  We consider the problem of learning a binary classifier from only positive
and unlabeled observations (called PU learning). Recent studies in PU learning
have shown superior performance theoretically and empirically. However, most
existing algorithms may not be suitable for large-scale datasets because they
face repeated computations of a large Gram matrix or require massive
hyperparameter optimization. In this paper, we propose a computationally
efficient and theoretically grounded PU learning algorithm. The proposed PU
learning algorithm produces a closed-form classifier when the hypothesis space
is a closed ball in reproducing kernel Hilbert space. In addition, we establish
upper bounds of the estimation error and the excess risk. The obtained
estimation error bound is sharper than existing results and the derived excess
risk bound has an explicit form, which vanishes as sample sizes increase.
Finally, we conduct extensive numerical experiments using both synthetic and
real datasets, demonstrating improved accuracy, scalability, and robustness of
the proposed algorithm.
