  Linguistic structures exhibit a rich array of global phenomena, however
commonly used Markov models are unable to adequately describe these phenomena
due to their strong locality assumptions. We propose a novel hierarchical model
for structured prediction over sequences and trees which exploits global
context by conditioning each generation decision on an unbounded context of
prior decisions. This builds on the success of Markov models but without
imposing a fixed bound in order to better represent global phenomena. To
facilitate learning of this large and unbounded model, we use a hierarchical
Pitman-Yor process prior which provides a recursive form of smoothing. We
propose prediction algorithms based on A* and Markov Chain Monte Carlo
sampling. Empirical results demonstrate the potential of our model compared to
baseline finite-context Markov models on part-of-speech tagging and syntactic
parsing.
