ML Week 5

ML Week 5

Linear Regression with Multiple Variables

Poll

Attendance

• Present

• Absent

Overview of training an ML model

1. Initialisation

Initialise the parameters (thetas), so that you have a hypothesis

2. Calculate cost

Calculate (plot) the cost function of the hypothesis

a. gives an indication of how good or how bad the hypothesis is

b. helps gradient descent take the next step.

2. Calculate cost

Calculate (plot) the cost function of the hypothesis

a. gives an indication of how good or how bad the hypothesis is

b. helps gradient descent take the next step.

3. Gradient descent

Take one step of gradient descent towards lowering the cost, which will give you new updated parameters.

3. Gradient descent

Take one step of gradient descent towards lowering the cost, which will give you new updated parameters.

4. Update parameters

Update the hypothesis with the new parameters

4. Repeat steps 2 - 4

1. Calculate cost for the updated hypothesis

2. Take one step gradient descent

3. Update parameters to create a new hypothesis

Linear Regression with Multiple Variables

Multiple Choice

In the training set shown in the image, what is $x_1^{\left(4\right)}$ ? 

• The size (in sq. feet) of the 1st home in the training set

• The age (in years) of the 1st home in the training set

• The size (in sq. feet) of the 4th home in the training set

• The age (in years) of the 4th home in the training set

Multiple Choice

Suppose you are using a learning algorithm to estimate the price of houses in a city. You want one of your features $x_i$ to capture the age of the house. In your training set, all of your houses have an age between 30 and 50 years, with an average age of 38 years. Which of the following would you use as features, assuming you use feature scaling and mean normalization?

•  $x_i=age\ of\ house$  

•  $x_i=\frac{age\ of\ house}{50}$  

•  $x_i=\frac{age\ of\ house\ -38}{50}$  

•  $x_i=\frac{age\ of\ house\ -38}{20}$  

Multiple Choice

Suppose a friend ran gradient descent three times, with α=0.01, α=0.1, and α=1, and got the following three plots, labeled A, B, and C (in the image) :

• A is α=0.01, B is α=0.1, C is α=1.

• A is α=0.1, B is α=0.01, C is α=1.

• A is α=1, B is α=0.01, C is α=0.1.

• A is α=1, B is α=0.1, C is α=0.01.

Multiple Choice

Suppose you want to predict a house's price as a function of its size. Your model is $h_{\theta}\left(x\right)=\theta_0+\theta_1\left(size\right)+\theta_2\sqrt{\left(size\right)}$ 
Suppose size ranges from 1 to 1000 (sq. feet). You will implement this by fitting a model $h_{\theta}\left(x\right)=\theta_0+\theta_1x_1+\theta_2\ x_2$ 
Finally, suppose you want to use feature scaling (without mean normalization). Which of the following choices for $x_1$ and $x_2$ should you use? (Note:  $\sqrt{1000}\approx32$  )

•  $x_1=size,\ x_2=32\sqrt{\left(size\right)}$  
  

•  $x_1=32\left(size\right),\ x_2=\sqrt{\left(size\right)}$  
  

•  $x_1=\frac{size}{1000},\ x_2=\frac{\sqrt{\left(size\right)}}{32}$  
  

•  $x_1=\frac{size}{32},\ x_2=\sqrt{\left(size\right)}$