On the Theory of Weak Supervision for Information Retrieval

Neural network approaches have recently shown to be effective in several information retrieval (IR) tasks. However, neural approaches often require large volumes of training data to perform effectively, which is not always available. To mitigate the shortage of labeled data, training neural IR models with weak supervision has been recently proposed and received considerable attention in the literature. In weak supervision, an existing model automatically generates labels for a large set of unlabeled data, and a machine learning model is further trained on the generated "weak" data. Surprisingly, it has been shown in prior art that the trained neural model can outperform the weak labeler by a significant margin. Although these obtained improvements have been intuitively justified in previous work, the literature still lacks theoretical justification for the observed empirical findings. In this paper, we provide a theoretical insight into weak supervision for information retrieval, focusing on learning to rank. We model the weak supervision signal as a noisy channel that introduces noise to the correct ranking. Based on the risk minimization framework, we prove that given some sufficient constraints on the loss function, weak supervision is equivalent to supervised learning under uniform noise. We also find an upper bound for the empirical risk of weak supervision in case of non-uniform noise. Following the recent work on using multiple weak supervision signals to learn more accurate models, we find an information theoretic lower bound on the number of weak supervision signals required to guarantee an upper bound for the pairwise error probability. We empirically verify a set of presented theoretical findings, using synthetic and real weak supervision data.