List Decodable Subspace Recovery [article]

Prasad Raghavendra, Morris Yau
2020 arXiv   pre-print
Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where an α fraction (less than half) of the data is distributed uniformly in an unknown k dimensional subspace in d dimensions, and with no additional assumptions on the remaining data, the goal is to recover a succinct list of O(1/α) subspaces one of which is
more » ... rivially correlated with the planted subspace. We provide the first polynomial time algorithm for the 'list decodable subspace recovery' problem, and subsume it under a more general framework of list decoding over distributions that are "certifiably resilient" capturing state of the art results for list decodable mean estimation and regression.
arXiv:2002.03004v1 fatcat:hwlg67ldsrbwhcjtbqnwj5lmkm