<s>
Pattern	B-General_Concept
theory	I-General_Concept
,	O
formulated	O
by	O
Ulf	O
Grenander	O
,	O
is	O
a	O
mathematical	O
formalism	O
to	O
describe	O
knowledge	O
of	O
the	O
world	O
as	O
patterns	O
.	O
</s>
<s>
It	O
differs	O
from	O
other	O
approaches	O
to	O
artificial	B-Application
intelligence	I-Application
in	O
that	O
it	O
does	O
not	O
begin	O
by	O
prescribing	O
algorithms	O
and	O
machinery	O
to	O
recognize	O
and	O
classify	O
patterns	O
;	O
rather	O
,	O
it	O
prescribes	O
a	O
vocabulary	O
to	O
articulate	O
and	O
recast	O
the	O
pattern	O
concepts	O
in	O
precise	O
language	O
.	O
</s>
<s>
Broad	O
in	O
its	O
mathematical	O
coverage	O
,	O
Pattern	B-General_Concept
Theory	I-General_Concept
spans	O
algebra	O
and	O
statistics	O
,	O
as	O
well	O
as	O
local	O
topological	O
and	O
global	O
entropic	O
properties	O
.	O
</s>
<s>
Identify	O
the	O
hidden	O
variables	O
of	O
a	O
data	B-General_Concept
set	I-General_Concept
using	O
real	O
world	O
data	O
rather	O
than	O
artificial	O
stimuli	O
,	O
which	O
was	O
previously	O
commonplace	O
.	O
</s>
<s>
Formulate	O
prior	O
distributions	O
for	O
hidden	O
variables	O
and	O
models	O
for	O
the	O
observed	O
variables	O
that	O
form	O
the	O
vertices	O
of	O
a	O
Gibbs-like	O
graph	O
.	O
</s>
<s>
The	O
Brown	O
University	O
Pattern	B-General_Concept
Theory	I-General_Concept
Group	O
was	O
formed	O
in	O
1972	O
by	O
Ulf	O
Grenander	O
.	O
</s>
<s>
Mumford	O
regards	O
Grenander	O
as	O
his	O
"	O
guru	O
"	O
in	O
Pattern	B-General_Concept
Theory	I-General_Concept
.	O
</s>
