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Current speech recognition systems, for example, typically use Gaussian mixture models (GMMs), to estimate the observation (or emission) probabilities of hidden Markov models (HMMs), and GMMs are generative models that have only one layer of latent variables. Instead of developing more powerful models, most of the research effort has gone into finding better ways of estimating the GMM parameters so that error rates are decreased or the margin between different classes is increased. The same observation holds for natural language processing (NLP) in which maximum entropy (MaxEnt) models and conditional random fields (CRFs) have been popular for the last decade. Both of these approaches use shallow models whose success largely depends on the use of carefully handcrafted features.