Subspace Learning with Partial Information
  The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity 
Alon Gonen, Dan Rosenbaum, Yonina Eldar, Shai Shalev-Shwartz
cs.LG stat.ML