Probabilistic Models of Cognition

imminentpoppedAI and Robotics

Feb 23, 2014 (3 years and 1 month ago)

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Probabilistic Models of Cognition

Conceptual Foundations

Chater, Tenenbaum, & Yuille

TICS, 10
(7), 287
-
291 (2006)

Probabilistic Models


Powerful recent approach to perception &
cognition


Probability theory and Bayesian inference


Alternative to classical AI


Focus on function over mechanism


Suggest reasoning is generally optimal

Bayesian Inference


Probabilities as beliefs about world


Not limiting frequencies


Reasoning from effects to causes


200 “B”

200 “R”

100 “S”


P
(
B
|
b
)

P
(
B
&
b
)
P
(
b
)

P
(
b
|
B
)

P
(
B
)
P
(
b
)
5
4
1
2
1
5
2



0
0
)
(
)
(
)
|
(
)
|
(
2
1
5
2





b
P
R
P
R
b
P
b
R
P
5
1
)
(
)
(
)
|
(
)
|
(
2
1
5
1
2
1





b
P
S
P
S
b
P
b
S
P
P(hypothesis | data)


P(data | hypothesis) * P(hypothesis)

Prior beliefs + Data

Bayes’ rule

Posterior beliefs

)
(
)
(
)
|
(
)
|
(
b
P
B
P
B
b
P
b
B
P


)
(
)
(
)
|
(
)
|
(
b
P
R
P
R
b
P
b
R
P


)
(
)
(
)
|
(
)
|
(
b
P
S
P
S
b
P
b
S
P


Probabilistic Cognitive Models




Hypotheses over structured representations


Grammars, casual networks, taxonomies, scenes


Hierarchies of hypotheses


Sophisticated learning and estimation techniques


Application to language, vision, navigation, causal
learning, categorization, memory, reasoning


Mapping to heuristics and neural organization

Round

Red or green

4 legs, tail, ears

Various colors

“apple”

“apple”

“apple”

“cat”

“cat”

“cat”

Shape > color