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Transcript of University of Southern California Department Computer Science Bayesian Logistic Regression Model...
University of Southern California Department Computer Science
Bayesian Logistic Regression Model (Final Report)Graduate Student Teawon HanProfessor Schweighofer, Nicolas
9/23/2011
• Introduction
Bayesian Logistic Regression Model (Final Report)
1. The purpose of the project - Experiment ?
2. Summary of Bayesian Logistic Regression (BLR) - How do I apply BLR to the BART or ART
3. What is next?
• The purpose of the project
Bayesian Logistic Regression Model (Final Report)
1. Predict accurate status of rehabilitation - Reduce rehabilitation time ( No un-necessary
training )- Rise efficiency in rehabilitation process
2. Data Collection method - use 3 days data in my program (regression)
for test
• The purpose of the project
Bayesian Logistic Regression Model (Final Report)
3. Experiment Environment
`
Success!
• The purpose of the project
Bayesian Logistic Regression Model (Final Report)
4. Given Data type (collected data 150)Error ==0 && Hit Hand ==1
Data (1 day)
Data (2 day)
Pattern analysi
s
Prior Weight value
New Weight value
Pattern analysi
s
NewNew
Weight value
Successcondition
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
1. What is regression? Why do we use regression?2. Example ( Linear Regression )
Regression can help
to represent complete model
by partially
observed data.
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
3. How do I apply BLR to the project - First, we have two classes for classification. ( Success and Fail ) - Expression a. p(C1 | Ф ) = y (Ф) = Ϭ (WT Ф) success
b. p(C2 | Ф ) = 1 - p(C1 | Ф ) fail
where Ф is feature vector ( data ) and w is weight vector.
Error ==0 && Hit Hand ==1
Successcondition
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
3. How do I apply BLR to the project (continue) - Second, to represent Logistic Regression, I
used Ϭ(·). where Ϭ(α) = 1 / 1 + exp (-α) a. range is limited (0 ~ 1) b. TO MAKE EASY, I used simplest formula (next page)
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
3. How do I apply BLR to the project (continue) b. TO MAKE EASY, I used simplest formula
which includes the least number of parameters
(features) Formula : W0 + W1Ф1 +W2Ф2
this should be updated more accurately by
Nuero-Scientific knowledge.
4. The goal in here is ‘Finding accurate W vector’ to predict posterior result. (next page)
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
4. The goal in here is ‘Finding accurate W vector’ to predict posterior result.
- Process of calculation W vector (W can be represented by Gaussian) a. Wmap (mean) SN (covariance)
: Wmap can be calculated by Newton-Raphson rule.
b. Newton-Raphson rule
: Iterative Optimization Scheme to make minimize
the error of weight vector. [link]
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
4. The goal in here is ‘Finding accurate W vector’ to predict posterior result.
- Process of calculation posterior W vector c. Equation of Newton’s method (Wmap )
( Pattern Recognition and machine learning book
p208 )
d. Covariance of W
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
4. The goal in here is ‘Finding accurate W vector’ to predict posterior result.
- Process of calculation W vector e. Finally, we can get distribution of posterior
W
5. To get the posterior probability given data with posterior W
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
5. To get the posterior probability given data with posterior W (derivation)
- you can find “Pattern recognize and machine learning
book” - I also attached from Srihari’s lecture note.
• Summary of Bayesian Logistic Regression (BLR)
Bayesian Logistic Regression Model (Final Report)
6. How do I apply BLR to the project
a. Initial weight vector = [0.001,0.001,0.001] b. Initial covariance vector = [1,0,0 ; 0,1,0; 0,0,1]
Data (1 day)
Data (2 day)
Pattern analysi
s
Prior Weight value
New Weight value
Pattern analysi
s
NewNew
Weight value
new
NewNew