PLDP: Personalized Local Differential Privacy for Multidimensional Data Aggregation

Algorithm 2

Information entropy-based multidimensional joint distribution estimation.

(i)	Input: : the set of k attributes for which the sever wants
	to estimate the joint distribution and is the setof data records with  = , where could be empty.
	Output: HD: the joint distribution of
(1)	for r = 1 to do
(2)	Initialize a result list, ;
(3)	Divided into two parts: and , where  = k - r and  = r, and there are n =  different divisions;
(4)	for i = 1 to n do
(5)	For the i-th division, if there are enough records that have all the attributes in and , the sever estimatesthe joint distributions of and by LASSO regression algorithm, respectively. Denote the domains of candidate values of and as and, respectively, and then the estimated joint distribution can be denoted as  =  and  = .
(6)	Calculate  = ,  = , and then the total information entropy in this division  =  + .
(7)	Finally, add the triplet , , into ;
(8)	end for
(9)	IfBreak;
(10)	end for
(11)	Choose the triplet with the largest and calculate the joint distribution with the corresponding , by the multiplication principle.