Title: Nonconvex One-bit Single-label Multi-label Learning,
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 $O(\epsilon)$
recovery error after retrieving $O(k^{1.5}d_1 d_2/\epsilon)$ one-bit labels
within $O(kd)$ memory. Our bound is nearly optimal in the order of
$O(1/\epsilon)$. 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.