Linear Regression with One Variable (Week 1)

Week 1.mdp

Linear Regression with One Variable (Week 1)

Two types:

• Supervised Learning

• Unsupervised Learning

Linear Regression with One Variable

• Hypothesis

  hθ(x)=θ0+θ1x

• Parameters

  θ0,θ1

• Cost Function

  J(θ0,θ1)=12m∑i=1m(hθx(i)−y(i))2

• Goal

  minimizeθ0,θ1J(θ0,θ1)

Gradient Descent

• Problem Description

  Have some function J(θ0,θ1) , want minθ0,θ1J(θ0,θ1)

• Algorithm

  θj:=θj−α∂∂θjJ(θ0,θ1) (for j=0 and j=1)

• α : learning rate

• Repeat until convergence

• Simultaneously update

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