SNIPE for memory-limited PCA with incomplete data: From failure to success

Consider the problem of identifying an unknown subspace S from data with erasures and with limited memory available. To estimate S, suppose we group the measurements into blocks and iteratively update our estimate of S with each new block. In the first part of this talk, we will discuss why estimating S by computing the "running average" of span of these blocks fails in general. Based on the lessons learned, we then propose SNIPE for memory-limited PCA with incomplete data, useful also for streaming data applications. SNIPE provably converges (linearly) to the true subspace, in the absence of noise and given sufficient measurements, and shows excellent performance in simulations. This is joint work with Laura Balzano and Mike Wakin.