We present an objective function for learning with unlabeled data that utilizes auxiliary expectation constraints. We optimize this objective function using a procedure that alternates between information and moment projections. Our method provides an alternate interpretation of the posterior regularization framework (Graca et al., 2008), maintains uncertainty during optimization unlike constraint-driven learning (Chang et al., 2007), and is more efficient than generalized expectation criteria (Mann & McCallum, 2008). Applications of this framework include minimally supervised learning, semisupervised learning, and learning with constraints that are more expressive than the underlying model. In experiments, we demonstrate comparable accuracy to generalized expectation criteria for minimally supervised learning, and use expressive structural constraints to guide semi-supervised learning, providing a 3%-6 % improvement over stateof-the-art constraint-driven learning. 1

We develop a semi-supervised learning method that constrains the posterior distribution of latent variables under a generative model to satisfy a rich set of feature expectation constraints estimated with labeled data. This approach encourages the generative model to discover latent structure that is relevant to a prediction task. We estimate parameters with a coordinate ascent algorithm, one step of which involves training a discriminative log-linear model with an embedded generative model. This hybrid model can be used for test time prediction. Unlike other high-performance semi-supervised methods, the proposed algorithm converges to a stationary point of a single objective function, and affords additional flexibility, for example to use different latent and output spaces. We conduct experiments on three sequence labeling tasks, achieving the best reported results on two of them, and showing promising results on CoNLL03 NER. 1.