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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.
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 x2≤1 (Recall x2=∑ixi2.
Region c of R2 is defined by vectors xsuch thatx1≤1 (Recall x1=∑ixi) .
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=1y=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(AB)=P(BA)
True
False
Question 13
1 / 1 pts
P(A1∩A2∩A3)=P(A3(A2∩A1))P(A2A1)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