Title: Provable Inductive Robust PCA via Iterative Hard Thresholding,
Abstract: The robust PCA problem, wherein, given an input data matrix that is the
superposition of a low-rank matrix and a sparse matrix, we aim to separate out
the low-rank and sparse components, is a well-studied problem in machine
learning. One natural question that arises is that, as in the inductive
setting, if features are provided as input as well, can we hope to do better?
Answering this in the affirmative, the main goal of this paper is to study the
robust PCA problem while incorporating feature information. In contrast to
previous works in which recovery guarantees are based on the convex relaxation
of the problem, we propose a simple iterative algorithm based on
hard-thresholding of appropriate residuals. Under weaker assumptions than
previous works, we prove the global convergence of our iterative procedure;
moreover, it admits a much faster convergence rate and lesser computational
complexity per iteration. In practice, through systematic synthetic and real
data simulations, we confirm our theoretical findings regarding improvements
obtained by using feature information.