Classification with Low Rank and Missing Data

TL;DR

This paper introduces an efficient algorithm for classification with missing data, assuming data lies in a low-rank subspace, achieving performance comparable to classifiers with complete data.

Contribution

It presents a novel non-proper formulation and an agnostic algorithm that effectively classifies missing data by leveraging low-rank assumptions.

Findings

Algorithm classifies as well as the best linear classifier with full data

Works with both linear and kernel methods

Handles missing data efficiently

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.