FIT5149 Sample Exam
Question Marks Score
Multiple Choice Questions 23
Regression & Classification 18
Tree-based Method 8
Model selection, Regularisation and Dimensionality 10
Hierarchical Clustering and Splines 6
Total: 65
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FIT5149 Sample Exam
1. Multiple Choice Questions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Total: 23 marks
For each multiple choice question, you should always check all that apply, which means the number of correct
choices can be one or greater than one. Marks will be given to an answer without any wrong choices. For
example, if the true answer is A and B, an answer including C or D will receive zero mark. Please write your
answers in the given place.
(1)(2 marks) Which of the following statement(s) is/are appropriate regarding bias and variance
A. Models which overfit generally have a high bias
B. Models which under-fit generally have a low variance
C. Models with low bias were often found better fitted with the training data
D. Models with high variance were often found better fitted with both training and testing
data.
(1) B, C
(2)(2 marks) The following histogram are generated from data drawn from a Beta distribution:
x ～ beta(0.5, 0.5)
Histgram of Beta distribution
x
Fr
eq
ue
nc
y
0.0 0.2 0.4 0.6 0.8 1.0
0
50
10
0
15
0
20
0
Which qqPlot below corresponds to the distribution given by the histgram
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FIT5149 Sample Exam
3 2 1 0 1 2 3
0.
0
0.
1
0.
2
0.
3
0.
4
0.
5
A
Theoretical Quantiles
Sa
m
pl
e
Qu
an
tile
s
3 2 1 0 1 2 3
70
0
90
0
11
00
13
00
B
Theoretical Quantiles
Sa
m
pl
e
Qu
an
tile
s
3 2 1 0 1 2 3
0.
5
0.
6
0.
7
0.
8
0.
9
1.
0
C
Theoretical Quantiles
Sa
m
pl
e
Qu
an
tile
s
3 2 1 0 1 2 3
0.
0
0.
2
0.
4
0.
6
0.
8
1.
0
D
Theoretical Quantiles
Sa
m
pl
e
Qu
an
tile
s
(2) D
(3)(2 marks) Suppose you have m = 30 training examples with n = 5 features (excluding the additional all-ones
feature for the interception term, however which you should add). The normal equation is
β = X
Ty
XTX
For the given values of m and n, what are the dimensions of β, X, and y in this equation
A. β is 6× 6, X is 30× 6, y is 30× 6
B. β is 6× 1, X is 30× 6, y is 30× 1
C. β is 5× 5, X is 30× 5, y is 30× 5
D. β is 5× 1, X is 30× 5, y is 30× 1
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FIT5149 Sample Exam
(3) B
(4)(2 marks) Given (x1, y1), (x2, y2), . . . , (xn, yn), which of the following is total sum of squares (TSS)
A.
n∑
i=1
(yi f(xi))2
B.
n∑
i=1
(yi yˉ)2,where yˉ =
n∑
i=1
yi/n
C. √√√√ 1
n p 1
n∑
i=1
(yi f(xi))2
D.
n∑
i=1
(f(xi) yˉ)2,where yˉ =
n∑
i=1
yi/n
(4) B
(5)(2 marks) Which of the following statements are true Check all that apply.
A. Linear regression always works well for classificati
on if you classify by using a threshold
on the prediction make by linear regression.
B. The cost function L(β) for logistic regression trained with more than one observations is
always greater than or equal to zero.
C. If the order of the labels must be retained in an analysis, you can use multinomail logitic
regression.
D. The sigmoid function g(z) = 11+e z is never greater than one.
(5) B,D
(6)(2 marks) Please select any of the following methods are designed for the multi-class classification task (e.g.,
predicting a outcome of 5 categories).
A. LDA
B. QDA
C. Logistic regression
D. Multinomial logistic regression
(6) A, B, D
(7)(2 marks) Suppose you ran logistic regression twice with L2 regularisation, once with with the tuning (or
regularisation) parameter λ = 0, and once with λ = 1. One of the times, you got parameter
βt = (81.47, 12.69), and the other time you got βt = (13.01, 0.91). However, you forgot which value
of λ corresponds to which value of β. Which one do you think corresponds to λ = 0
A. βt = (81.47, 12.69)
B. βt = (13.01, 0.91)
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FIT5149 Sample Exam
(7) A
When λ is set to 1, we use L2 regularisation to penalise the large value of β. Thus, the parameters
β obtained will in general have smaller values
(8)(2 marks) Suppose we estimate the regression coefficients in a linear regression model by minimizing
n∑
i=1
(
yi βTxi
)
+ λ ‖ β ‖22
for a particular value of λ. As we increase λ from 0, which of the following will steadily increase
Check all that apply.
A. The training RSS
B. The test RSS
C. Variance
D. (Squared) bias
E. The irreducible error
(8) A, D
(9)(2 marks) Assume you have a training dataset consisting of N observations and D features. You used the
closed-form solution to fit a multiple linear regression model using ridge regression. To choose
the tuning parameter λ, you use LOOCV searching over L values of λ. Let Cost(N,D) be the
computation cost of running ride regression with N data points and D features. Which of the
following represents the computational cost of your LOOCV procedure
A. L×D × Cost(N 1, D)
B. L×D × Cost(N,D)
C. L×N × Cost(N,D)
D. L×N × Cost(N 1, D)
E. N × Cost(N,D)
F. L× Cost(N,D)
(9) D
(10)(2 marks) Which of the following methods grows the tree sequentially
A. Random forests
B. Bagging (Bootstrap aggregation )
C. Boosting
D. None
(10) C
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FIT5149 Sample Exam
(11)(2 marks) Which of the following is true: For a fixed model complexity, in the limit of an infinite amount of
training data,
A. The noise goes to 0.
B. Bias goes to 0.
C. Variance goes to 0.
D. Training error goes to 0.
(11) C
(12)(1 mark) Select any of the following residual plot(s) that satisfy assumptions of linear regression
0 200 400