Dependency Diagrams (DDs) and Graph-Constrained Correlation Dynamics (GCCD) expand the universe of probabilistic graphical models to allow their application in a number of new domains. Dependency Diagrams are a new graphical modeling language which permit graphical representation of model structure and logic beyond the scope of existing formalisms. This allows the generation of graphical models that represent new classes of objects, such as algorithms for sampling and inference, and for the transformation between graphical representations of probabilistic domain models and graphical representations of algorithms acting on those models. This thesis provides semantics for the probability distributions defined by DDs, and describes a process for generating diagrams that specify sampling procedures. Graph-Constrained Correlation Dynamics adds to existing graphical modeling formalisms the ability to represent distributions that evolve continuously in time. In particular, with GCCD a Markov random field is be used to specify continuously evolving parametrized probability distributions in the domain of reaction networks. This capability opens the possibility of representing continuously in time distributions over subsets of complex stochastic systems, permitting model reduction by allowing larger stochastic models the freedom to avoid explicitly representing reactions over these subsets without sacrificing statistical properties of their simulations. This thesis derives algorithms for optimizing the approximation of a target distribution by a GCCD model, and demonstrates the success of these algorithms. Together, DDs and GCCD represent significant advancements in the available vocabularies of probabilistic graphical modeling, and open the door for exciting new scientific applications.
|Commitee:||Baldi, Pierre, Ihler, Alexander, Kaiser, Peter|
|School:||University of California, Irvine|
|Department:||Computer Science - Ph.D.|
|School Location:||United States -- California|
|Source:||DAI-B 73/07(E), Dissertation Abstracts International|
|Subjects:||Biophysics, Computer science|
|Keywords:||Dependency diagrams, Graph-constrained correlation, Graphical modeling language, Probability distributions, Reaction networks, Sampling procedures|
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