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The Chinese Universg of Hong Kong 0 n e e Course Examinations 200102 Course Code & Title CSC5150 ..... LEARNINGTHEORY8£COVIPUTATIONALFINANCE Time allowed : ___________ Two _____________________________ hourSWQ _____________________________________ minutes
Student ID NO 1 ___________________________________________________________________________ Seat No.
1. (a) Describe the learning principle of MSE (Mean Square Error) clustering. Discuss the to relationship between KMEAN algorithm and MSE clustering. (10%) (b) What is the basic difference between supervised learning and unsupervised learning?
Describe the learning principle of supervised learning in the sense of MSE. (10%) (c) Via the KMEAN algorithm to demonstrate the importance of model selection. (10%) (a) State the basic idea of the EM algorithm for mixture model. (10%)
(b) Discuss why MSE clustering can be regarded as a special case of Maximum Likelihood
learning on Gaussian mixture. (10%) Suppose onedimensional samples xl,.\72,...,x~ are from Normal distribution N (,LtJ), and
the a priori density of,u is N(m, 0'1) with known m,0'2.
(a) Estimate ,u via maximum likelihood learning and Bayesian learning, respectively. (15%) (b) Discuss the relationship between the two learning principles based on your obtained
results in (a). (10%) (a) What is their key difference between the Capital Market Line and CAPM model? (10%)
(b) Consider a portfolio consisting of Stock A and B only, with the following characteristics
shown in the Table. Illustrate, using three separate diagrams. the riskretum of the portfolio
for different proportions of Stock A and B, assuming the correlation coefficient of Stock A
and B are 0 and i 1 respectively. What conclusion can you draw ? (15%) 
Return Deviation — End of Paper—
"a a 5—2 ...
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 Spring '09
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