Homework answers / question archive / Question 1Consider the matrix X and the vectors y  and z below:X=[2413],y=[13],z=[23] What is the dot product  of the vectors y  and z (aka inner product, sometimes written y?z)?      9      [29]    [2369]    11   yes

Question 1Consider the matrix X and the vectors y  and z below:X=[2413],y=[13],z=[23] What is the dot product  of the vectors y  and z (aka inner product, sometimes written y?z)?      9      [29]    [2369]    11   yes

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Question 1Consider the matrix X and the vectors y  and z below:X=[2413],y=[13],z=[23] What is the dot product  of the vectors y  and z (aka inner product, sometimes written y?z)?

 

  

9

 

  

[29]

  

[2369]

  

11

 

yes.

 

Question 2

1 / 1 pts

What is the product Xy?

  

Xy=[23]
 

  

Xy=[2439]

  

Xy=[1410]

  

Xy=[21129]

 

Question 3

2 / 2 pts

 

 

 

 

In the figure above

 

Region a of R2 is defined by vectors xsuch that ||x||2≤1 (Recall ||x||2=∑ixi2.

Region c   of R2 is defined by vectors xsuch that||x||1≤1 (Recall ||x||1=∑i|xi|) .

Answer 1:

a

 

Answer 2:

c

 

 

Question 4

1 / 1 pts

Consider the line defined by w?x+b=0. 

Consider two points x1and x2 that lie on the line: w?(x1−x2)= 0

This tells us that w is orthogonal to the line.

Answer 1:

0

 

Answer 2:

orthogonal

 

 

Question 5

1 / 1 pts

If y=x3−x+2, what is the derivative of y with respect to x ?

  

dydx=x2−x+2

  

dydx=−x+2

  

dydx=2

  

dydx=3x2−1

  

none of the above

 

 

Question 6

1 / 1 pts

if y=x×tanh?(z)×e−x, what is the partial derivative of y with respect to x?

  

∂y∂x=tanh(z)×e−x−x2×tanh(z)×e−x

  

∂y∂x=(1−x)×tanh(z)×e−x

  

∂y∂x=tanh(z)×e−x

 

Question 7

1 / 1 pts

Consider the following joint probability table over variables y and z, where y takes a value from the set y∈{a,b,c} and z∈{0,1}

 

	y = a	y = b	y =c
z = 1	0.2	0.1	0.2
z = 0	0.05	0.15	0.3

 

What is the value of p(z=1|y=b) ?

 

Question 8

1 / 1 pts

Consider a sample of data S={1,1,0,1,0}created by flipping a coin x five times. 0 denotes that the coin turned up heads, and 1 denotes that it turned up tails.

 

What is the sample mean for this data?

  

35

  

25

  

12

  

32

 

Question 9

1 / 1 pts

What is the probability of observing the data sample S, assuming that it was generated by flipping a coin with an equal probability of heads and tails (i.e. p(x=1)=0.5and p(x=0)=0.5)

  

132

  

35

  

25

  

18

 

Question 10

1 / 1 pts

P(A∪B)=P(A∩(B∩Ac)), where Ac is the complement of the event A

  

True

 

  

False

 

 

Question 11

1 / 1 pts

P(A∪B)=P(A)+P(B)−P(A∩B) 

  

True

 

  

False

 

 

Question 12

1 / 1 pts

P(A|B)=P(B|A)

  

True

 

  

False

 

 

Question 13

1 / 1 pts

P(A1∩A2∩A3)=P(A3|(A2∩A1))P(A2|A1)P(A1)

  

True

 

  

False

 

Question 1

1 / 1 pts

Consider the following set of training examples:

Instance	Class	Feature 1	Feature 2
1	1	1	1
2	1	1	1
3	0	1	0
4	1	0	0
5	0	0	1
6	0	0	1

 

What is the best classification accuracy that can be obtained on this dataset with a decision tree of depth 1 (these are sometimes called decision stumps'')?

  

36

Correct!

  

46

  

56

  

1

 

 

Question 2

1 / 1 pts

Is it possible for a decision tree to classify all examples correctly? If yes, what is the minimum tree depth needed to achieve it? If no, why?

  

Yes, minimum tree depth is 1

 

Correct!

  

Yes, minimum tree depth is 2

 

  

Yes, minimum tree depth is 3

 

  

No, the model is overfitting

 

  

No, at least one example can never be correctly classified

 

 

Question 3

1 / 1 pts

Imagine that the dataset got corrupted, so that the class of instance 2 is now 0 (instead of 1). Its features are unchanged. What is the best classification accuracy that can be obtained on the corrupted dataset with a decision tree of depth 1?

  

36

Correct!

  

46

  

56

  

1

 

 

Question 4

1 / 1 pts

Given the new corrupted dataset, is it possible for a decision tree to classify all examples correctly? If yes, what is the minimum tree depth needed to achieve it? If no, why?

  

Yes, minimum tree depth is 1

 

  

Yes, minimum tree depth is 2

 

  

Yes, minimum tree depth is 3

 

  

No, the model is overfitting

 

Correct!

  

No, at least one example can never be correctly classified

 

 

Question 5

1 / 1 pts

If you train a learning algorithm and get 10% training error and 40% test error, the model is probably:

  

underfitting the training data

 

Correct!

  

overfitting the training data

 

 

Question 6

1 / 1 pts

If you train a learning algorithm and get 40% training error and 10% test error, the model is probably:

Correct!

  

underfitting tha training data

 

  

overfitting the training data

 

 

Question 7

1 / 1 pts

When applying a learning algorithm, some things are properties of the problem you are trying to solve, and some things are up to you to choose as the ML programmer. Which of the following are properties of the problem?

Correct!

  

The data generating distribution

 

  

The train/dev/test split

 

  

The learning model