2 research outputs found
Statistical Query Complexity of Manifold Estimation
This paper studies the statistical query (SQ) complexity of estimating
-dimensional submanifolds in . We propose a purely geometric
algorithm called Manifold Propagation, that reduces the problem to three
natural geometric routines: projection, tangent space estimation, and point
detection. We then provide constructions of these geometric routines in the SQ
framework. Given an adversarial oracle and a target
Hausdorff distance precision , the
resulting SQ manifold reconstruction algorithm has query complexity , which is proved to be nearly
optimal. In the process, we establish low-rank matrix completion results for
SQ's and lower bounds for randomized SQ estimators in general metric spaces.Comment: 81 page