Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow

Xiao Zhang, Simon S. Du, Quanquan Gu

We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and computational complexities. We present and analyze a new gradient-based non-convex optimization algorithm that converges to the true underlying matrix at a linear rate with sample complexity only linearly depending on $n$ and logarithmically depending on $d$. To the best of our knowledge, all previous algorithms either have a quadratic dependency on the number of features in sample complexity or a sub-linear computational convergence rate. In addition, we provide experiments on both synthetic and real world data to demonstrate the effectiveness of our proposed algorithm.

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