1_classification

1_classification

1. linear regression

2. loss function

3. Bayesian classification rule

4. Discriminant analysis

5. Fisher linear discriminant analysis (LDA)

6. logistic regression

7. probit regression

8. terms

   • prediction rule-classifier
   • The Bayes Rule argmax
     • beta hat transpose times x0
   • X data matrix
     • N*(p+1)
   • Y indicator response matrix
     • N*K
   • B hat
     • (p+1)*k
   • decision boundary
     • k=2
       • x transpose times beta hat

9. naive Bayes classifiers target: G hat

   • numerical variable
     • box distribution
     • Gaussian distribution
   • category variable
   • the basic baayes rule
     • posteriori probability

10. distriminant analysis

    • Quadratic discriminant analysis
      • segama k (x)=log (pai k, fk (x))
        • prior probabillity
        • group covariance
    • Linear discriminant analysis
      • decision boundry
        • k-l
      • the probability of misclassification
    • estimation
    • prediction
    • Fsher's linear discriminant analysis
      • canonical analysis: a set of predictor vs a set of variable-mutiple correlation
      • between-class variance sb
      • within-class covariance sw
      • Fisher criterion J(w)

11. logisitc regression p(G=k/X)

    • Logistic Sigmoid function fk(x/seta)