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To create a large amount of training labels for machine learning models effectively and efficiently, researchers have turned to Weak Supervision (WS), which uses programmatic labeling sources rather than manual annotation. Existing works of WS for binary classification typically assume the presence of labeling sources that are able to assign both positive and negative labels to data in roughly balanced proportions. However, for many tasks of interest where there is a minority positive class, negative examples could be too diverse for developers to generate indicative labeling sources. Thus, in this work, we study the application of WS on binary classification tasks with positive labeling sources only. We propose WEAPO, a simple yet competitive WS method for producing training labels without negative labeling sources. On 10 benchmark datasets, we show WEAPO achieves the highest averaged performance in terms of both the quality of synthesized labels and the performance of the final classifier supervised with these labels. We incorporated the implementation of \method into WRENCH, an existing benchmarking platform.