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A Survey of Mathematical Models of Perception and InferenceProfessor David Mumford In the last decade there has been an explosion of research in the fields of speech and pattern recognition, neural nets and statistical learning theory. I will try to give an overview of this research, touching on some of the central ideas. In particular I want to describe Gibbs/graphical models, context-sensitive grammatical/compositional models, the PAC model of inductive inference, the MDL principle and various algorithms for inference. Applications to vision will be used to illustrate these ideas.
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