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We develop an efficient alternating framework for learning a generalizedversion of Factorization Machine (gFM) on steaming data with provableguarantees. When the instances are sampled from $d$ dimensional random Gaussianvectors and the target second order coefficient matrix in gFM is of rank $k$,our algorithm converges linearly, achieves $O(\epsilon)$ recovery error afterretrieving $O(k^{3}d\log(1/\epsilon))$ training instances, consumes $O(kd)$memory in one-pass of dataset and only requires matrix-vector productoperations in each iteration. The key ingredient of our framework is aconstruction of an estimation sequence endowed with a so-called ConditionallyIndependent RIP condition (CI-RIP). As special cases of gFM, our framework canbe applied to symmetric or asymmetric rank-one matrix sensing problems, such asinductive matrix completion and phase retrieval.

A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing