Pattern theory, formulated by
Ulf Grenander, is a mathematical
formalism to describe knowledge of the world as
patterns. It differs from other approaches to
artificial intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...
in that it does not begin by prescribing
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
s and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. Broad in its mathematical coverage, Pattern Theory spans
algebra and
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, as well as local topological and global entropic properties.
In addition to the new algebraic vocabulary, its
statistical approach is novel in its aim to:
* Identify the
hidden variables of a
data set
A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more table (database), database tables, where every column (database), column of a table represents a particular Variable (computer sci ...
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 Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
models applied by listing the deformations of the patterns.
* Synthesize (sample) from the models, not just analyze signals with them.
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 Pattern Theory.
See also
*
Abductive reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by Ameri ...
*
Algebraic statistics
*
Computational anatomy
*
Formal concept analysis
*
Grammar induction
*
Image analysis
*
Induction
*
Lattice theory
*
Spatial statistics
References
Further reading
* 2007.
Ulf Grenander and Michael Miller ''Pattern Theory: From Representation to Inference''. Oxford University Press. Paperback. ()
* 1994. Ulf Grenander ''General Pattern Theory''. Oxford Science Publications. ()
* 1996. Ulf Grenander ''Elements of Pattern Theory''. Johns Hopkins University Press. ()
External links
Pattern Theory Groupat Brown University
Pattern Theory: Grenander's Ideas and Examples- a video lecture by David Mumford
Pattern Theory and Applications- graduate course page with material by a Brown University alumnus
{{DEFAULTSORT:Pattern Theory
Formalism (philosophy)
Artificial intelligence