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To Cost Function Intuition 1

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jneira committed Oct 11, 2011
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+* Model Representation
+ - Supervised Learning:
+ - Given the "right answer" for each example in the data.
+ - Regression Problem:
+ - Predict real-values output
+ - Data set is called "Training set"
+ - Notation:
+ - m = Number of training examples
+ - x's = "input" variable/features
+ - y's = "output" variable/"target" variable
+ - (x,y) = one training example
+ - (x[i],y[i]) = i^th training example
+ - Model:
+ x
+ |
+ Training Set --> Learning Algorithm --> /h/ (hypothesis)
+ |
+ y
+ h: function x->y
+
+ - How do we represent h? *as a linear function*
+ - h[Θ](x) = Θ[0]+Θ[1]x Shorthand: h(x)
+ - To start with a simple building block
+ - Model name:
+ - Linear regression with one variable.
+ - aka Univariate linear regression.
+
+* Cost function
+ - How to choose Θ[i]'s parameters in hypothesis
+ - Idea: choose Θ[0],Θ[1] so that hΘ(x) is close to /y/ for our
+ training examples (x,y)
+ - Formalization:
+ - minimize J(Θ[1],Θ[2])=1/2m Σ(i=1..m)(h[Θ](x^(i))- y^(i))^2
+ - h[Θ](x^(i))=Θ[0]+Θ[1]x^(i)
+ - choose values for Θ[0],Θ[1] that minimez the function
+ - m -> #training examples
+ - squared error cost function
+
+* Cost function - Intuition I

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