4_9_09_InformationTheory

4_9_09_InformationTheory - Outline of the Lecture...

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Outline of the Lecture Outline of the Lecture Information Theory Information Theory Entropy                   Noise Entropy                   Mutual Information Entropy                   Noise Entropy                   Mutual Information  
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Mutual Information  Mutual Information  Measures How Much  Measures How Much  Responses Tell about  Responses Tell about  Stimuli Stimuli    
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In a black-box model, we try to describe a system well enough to predict its responses without knowing what is inside the system.
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If the firing is different when one presents the same stimulus twice, then how does the brain know what is in the stimulus?
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We can also ask how much a system can tell about the ensemble of stimuli in the world; the answer comes from information theory.
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Let’s represent the probability of each input, P(s), and each output, P(r), by color brightness. Input Variable (s) Output Variable (r)
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Let’s represent the probability of an output given an input, P(r|s), by an arrow thickness. Input Variable (s) Output Variable (r)
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Each input variable has its own probabilities to lead to different outputs. Input Variable (s) Output Variable (r)
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If the output distribution is sharp, then the output is not informative about the input.
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