4_21_09_BayesianInference

4_21_09_BayesianInference - Computations performed by...

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Computations performed by neural networks can be expressed as energy minimization.
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A link exists between energy minimization and Bayesian processes (and therefore, between these things and neural networks). P V ( ) = e −β E V ( ) e −β E V ( ) V If a system can be in a finite number of states, the transition between them tends to minimize energy (E( V )) except for noise, and the transition probabilities depend only on the current state, then in steady state The Gibbs distribution
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Neural Response ( r ) Sensory Input (s) a b c Bayes Theorem P s | r ( ) = P ( r | s ) P s ( ) P r ( ) b a + b = b b + c b + c a + b + c a + b a + b + c P r ( ) = a + b a + b + c P s ( ) = b + c a + b + c P r | s ( ) = b b + c b a + b P s | r ( ) =
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Response ( r ) Sensory Input (s) a b c Bayes Theorem Hence, one can often replace a network computation by a Bayesian one, thus understand- ing the computation and the noise. P s
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This note was uploaded on 06/08/2009 for the course BME 575L taught by Professor Grzywacz during the Spring '09 term at USC.

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4_21_09_BayesianInference - Computations performed by...

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