機器學習 - model and cost function

Model Representation : article

Housing Prices

• Supervised Learning:
  • Regression Problems
  • Classification Problems

Training set of housing prices

Size in feet^2 (x)	Price ($) in 1000’s (y)
2104	460
1416	232
1534	315
…	…

Notation:
m = Number of training examples
x's = "input" variable / features
y's = "output" variable / "target" variable

Process of Hypothesis Function:

When the target variable that we’re trying to predict is continuous, such as in our housing example, we call the learning problem a regression problem. When y can take on only a small number of discrete values (such as if, given the living area, we wanted to predict if a dwelling is a house or an apartment, say), we call it a classification problem.

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Cost Function : article

Cost function : will let us figure out how to fit the best possible straight line to our data

Linear Regression :

Hypothesis : hθ(x) = θ0 + θ1x
θi's : Parameters
Linear Regression Model:
J( θ0, θ1 ) =  1/2m * ∑ ( hθ * ( x^(i) ) - y^(i) )^2

Sometimes cost function is also called the squared error function

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Cost Function - Intuition i : article

• Goal : try to minimize the cost function J(θ0, θ1)

  

  Simplified: θ0 = 0
  J(θ0, θ1) ---> J(θ1)
  

  when θ1 = 1
  J(θ1) = 0
  

  

  when θ1 = 0.5
  

  

when θ1 = 0

• We can find out in this case θ1 = 1 is our goal

  when θ1 = 1
  J(θ1) = 0
  

  

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Cost Fuction - Intuition ii : article

• When we have 2 parameters the plot will be a 3D plot

  EX:
  θ0 = 50
  θ1 = 0.06
  hθ = 50 + 0.06x
  

• J(θ0, θ1): 2 parameters

• Contour graphs

  • hθ(x) θ0 + θ1x

  • hθ(x) 360

    θ0 = 360
    θ1 = 0
    

    

  • minimize the cost function