Learning and Inference with Constraints

Probabilistic modeling has been a dominant approach in Machine Learning research. As the field evolves, the problems of interest become increasingly challenging and complex. Making complex decisions in real world problems often involves assigning values to sets of interdependent variables where the expressive dependency structure can influence, or even dictate, what assignments are possible. However, incorporating nonlocal dependencies in a probabilistic model can lead to intractable training and inference. This paper presents Constraints Conditional Models (CCMs), a framework that augments probabilistic models with declarative constraints as a way to support decisions in an expressive output space while maintaining modularity and tractability of training. We further show that declarative constraints can be used to take advantage of unlabeled data when training the probabilistic model.