4_23_09_KalmanFiltering

4_23_09_KalmanFilter - Outline of the Lecture Kalman Filtering Kalman Filtering Changing Environments Contrast Adaptation Kalman Filtering Models

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Outline of the Lecture Outline of the Lecture Kalman Filtering Kalman Filtering Changing Environments    Kalman Filtering     Contrast  Changing Environments    Kalman Filtering     Contrast  Adaptation Adaptation    
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Kalman Filtering Models  Kalman Filtering Models  Optimal Neural Adaptation  Optimal Neural Adaptation  over Time over Time    
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Optimal Probabilistic Adaptation
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When flying from the outside of a canyon into. ..
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… the corridors of the canyon…
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… the statistics of the environment change.
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Optimal Probabilistic Adaptation
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Kalman- filtering Adaptation
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The goal is to update the estimate of the environment Λ k at time k to have the prior probability distribution P( I | Λ k ) of inputs I . For this, we use responses measured in the past Ř k = { R k , R k-1 , … , R 0 }. Responses are with adaptation states Ă k = { A k , A k-1 , … , A 0 }, where P( R | I , A k ) is the likelihood function.
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Present Environment History of Response P Λ κ ( Ρ , ( Α ( 29 = We want to estimate History of Adaptation
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Neural Response ( r ) Sensory Input (s) a b c Bayes Theorem P s | r ( 29 = Π(ρ|σ 29 Π σ ( 29 Πρ ( 29 b a + β = β+χ α+β+χ α+β P r ( 29 = a + P s ( 29 = b + χ P r | s ( 29 = b b + b a + P s | r ( 29 =
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Neural Response 1 (R1) Sensory Input (I) a b c Generalization of Bayes Theorem P I | R 1 , R 2 ( 29 = Π(Ρ 1 | Ι,Ρ 2 29 Π Ι | Ρ 2 ( 29 ΠΡ 1 | Ρ 2 ( 29 Neural Response 2 (R2) d A B C
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Present Environment History of Response P Λ κ ( Ρ , ( Α ( 29 = We want to estimate History of Adaptation KP R k , A k Λ , ( κ-1 , ( -1 ( 29 ΠΛ ( , ( -1 ( 29 Measurement Term Prediction Term
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Kalman Adaptation Early Measurements
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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_23_09_KalmanFilter - Outline of the Lecture Kalman Filtering Kalman Filtering Changing Environments Contrast Adaptation Kalman Filtering Models

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