Peter N. Yianilos
Motivated by the goal of establishing stochastic and information theoretic foundations for the study of intelligence and synthesis of intelligent machines, this thesis probes several topics relating to hidden state stochastic models.
Finite Growth Models (FGM) are introduced. These are nonnegative functionals that arise from parametrically-weighted directed acyclic graphs and a tuple observation that affects these weights. Using FGMs the parameters of a highly general form of stochastic transducer can be learned from examples, and the particular case of stochastic string edit distance is developed. Experiments are described that illustrate the application of learned string edit distance to the problem of recognizing a spoken word given a phonetic transcription of the acoustic signal. With FGMs one may direct learning by criteria beyond simple maximum-likelihood. The MAP (maximum a posteriori estimate) and MDL (minimum description length) are discussed along with the application to causal-context probability models and unnormalized noncausal models. The FGM framework, algorithms, and data structures describe hidden Markov models, stochastic context free grammars, and many other conventional similar models while providing a unified and natural way for computer scientists to learn and reason about them and their many variations. A software system and scripting language is proposed to serve as an assembly language or sorts for many higher level model types.
This thesis also illuminates certain fundamental aspects of the nature of normal (Gaussian) mixtures and the reparameterization of related optimization problems. The use of conditional normal mixtures is proposed as a tool for image modeling, and issues relating to the estimation of their parameters are discussed.
I must begin by thanking my first mentor Joeseph Vargo, and my parents and grandparents who valued education and always encouraged me to follow my own interests. I also thank my advisor Bob Tarjan and Bruce Maggs for urging me to complete my graduate studies at Princeton.
Many of the results of this thesis arose from a collaboration with Eric Ristad and I acknowledge his important influence on and contributions to this research. I am also grateful for the participation and advice of my other committee members Andrew Appel, Bob Sedgewick, and Vince Poor.
Finally, this work would not have been possible without the support and patience of my wife Angela and our children Nicholas, Jonathan, Geoffrey, and Lauren.