Learning from measurements in exponential families

Given a model family and a set of unlabeled examples, one could either label specific examples or state general constraints---both provide information about the desired model. In general, what is the most cost-effective way to learn? To address this question, we introduce measurements, a general class of mechanisms for providing information about a target model. We present a Bayesian decision-theoretic framework, which allows us to both integrate diverse measurements and choose new measurements to make. We use a variational inference algorithm, which exploits exponential family duality. The merits of our approach are demonstrated on two sequence labeling tasks.