A Novel Stochastic Gradient Descent Algorithm for LearningPrincipal Subspaces

Charline Le Lan, Joshua Greaves, Jesse Farebrother, Mark Rowland, Fabian Pedregosa, Rishabh Agarwal, Marc G Bellemare

Keywords: representation learning, deep learning, PCA

TL;DR: algorithm amenable to deep learning that learns a principal subspace from sample entries

Abstract: In this paper, we derive an algorithm that learns a principal subspace from sample entries, can be applied when the approximate subspace is represented by a neural network, and hence can bescaled to datasets with an effectively infinite number of rows and columns. Our method consistsin defining a loss function whose minimizer is the desired principal subspace, and constructing agradient estimate of this loss whose bias can be controlled.