Title: An analytic formulation for positive-unlabeled learning via weighted integral probability metric,
Abstract: We consider the problem of learning a binary classifier from only positive
and unlabeled observations (PU learning). Although recent research in PU
learning has succeeded in showing theoretical and empirical performance, most
existing algorithms need to solve either a convex or a non-convex optimization
problem and thus are not suitable for large-scale datasets. In this paper, we
propose a simple yet theoretically grounded PU learning algorithm by extending
the previous work proposed for supervised binary classification (Sriperumbudur
et al., 2012). 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 excess risk bound does not rely on an approximation
error term. To the best of our knowledge, we are the first to explicitly derive
the excess risk bound in the field of PU learning. Finally, we conduct
extensive numerical experiments using both synthetic and real datasets,
demonstrating improved accuracy, scalability, and robustness of the proposed
algorithm.