Nonconvex One-bit Single-label Multi-label Learning

Shuang Qiu; Tingjin Luo; Jieping Ye; Ming Lin

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arXiv · 1703.06104

Nonconvex One-bit Single-label Multi-label Learning

Shuang Qiu·Tingjin Luo·Jieping Ye·Ming Lin

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Abstract

We study an extreme scenario in multi-label learning where each training instance is endowed with a single one-bit label out of multiple labels. We formulate this problem as a non-trivial special case of one-bit rank-one matrix sensing and develop an efficient non-convex algorithm based on alternating power iteration. The proposed algorithm is able to recover the underlying low-rank matrix model with linear convergence. For a rank-$k$ model with $d_1$ features and $d_2$ classes, the proposed algorithm achieves $O(ε)$ recovery error after retrieving $O(k^{1.5}d_1 d_2/ε)$ one-bit labels within $O(kd)$ memory. Our bound is nearly optimal in the order of $O(1/ε)$. This significantly improves the state-of-the-art sampling complexity of one-bit multi-label learning. We perform experiments to verify our theory and evaluate the performance of the proposed algorithm.

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BibTeX RIS

Shuang Qiu, Tingjin Luo, Jieping Ye, Ming Lin. 2017-03-17. Nonconvex One-bit Single-label Multi-label Learning. https://arxiv.org/abs/1703.06104

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