a3 - CSCD11 Machine Learning and Data Mining, Fall 2010...

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CSCD11 Machine Learning and Data Mining, Fall 2010 Assignment 3: Classification and Bayesian Methods Due Thursday, November 18, 3pm (before tutorial) Note: This assignment comprises two theoretical questions and one programming question. For the theoretical questions, either hand-written or computer formatted answers should be handed in on paper. Please make sure that hand-written solutions are legible. For the programming part of this assignment you will write several functions and one main script in Matlab. You will hand in a tar- file containing these files electronically. Parts of Question 3 which ask for written responses can be answered as comments in your Matlab scipt. 1. Bayesian Prediction [18 marks; 2 marks per part] Suppose you visit a province where license plates numbers are numbered sequentially. After seeing some cars go by on the road and reading their license plate numbers, you wonder: how many cars in total are there? What might the next number I see be? To formalize the problem, we assume that all cars in the province are numbered from 1 to L , where L is the largest licence plate number. Let M be the largest possible value of L . To make things simple, we’ll assume that license plate numbers are three digits, so that M = 999 . We assume that all values of L are equally likely, so our prior for L is a uniform distribution from 1 to M . Furthermore, we assume that, when we see a new car, we are equally likely to see any of the L cars out there, so the likelihood of seeing licence plate number X is also uniform. Our observations will be the numbers X i of the N cars we see go by. To specify the model, we define f ( Z,A,B ) = b 1 B - A +1 A Z B 0 otherwise (1) P ( L ) = f ( L, 1 ,M ) (the prior) (2) P ( X | L ) = f ( X, 1 ,L ) (the likelihood of a single license plate number X ) (3) P ( X 1: N | L ) = N p i =1 P ( X i | L ) (the likelihood of observing numbers X 1: N ) (4) Additionally, define X max = max X 1: N (5) to be the largest license plate number observed. (a)
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This note was uploaded on 11/09/2010 for the course CS CSCD11 taught by Professor Davidfleet during the Spring '10 term at University of Toronto- Toronto.

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a3 - CSCD11 Machine Learning and Data Mining, Fall 2010...

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