Publications [#343701] of Rong Ge

Papers Published

1. Cheng, Y; Diakonikolas, I; Ge, R, High-dimensional robust mean estimation in nearly-linear time, Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms (January, 2019), pp. 2755-2771 [doi]
   (last updated on 2026/01/16)

   Abstract:
   We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent error guarantees for several families of structured distributions. In this work, we give the first nearly-linear time algorithms for high-dimensional robust mean estimation. Specifically, we focus on distributions with (i) known covariance and sub-gaussian tails, and (ii) unknown bounded covariance. Given N samples on R^d, an -fraction of which may be arbitrarily corrupted, our algorithms run in time O^e(Nd)/poly() and approximate the true mean within the information-theoretically optimal error, up to constant factors. Previous robust algorithms with comparable error guarantees have running times Ω(^eNd²), for = Ω(1). Our algorithms rely on a natural family of SDPs parameterized by our current guess ν for the unknown mean µ^?. We give a win-win analysis establishing the following: either a near-optimal solution to the primal SDP yields a good candidate for µ^?— independent of our current guess ν — or a near-optimal solution to the dual SDP yields a new guess ν⁰whose distance from µ^?is smaller by a constant factor. We exploit the special structure of the corresponding SDPs to show that they are approximately solvable in nearly-linear time. Our approach is quite general, and we believe it can also be applied to obtain nearly-linear time algorithms for other high-dimensional robust learning problems.