1. Optimal classification란?

$f^* = argmin_fP(f(X)\neq Y)$

classifier는 곡선형태인 확률분포를 통해 risk를 줄임 -logistic

curve를 만들어보는게 나이브 클래서파이어

2개의 class만 있을 경우

$f^* = argmax_{Y=y}P(Y= y

X=x) = argmax_{Y=y}P(X=x

Y= y)P(Y=y) = argmax_{Y=y}Class Conditional Density* Class Prior$

2. Conditional Independence

$x_1,.. x_i$ are conditionally indepenced given $y$

p(X=<x_1,…,.x_i

Y=y) -> P(X_i= x_i

Y=y)

Marginal independence vs. Conditional Independence (A,B)

Marginal Indepdence

X and Y and independent if and only if P(A)=P(A

B)

Conditional Independence

P(A

B,Y) = P(A

Y)