# 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.

### 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

### 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`

### 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

hθ(x) θ0 + θ1x

- hθ(x) 360
`θ0 = 360 θ1 = 0`

- minimize the cost function