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In binary classification, there are situations where negative (N) data aretoo diverse to be fully labeled and we often resort to positive-unlabeled (PU)learning in these scenarios. However, collecting a non-representative N setthat contains only a small portion of all possible N data can often be mucheasier in practice. This paper studies a novel classification framework whichincorporates such biased N (bN) data in PU learning. We provide a method basedon empirical risk minimization to address this PUbN classification problem. Ourapproach can be regarded as a novel example-weighting algorithm, with theweight of each example computed through a preliminary step that drawsinspiration from PU learning. We also derive an estimation error bound for theproposed method. Experimental results demonstrate the effectiveness of ouralgorithm in not only PUbN learning scenarios but also ordinary PU learningscenarios on several benchmark datasets.

Classification from Positive, Unlabeled and Biased Negative Data