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 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 was novel in its aim to:
- Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was commonplace at the time.
- 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.
Read more about Pattern Theory: Algebraic Foundations, Topology, Entropy, Statistics, Further Reading
Famous quotes containing the words pattern and/or theory:
“Why it was that upon this beautiful feminine tissue, sensitive as gossamer, and practically blank as snow as yet, there should have been traced such a coarse pattern as it was doomed to receive; why so often the coarse appropriates the finer thus, the wrong man the woman, the wrong women the man, many years of analytical philosophy have failed to explain to our sense of order.”
—Thomas Hardy (1840–1928)
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)