# (05/08/18) Subspace estimation from incomplete observations: a high dimensional analysis

May 7, 2018
In our recent paper, we present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations.  We show that, with proper time scaling, the time-varying principal angles between the true subspace and its estimates given by the algorithms converge weakly to deterministic processes when the ambient dimension $$n$$ tends to infinity. Moreover, the limiting processes can be exactly characterized as the unique solutions of certain ordinary differential equations (ODEs). A finite sample bound is also given, showing that the rate of convergence towards such limits is $$\mathcal{O}(1/\sqrt{n})$$.