Key-Value Data Collection with Distribution Estimation under Local Differential Privacy

Algorithm 3

Numerical distribution estimation.

	Input: Perturbed results, estimated frequency , padding length , number of bins .
	Output: Reconstructed histogram
(1)	Discretize the perturbed results into bins.
(2)	Subtract from each bin.
(3)	Divide each bin by to generate .
(4)	Initialize for all .
(5)	while not converging do
(6)	E-step ,
(7)	M-step ,
(8)	end while
(9)	Reconstructed histogram
(10)	return reconstructed histogram