Online and Differentially-Private Tensor Decomposition

Tensor decomposition is positioned to be a pervasive tool in the era of big data. In this paper, we resolve many of the key algorithmic questions regarding robustness, memory efficiency, and differential privacy of tensor decomposition. We propose simple variants of the tensor power method which enjoy these strong properties. We propose the first streaming method with a linear memory requirement. Moreover, we present a noise calibrated tensor power method with efficient privacy guarantees. At the heart of all these guarantees lies a careful perturbation analysis derived in this paper which improves up on the existing results significantly.