Karl Jones: /* External links */

2016-09-06T21:37:51Z

‎External links

Karl Jones at 21:37, 6 September 2016

2016-09-06T21:37:31Z

Karl Jones: Created page with "'''Pattern theory''', formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as Pattern|pa..."

2016-09-06T21:03:46Z

Created page with "'''Pattern theory''', formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as Pattern|pa..."

New page

'''Pattern theory''', formulated by [[Ulf Grenander]], is a [[Formalism (philosophy of mathematics)|mathematical formalism]] to describe knowledge of the world as [[Pattern|patterns]].

== Description ==

Pattern theory differs from other approaches to [[artificial intelligence]] in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language.

In addition to the new algebraic vocabulary, its statistical approach is novel in its aim to:

* Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was previously commonplace.
* Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph.
* Study the randomness and variability of these graphs.
* Create the basic classes of stochastic models applied by listing the deformations of the patterns.
* Synthesize (sample) from the models, not just analyze signals with it.

Broad in its mathematical coverage, Pattern Theory spans [[algebra]] and [[statistics]], as well as local topological and global entropic properties.

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]]. Mumford regards Grenander as his "guru" in this subject.

== See also ==

* [[Abductive reasoning]]
* [[Algebraic statistics]]
* [[Formal concept analysis]]
* [[Formalism (philosophy of mathematics)]]
* [[Grammar Induction]]
* [[Image analysis]]
* [[Induction]]
* [[Lattice theory]]
* [[Spatial statistics]]

== External links ==

* [https://en.wikipedia.org/wiki/Pattern_theory Pattern theory] @ Wikipedia

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Pattern theory - Revision history

Karl Jones: /* External links */

Karl Jones at 21:37, 6 September 2016

Karl Jones: Created page with "'''Pattern theory''', formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as Pattern|pa..."