Week 2

Question 1

What is linear regression with multiple variables?

Answer 1

They are also known as “multivariate linear regression”

Question 2

Notation: n

Answer 2

Number of features.

Question 3

Notation: x_i

Answer 3

Input (features) of ith training example

Question 4

Notation: x_ji

Answer 4

Value of feature j in ith training example.

Question 5

What is the hypothesis function?

Answer 5

h_t(x)=t^Tx (Theta - transposed times x)

Question 6

Is theta a vector?

Answer 6

Yes.

Question 7

What are parameters?

Answer 7

Theta

Question 8

How do you update the thetas?

Answer 8

theta_j:=theta_j-alpha*dJ(theta)/dtheta_j

Question 9

What is feature scaling?

Answer 9

Feature scaling is normalizing features

Question 10

What does feature scaling do?

Answer 10

Feature scaling speeds up gradient descent. It puts inputs roughly in same range.

Question 11

What does theta do on smaller ranges?

Answer 11

Theta descends quickly on smaller ranges.

Question 12

What does theta do on larger ranges?

Answer 12

Theta descents slowly on larger ranges.

Question 13

Where do you put inputs variables into ranges ideally?

Answer 13

-1<=x_i<=1 or -0.5<=x_i<=0.5

Question 14

What is the definition of feature scaling?

Answer 14

Feature scaling involves dividing the input values by the range of the input variable, resulting in a new range of just one.

Question 15

What is the definition of mean normalization?

Answer 15

Mean normalization involves subtracting the average value of the input variable from the values for that input variable resulting in a new average for the input variable of just zero.

Question 16

How to implement both feature scaling and normalization?

Answer 16

x_i:=(x_i-u_i)/s_i

Where u_i is the average of all the values for the feature (i) and s_i is the range of values (max-min). Or s_i is the standard deviation.

Question 17

How do you make sure gradient descent is working correctly?

Answer 17

J(theta) should decrease after ever iteration.

Question 18

What is an example of automatic convergence test?

Answer 18

Declare convergence if J(theta) decreases by less than 10^-3 in one iteration.

Question 19

What are examples where gradient descent is not working?

Answer 19

When the cost goes up.
When cost goes down then up over time.
When cost fluctuates.
There is a bug in the code.

Question 20

What happens if you have a sufficiently small alpha?

Answer 20

Cost should decrease for every iteration.

Question 21

What happens if alpha is too small?

Answer 21

Gradient decent can be too slow to converge.

Question 22

What is an example to choose alpha?

Answer 22

By …,0.001, 0.01, 0.1, 1,…

Question 23

What is an example of choosing features efficiently?

Answer 23

Combining 2 input features into 1.

Question 24

What happens if you simplify the hypothesis

Answer 24

You MAY get a better model.

Question 25

What is polynomial regression?

Answer 25

Regression that uses a hypothesis function that uses a polynomial equation.

Question 26

What are the types of polynomial equation?

Answer 26

Quadratic, Cubic, square root, etc

Question 27

What happens if x values get too high?

Answer 27

You use feature scaling.

Question 28

How do you change the curve of the hypothesis function.

Answer 28

We can change the behavior or curve of the hypothesis function by making it quadratic, cubic or square root function or any other form,

Question 29

What is a normal equation?

Answer 29

A method to solve for theta analytically.

Question 30

How does the normal equation work?

Answer 30

If 1D (theta into R)
J(theta)=atheta^2+btheta+c
dJ(theta)/dtheta=…set=0
solve for theta

Question 31

What is an example of normal equation?

Answer 31

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Question 32

What is the normal equation method about?

Answer 32

Normal equation method is to minimize J by explicitly taking its derivatives with respect to the theta j’s, and setting them to zero. This allows us to find the optimum theta without iteration.

Question 33

What is the normal equation equation?

Answer 33

thetha=(X^TX)^-1x^T*y

Question 34

What does the normal equation do?

Answer 34

Find the optimal value of theta

Question 35

What are the advantages and disadvantages of gradient descent and normal equation?

Answer 35

With gradient descent, you need to choose the alpha and it needs many iterations to find the optimal value of theta but it still works well even when n is large. Compared to the normal equation which doesn’t need an alpha and no need to iterate. But you need to compute its equation and its slow when n is very large.

Question 36

What features is considered too large for normal equation?

Answer 36

when N is and exceeds 10,000. Unless the computer is really fast at computing.

Question 37

What happens if X^TX is non-invertible?

Answer 37

You can delete a feature that is linearly dependent with another or deleting one or more features when there are too many features.

Question 38

If X^TX noninvertible, the common causes might be having…

Answer 38

1. Redundant features (linearly dependant)

2. Too many features (eg. m<=n). In this case, delete some features or use regularization.