Private Hypothesis Selection

We provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution P and set of m distributions H, the goal is to output, in ?-differentially manner, H whose total variation distance comparable that best such (which we denote by ?). The sample complexity our basic O(log m/? 2 + log m/??), representing minimal cost privacy when compared non-private algorithm. also can handle infinite classes relaxing (?, ?)-differential privacy. apply selection give learning algorithms number natural classes, including Gaussians, product distributions, sums independent random variables, piecewise polynomials, mixture classes. Our procedure allows us generically convert cover class algorithm, complementing known lower bounds which are terms size packing class. As covering numbers often closely related, constant ?, achieve optimal many interest. Finally, describe application distribution-free PAC learning.