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2019F-178-Mid

Bayes classifiers are probabilistic models based on Bayes' Theorem. They predict class membership by calculating the probability of a sample belonging to a class, assuming feature independence (as in Naive Bayes).

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    CS 178 Midterm Exam Machine Learning and Data Mining: Fall 2019 Monday November 4th, 2019 Your name: Row/Seat Number: Your ID #(e.g., 123456789) UCINetID (e.g.ucinetid@uci.edu) « Please put your name and ID on every page. « Total time is 50 minutes. READ THE EXAM FIRST and organize your time; don't spend too long on any one problem. « Please write clearly and show all your work. o If you need clarification on a problem, please raise your hand and wait for the instructor or TA to come over. You may use one sheet containing handwritten notes for reference, and a (basic) calculator. Tum in your notes and any scratch paper with your exam. Problems 1 Bayes Classifiers, (10 points.) 3 2 Nearest Neighbor Regression, (12 points.) 5 3 Truo/False, (10 points.) 7 4 Support Vector Machines, (10 points.) 9 5 VC Dimensionality, (10 points.) 1 Total, (52 points.)

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    Bayes Classifiers, (10 points.) I 1 2 Consider the table of measured data given at right. We will use the c blo two observed features , , 7, to predict the class y. Each feature b bo can take on one of three values, x; € {a,b,c}. b c|0 Tn the case of a tie, we will prefer to predict class y = 0. a cll (1) Write down the probabilities learned by a naive Bayes classificr:(§ points.) N N h —0- 1 a a 1 ply =0): ply=1): gl c all por =aly=0): on =aly=1): : per =bly=0): pn =bly=1): po =cly=0): pn =cly=1): prz=aly=0): pm=aly=1): Pra =bly=0): zy =bly =1): Pay =cly=0): ory =cly =1): (2) Using your naive Bayes model, what value of y would you predict given (x1 = a, x2 = b)?:(3 points.) (3) Using your naive Bayes model, compute the probabilities: (3 points.) ply=01 =bz2=c): py=11=br=c):

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