|제목||[학술세미나] [학과세미나] 10월 2일(화) 특별세미나 안내|
|내용||[학과세미나] 10월 2일(화) 특별세미나 안내
▪제목 : Geometrizing rates of convergence under differential privacy constraints
▪연사 : Angelika Rohde (Unversity of Freiburg)
▪일시 : 2018년 10월 2일(화) PM 17:00 – 18:00
▪장소 : 25동 405호
We study the problem of estimating a functional θ(P) of an unknown probability distribution P ∈ P in which the original iid sample X1, . . . , Xn is kept private even from the statistician via an α-local differential privacy constraint. Let ωT V denote the modulus of continuity of the functional θ over P, with respect to total variation distance. For a large class of loss functions l, we prove that the privatized minimax risk is equivalent to l(ωT V (n−1/2)) to within constants, under regularity conditions that are satisfied, in particular, if θ is linear and P is convex. Our results complement the theory developed by Donoho and Liu (1991) with the nowadays highly relevant case of privatized data. Somewhat surprisingly, the difficulty of the estimation problem in the private case is characterized by ωT V , whereas, it is characterized by the Hellinger modulus of continuity if the original data X1, . . . , Xn are available. We also provide a general recipe for constructing rate optimal privatization mechanisms and illustrate the general theory in numerous examples. Our theory allows to quantify the price to be paid for local differential privacy in a large class of estimation problems.
세미나 안내_181002_Angelika Rohde.hwp [16KB]