5  Chapter 4: Parametric Classification

5.1 Outline

• Gaussian discriminant
  • Linear Discriminant analysis
  • Quadratic discriminant analysis
• Logistic classification
• Regularized discriminant analysis
• Bayesian parametric classification

5.2 Parametric Plug-in Rules

• Feature-label distribution is coded into pdf
  • \(\{p(x|\theta)|\theta\in \Theta \subseteq R^m\}\)
  • \(\theta_{0,n}\) and \(\theta_{1,n}\) be estimators of \(\theta^{*}_{0}\) and \(\theta^{*}_{1}\) based on sample data \(S_n = \{(X_1, Y_1),\dots, (X_n,Y_n)\}\).
• Sample space discriminant
  • \(D_n(x) = \ln\frac{p(x|\theta_{1,n})}{p(x|\theta_{0,n})}\)

5.2.1 Strategy for the knowledge about the prior

Let \(c_0=P(Y=0)\) and \(c_1 = P(Y=1)\),

|Knowledge about prior||