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We introduce a new algorithm, Construction of dIfferentially PrivateEmpirical Distributions from a low-order marginals set tHrough solving linearEquations with l2 Regularization (CIPHER), that produces differentially privateempirical joint distributions from a set of low-order marginals. CIPHER isconceptually simple and requires no more than decomposing joint probabilitiesvia basic probability rules to construct a linear equation set and subsequentlysolving the equations. Compared to the full-dimensional histogram (FDH)sanitization, CIPHER has drastic\-ally lower requirements on computationalstorage and memory, which is practically attractive especially considering thatthe high-order signals preserved by the FDH sanitization are likely just samplerandomness and rarely of interest. Our experiments demonstrate that CIPHERoutperforms the multiplicative weighting exponential mechanism in preservingoriginal information and has similar or superior cost-normalized utility to FDHsanitization at the same privacy budget.

Construction of Differentially Private Empirical Distributions from a  low-order Marginals Set through Solving Linear Equations with l2  Regularization