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arXiv · 2002.03004

List Decodable Subspace Recovery

Prasad Raghavendra·Morris Yau
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Abstract

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 $\alpha$ 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 $O(\frac{1}{\alpha})$ subspaces one of which is nontrivially 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.

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Prasad Raghavendra, Morris Yau. 2020-02-07. List Decodable Subspace Recovery. https://arxiv.org/abs/2002.03004

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