A Perturbation Bound on the Subspace Estimator from Canonical Projections
Abstract
This paper derives a perturbation bound on the optimal subspace estimator obtained from a subset of its canonical projections contaminated by noise. This fundamental result has important implications in matrix completion, subspace clustering, and related problems.
I worked with Daniel Pimentel-Alarćon on a project on approximating incomplete data with varieties. If there’s some unknown data that we think has linear structure and we only have access to noisy low dimensional projections (think - an unknown (linear) object in a dark room and I only show you the shadows after we shine a light), how accurately can we reconstruct the original unknown data? We derived an upper bound to this in our paper: a perturbation bound for the optimal subspace estimator from canonical projections.
You can find my ISIT 22 presentation slides on this paper here .
Karan Srivastava
PhD Student, Mathematics
My research interests include machine learning, reinforcement learning, combinatorics, and algebraic geometry