[机器学习]监督学习应用.梯度下降

Notation:

1.m : # training examples

2.x : input variables \ features

3.y : output variables \”target”variables

4.(x,y) : training example

5.ith training example : (x(i),y(i))

Flow Path

training set→learning algorithm→h(hypothesis)

Hyposthesis Function

New Living Area → Hypothesis → Estimate Price

Linar function(regression problems)

h(θ)=hθ(X)=θ0+θ1X1+θ2X2（X1 = size X2 = #bedrooms X0=1）

⟹hθ(X)=∑Nk=0θkXk(θi is called parameters)

⟹θTx(n = #featrues)

minθ=12∑mi=1(hθ(x(i))−y(i))2⟹J(θ)

梯度下降公式推导

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