We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point processes, which arise in quantum physics as models of particles with repulsive interactions. We extend the determinantal point process model to handle an exponentially-sized set of particles (structures) via a natural factorization of the model into parts. We show how this factorization leads to tractable algorithms for exact inference, including computing marginals, computing conditional probabilities, and sampling. Our algorithms exploit a novel polynomially-sized dual representation of determinantal point processes, and use message passing over a special semiring to compute relevant quantities. We illustrate the advantages of the model on tracking and articulated pose estimation problems. 1

with continuous rational kernels using the expectation semiring

Abstract—Accurate estimates of language model parameters are critical for building quality text generation systems, such as automatic speech recognition. However, text training data for a domain of interest is often unavailable. Instead, we use semi-supervised model adaptation; parameters are estimated using both unlabeled in-domain data (raw speech audio) and labeled out of domain data (text.) In this work, we present a new semi-supervised language model adaptation procedure for Maximum Entropy models with n-gram features. We augment the conventional maximum likelihood training criterion on out-ofdomain text data with an additional term to minimize conditional entropy on in-domain audio. Additionally, we demonstrate how to compute conditional entropy efficiently on speech lattices using first- and second-order expectation semirings. We demonstrate improvements in terms of word error rate over other adaptation techniques when adapting a maximum entropy language model from broadcast news to MIT lectures. I.