enjoy an exact version, as the E step must be (unbiasedly) approximated by a Monte Carlo representation that relies on the same ABC algorithm. Which usually makes the M step harder, although a Monte Carlo version of the gradient is also available.

This entry was posted on September 10, 2023 at 12:23 am and is filed under Books, Mountains, pictures, Running, Statistics, Travel, University life with tags 23w5106, ABC algorithm, Approximate Bayesian computation, Bayesian inference, British Columbia, Canada, data privacy, differential privacy, EM algorithm, exact inference, Journal of Privacy and Confidentiality, Kelowna, Okanagan Valley, UBCO. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.