The Canonical Representations of General Pattern Theory
Keyword(s):
Pattern theory is combinatory in spirit or, to use a fashionable term, connectionist: complex structures are built from simpler ones. To construct more general patterns, we will generalize from combinations of sites to combinations of primitives, termed generators, which are structured sets. The interactions between generators is imposed via the directed and undirected graph structures, defining how the variables at the sites of the graph interact with their neighbors in the graph. Probabilistic structures on the representations allow for expressing the variation of natural patterns. Canonical representations are established demonstrating a unified manner for viewing DAGs, MRFs, Gaussian random fields and probabilistic formal languages.
1998 ◽
Vol 14
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pp. 883-903
2002 ◽
Vol 7
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pp. 31-42
2016 ◽
Vol 126
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pp. 883-905
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1988 ◽
Vol 12
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pp. 237-263
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2014 ◽
Vol 445
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pp. 256-269
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2012 ◽
Vol 44
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pp. 603-616
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2015 ◽
Vol 83
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pp. 37-51
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1991 ◽
Vol 249
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pp. 678-683
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