Differentially Private Metropolis–Hastings Algorithms

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Title: Differentially Private Metropolis–Hastings Algorithms
Author: Räisä, Ossi
Other contributor: Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta
University of Helsinki, Faculty of Science
Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten
Publisher: Helsingin yliopisto
Date: 2021
Language: eng
URI: http://urn.fi/URN:NBN:fi:hulib-202105112135
Thesis level: master's thesis
Degree program: Datatieteen maisteriohjelma
Master's Programme in Data Science
Magisterprogrammet i data science
Specialisation: ei opintosuuntaa
no specialization
ingen studieinriktning
Abstract: Differential privacy has over the past decade become a widely used framework for privacy-preserving machine learning. At the same time, Markov chain Monte Carlo (MCMC) algorithms, particularly Metropolis-Hastings (MH) algorithms, have become an increasingly popular method of performing Bayesian inference. Surprisingly, their combination has not received much attention in the litera- ture. This thesis introduces the existing research on differentially private MH algorithms, proves tighter privacy bounds for them using recent developments in differential privacy, and develops two new differentially private MH algorithms: an algorithm using subsampling to lower privacy costs, and a differentially private variant of the Hamiltonian Monte Carlo algorithm. The privacy bounds of both new algorithms are proved, and convergence to the exact posterior is proven for the latter. The performance of both the old and the new algorithms is compared on several Bayesian inference problems, revealing that none of the algorithms is clearly better than the others, but subsampling is likely only useful to lower computational costs.
Subject: Differential privacy
Markov chain Monte Carlo
Hamiltonian Monte Carlo

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