Classification with Low Rank and Missing Data

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Elad Hazan, Roi Livni, Yishay Mansour ;
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:257-266, 2015.

Abstract

We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace. Finding a hidden subspace is known to be computationally hard. Nevertheless, using a non-proper formulation we give an efficient agnostic algorithm that classifies as good as the best linear classifier coupled with the best low-dimensional subspace in which the data resides. A direct implication is that our algorithm can linearly (and non-linearly through kernels) classify provably as well as the best classifier that has access to the full data.

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