Approximating incomplete data with varieties

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. See github for some code the publication page for a copy of the paper and slides from my presentation at the IEEE International Symposium on Information Theory.