Carlos Rodriguezon

Heat, Learning and Prediction

July 10, 2007

(52)

Problem:

I have a brain I observe x I want to understand x I need to predict future x'

How ?

Brain ?

Why ?

movement brain

sea squirtat home

CNS for navigation

Bio

Phys

Math

t

Truth: t(x)

Model: { p(x|)}

Geometrization of Inference

I±(p®¼: t®! )

minimized when: Gibbs distribution !

negative free energy !

I G N O R A N C E

t

Truth: t(x)

Model: { p(x|)}

Geometrization of Inference

I±(p®¼: t®! )

minimized when: Gibbs distribution !

negative free energy !

I G N O R A N C E

t

Truth: t(x)

Model: { p(x|)}

Geometrization of Inference

I±(p®¼: t®! )

minimized when: Gibbs distribution !

negative free energy !

I G N O R A N C E

t

Truth: t(x)

Model: { p(x|)}

Geometrization of Inference

I±(p®¼: t®! )

minimized when: Gibbs distribution !

negative free energy !

I G N O R A N C E

** I G N O R A N C E **

minimized when

OPTIMALITY OF CONJUGATE PRIORS

minimizes:

provided

Example:

need