Principled analytic classifier for positive-unlabeled learning via weighted integral probability metric
This work addresses the challenge of scalable PU learning for large datasets, offering a solution that reduces computational overhead compared to existing methods.
The paper tackles the problem of learning a binary classifier from only positive and unlabeled data (PU learning) by proposing a computationally efficient and theoretically grounded algorithm that yields a closed-form classifier, with experiments showing improved accuracy, scalability, and robustness.
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.