Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision

Deep learning has emerged as a versatile tool for a wide range of NLP tasks, due to its superior capacity in representation learning. But its applicability is limited by the reliance on annotated examples, which are difficult to produce at scale. Indirect supervision has emerged as a promising direction to address this bottleneck, either by introducing labeling functions to automatically generate noisy examples from unlabeled text, or by imposing constraints over interdependent label decisions. A plethora of methods have been proposed, each with respective strengths and limitations. Probabilistic logic offers a unifying language to represent indirect supervision, but end-to-end modeling with probabilistic logic is often infeasible due to intractable inference and learning. In this paper, we propose deep probabilistic logic (DPL) as a general framework for indirect supervision, by composing probabilistic logic with deep learning. DPL models label decisions as latent variables, represents prior knowledge on their relations using weighted first-order logical formulas, and alternates between learning a deep neural network for the end task and refining uncertain formula weights for indirect supervision, using variational EM. This framework subsumes prior indirect supervision methods as special cases, and enables novel combination via infusion of rich domain and linguistic knowledge. Experiments on biomedical machine reading demonstrate the promise of this approach.