4_23_09_KalmanFiltering

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

This preview shows pages 1–16. Sign up to view the full content.

Outline of the Lecture Outline of the Lecture Kalman Filtering Kalman Filtering Changing Environments    Kalman Filtering     Contrast  Changing Environments    Kalman Filtering     Contrast  Adaptation Adaptation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Kalman Filtering Models  Kalman Filtering Models  Optimal Neural Adaptation  Optimal Neural Adaptation  over Time over Time

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
When flying from the outside of a canyon into. ..
… the corridors of the canyon…

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
… the statistics of the environment change.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
Present Environment History of Response P Λ κ ( Ρ , ( Α ( 29 = We want to estimate History of Adaptation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 =
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/08/2009 for the course BME 575L taught by Professor Grzywacz during the Spring '09 term at USC.

### Page1 / 44

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

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online