Pattern theory
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Pattern theory is a mathematical and probabilistic formalism to create representations of complex real world phenomena. Some of its tenets are:
- The representations are compositional, that is, they are built up from simple primitives, combined according to some rules that may be deterministic or random. Examples are language (built from words), motor actions (built from primitive movements).
- The signal is used in pattern cognition to infer the hidden variable, using a Bayesian model of probability.
- The variations can be described by groups or semigroups of transformations, operating on the primitives. For instance, given two resembling pictures, we may be interested in the difffeomorphisms taking the first picture to a picture that very closely resembles the second.
The Brown University Pattern Theory Group was formed in 1972 by Ulf Grenander. Many mathematicians are currently working in this group, noteworthy among them being the Fields Medalist David Mumford.
Their current aim is to create algorithms for patern cognition that can be implemented on current hardware.