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Poster

On Differentially Private Sampling from Gaussian and Product Distributions

Badih Ghazi · Xiao Hu · Ravi Kumar · Pasin Manurangsi

Great Hall & Hall B1+B2 (level 1) #817

Abstract: We study the problem, where given a dataset of n i.i.d. samples from an unknown distribution P, we seek to generate a sample from a distribution that is close to P in total variation distance, under the constraint of differential privacy. We study the settings where P is a multi-dimensional Gaussian distribution with different assumptions: known covariance, unknown bounded covariance, and unknown unbounded covariance. We present new differentially private sampling algorithms, and show that they achieve near-optimal sample complexity in the first two settings. Moreover, when P is a product distribution on the binary hypercube, we obtain a pure-DP algorithm whereas only an approximate-DP algorithm (with slightly worse sample complexity) was previously known.

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