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CSC5150 4 - Page 1 of 1 7 it 4 I k g3 iii-limit NHHFP W The...

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Unformatted text preview: Page 1 of 1 7;; it 4, I k g3: iii-limit NHHFP . . . W The Chinese Universg of Hong Kong 0 n e e Course Examinations 2001-02 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 K-MEAN 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 K-MEAN 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 one-dimensional 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 risk-retum 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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