In this paper, we study the sparse covariance matrix estimation problem in the local differential privacy model, and give a non-trivial lower bound on the non-interactive private minimax risk in the metric of squared spectral norm. We show that the lower bound is actually tight, as it matches a previous upper bound. Our main technique for achieving this lower bound is a general framework, called General Private Assouad Lemma, which is a considerable generalization of the previous private Assouad lemma and can be used as a general method for bounding the private minimax risk of matrix-related estimation problems.
|Original language||English (US)|
|Title of host publication||IJCAI International Joint Conference on Artificial Intelligence|
|Publisher||International Joint Conferences on Artificial IntelligenceThomas.firstname.lastname@example.org|
|Number of pages||7|
|State||Published - Jan 1 2019|