Week 2

Andrew Ng 교수님의 Machine Learning 강좌 주요 키워드 및 내용입니다.

Linear Regression with Multiple Variables

Hypothesis, Cost Function, and Gradient

• Hypothesis $h_\theta(x) = \theta^{T}x = \theta_0 + \theta_1x_1 + \theta_2x_2 + ... + \theta_nx_n$
• Cost Function $J(\theta) = \frac{1}{2m} \Sigma_{i=1}^{m}(h_\theta(x)-y)^{2}$
• Gradient $\theta_j := \theta_j - \alpha \frac{\delta}{\delta \theta_j}J(\theta) = \theta_j - \alpha \Sigma_{i=1}^{m}(h_\theta(x)-y)x_j$

Feature Scaling/Mean Normalization

Learning Rate

• Low → Slow Learning
• High → Divergence

Linear Regression with Polynomial Variables

Normal Equation

• Optimizer Parameter $\theta = (X^{T}X)^{-1}X^{T}Y$
• Invertible Matrix $(X^{T}X)^{-1}X^{T}Y$ Problem → Remove Linear Dependency, Reduce Number of Features

Gradient Descent vs Normal Equation

• Gradient Descent → Large Number of Features
• Normal Equation → Small Number of Features (Computationally Expensive to Calculate $(X^{T}X)^{-1}X^TY$)

Octave/MATLAB Tutorial

Vectorization Computation