Lecture 2

Question 1

What is x?

Answer 1

feature or independent variable

Question 2

What is y?

Answer 2

target or dependent variable

Question 3

What do we use x for?

Answer 3

to predict y

Question 4

How is the ith observation denoted?

Answer 4

(x_i, y_i)

Question 5

What is H?

Answer 5

the hypothesis function

Question 6

What does the hypothesis function do?

Answer 6

takes in an x as input and returns a predicted y

Question 7

What are parameters?

Answer 7

define the relationship between the input and output of a hypothesis function

Question 8

What is the constant model?

Answer 8

H(x) = h

Question 9

How many parameters does the constant model have?

Answer 9

one: h

Question 10

How do we calculate the mean?

Answer 10

adding all the numbers in our set up and divide by n numbers

Question 11

How do we calculate the median?

Answer 11

sort our numbers in ascending order and take the middle number

Question 12

What are both the mean and the median?

Answer 12

they are summary statistics

Question 13

What are summary statistics?

Answer 13

they summarize a collection of numbers with a single number

Question 14

What is a loss function?

Answer 14

quantifies how bad a prediction is for a single data point

Question 15

What can we say about our loss if our prediction is close to the actual value?

Answer 15

that we should have low loss

Question 16

What can we say about our loss if our prediction is far from the actual value?

Answer 16

that we should have high loss

Question 17

What is error?

Answer 17

the difference between actual and predicted values

Question 18

What does y_i - H(x_i) mean?

Answer 18

actual - predicted

Question 19

What does y_i stand for?

Answer 19

actual

Question 20

What does H(x_i) stand for?

Answer 20

predicted

Question 21

What is the squares loss function?

Answer 21

L_sq(y_i, H(x_i)) = (y_i - H(x_i))^2

Question 22

How can we simplify the squared loss function for the constant model?

Answer 22

L_sq(y_i, h) = (y_i - h)^2

Question 23

What is the average of squared losses?

Answer 23

a single number that describes the quality of our predictions across our entire dataset

Question 24

What is another term for the average squared loss?

Answer 24

mean square error (MSE)

Question 25

What does L stand for?

Answer 25

loss for a single point

Question 26

What does R stand for?

Answer 26

average loss over all points; empirical risk

Question 27

What is the notation for mean squared error?

Answer 27

R_sq(h)

Question 28

What is the summation notation for mean squared error?

Answer 28

R_sq(h) = 1/n En i=1 (y_i - h)^2

Question 29

What is the first step of minimizing our loss?

Answer 29

take its derivative with respect to h

Question 29

What does h* stand for?

Answer 29

the best prediction

Question 30

What is the second step of minimizing our loss?

Answer 30

set it equal to 0

Question 31

What is the third step of minimizing our loss?

Answer 31

solve for the resulting h*

Question 32

What is the final step of minimizing our loss?

Answer 32

perform a second derivative test to ensure we found a minimum

Question 33

What is the derivative of x^n?

Answer 33

d/dx x^n = nxn^n-1

Question 34

What is the derivative of f(g(x))?

Answer 34

d/dx (f(g(x))) = f'(g(x)) * g'(x)

Question 35

What is the derivative of (y_i - h)^2?

Answer 35

2(h - y_i)

Question 36

What is the total derivative of R_sq(h)?

Answer 36

-2/n En i=1 (y_i - h)

Question 38

What is h* of R_sq(h)?

Answer 38

1/n En i=1 y_i; the mean

Question 39

What shape is R_sq(h)?

Answer 39

convex

Question 40

If R_sq(h) opens upwards, what is h*?

Answer 40

it is a minimum

Question 41

What is the best constant prediction in terms of the mean squared error?

Answer 41

the mean

Question 42

What is h* the solution to?

Answer 42

an optimization problem

Question 43

What is the first step of the modeling recipe?

Answer 43

choose a model

Question 44

What is the second step of the modeling recipe?

Answer 44

choose a loss function

Question 45

What is the third step of the modeling recipe?

Answer 45

minimize average loss to find optimal model parameters