  In this paper, we propose a \textit{weak supervision} framework for neural
ranking tasks based on the data programming paradigm \citep{Ratner2016}, which
enables us to leverage multiple weak supervision signals from different
sources. Empirically, we consider two sources of weak supervision signals,
unsupervised ranking functions and semantic feature similarities. We train a
BERT-based passage-ranking model (which achieves new state-of-the-art
performances on two benchmark datasets with full supervision) in our weak
supervision framework. Without using ground-truth training labels, BERT-PR
models outperform BM25 baseline by a large margin on all three datasets and
even beat the previous state-of-the-art results with full supervision on two of
the datasets.
