# 机器学习代写 | Statistical Machine Learning Practice Exam

Section A: Short Answer Questions [25 marks]

Answer each of the questions in this section as brie y as possible. Expect to answer each question in 1-3
lines, with longer responses expected for the questions with higher marks.

Question 1: [25 marks]

(a) In words or a mathematical expression, what quantity is minimised by linear regression? [5 marks]

(b) In words or a mathematical expression, what is the marginal likelihood for a Bayesian probabilistic
model? [5 marks]

(c) In words, what does Pr(A;B | C) = Pr(A | C)Pr(B | C) say about the dependence of A,B,C?
[5 marks]

(d) What are the free parameters of a Gaussian mixture model? What algorithm is used to fit them for
maximum likelihood estimation? [10 marks]

Section B: Method & Calculation Questions [45 marks]

In this section you are asked to demonstrate your conceptual understanding of methods that we have
studied in this subject, and your ability to perform numeric and mathematical calculations. NOTE: in
the real exam, a small number of questions from this section will be a bit harder/longer than others.

Question 2: [10 marks]

(a) Consider a 2-dimensional dataset , where each point is represented by two features and the label
(x1; x2; y). The features are binary, the label is the result of XOR function, and so the data consists
of four points (0; 0; 0), (0; 1; 1), (1; 0; 1) and (1; 1; 0). Design a feature space transformation that
would make the data linearly separable. [5 marks]

(b) How does SVM handle data that is not linearly separable? List two possible strategies [5 marks]

Question 3: [10 marks]

Consider the data shown below with hard-margin linear SVM decision boundary shown between the
classes. The right half is classified as red squares and the left half is classified as blue circles. Answer the (a) Which points (by index 1{6) would be the support vectors of the SVM? [5 marks]

(b) What is the value of the hard margin SVM loss for point 3? [5 marks] E-mail: itcsdx@outlook.com  微信:itcsdx 