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A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing
Ming Lin · Jieping Ye

Tue Dec 06 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #121 #None
We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm converges linearly, achieves $O(\epsilon)$ recovery error after retrieving $O(k^{3}d\log(1/\epsilon))$ training instances, consumes $O(kd)$ memory in one-pass of dataset and only requires matrix-vector product operations in each iteration. The key ingredient of our framework is a construction of an estimation sequence endowed with a so-called Conditionally Independent RIP condition (CI-RIP). As special cases of gFM, our framework can be applied to symmetric or asymmetric rank-one matrix sensing problems, such as inductive matrix completion and phase retrieval.

Author Information

Ming Lin (University of Michigan)
Jieping Ye (University of Michigan)

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