The Discrete Gaussian Expectation Maximization (Gradient) Algorithm for Differential Privacy

Algorithm 1

Differentially private DG-EM (gradient) algorithm.

	Input:, privacy parameter and , initial parameter and satisfy Assumption 1, the number of iterations , step size , and failure probability .
(1)	Let ,
(2)	fordo
(3)	For each , calculate the robust gradient and add a discrete Gaussian noise, that is,
	where .
(4)	Let vector denote
(5)	Update .
(6)	end for