Week 3: Logistic Regression (feat. Regularization)

Andres Ng 교수님의 Machine Learning 3주차 키워드 및 간단 정리입니다.

Logistic Regression

Hypothesis, Cost Function, Gradient

• Hypothesis
  $h_\theta(x) = \frac{1}{1+e^{-\theta^{T}x}}$
• Cost Function: Crossentropy
  $J(\theta) = -\frac{1}{m}\Sigma ylog(h_\theta(x)) + (1-y)log(1-h_\theta(x))$
• Gradient
  $\theta_j := \theta_j - \alpha\frac{\delta}{\delta \theta_j}J(\theta)$
  $:= \theta_j - \alpha \frac{1}{m} \Sigma (h_\theta(x) - y)x_j$

Decision Boundary

Muti Class Classification

• One vs All Logistic Regression

Regularization

Prevent Overfitting

• Reduce Features
• Regularization

Regularization in Cost Function

• $J(\theta) = -\frac{1}{m}\Sigma ylog(h_\theta(x)) + (1-y)log(1-h_\theta(x)) + \frac{\lambda}{2m}\Sigma \theta ^2 $