Stat231_HW1

# Stat231_HW1 - Stat 231 CS 276A assignment#1 total 10 points...

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Stat 231 - CS 276A assignment #1: total 10 points Due: Oct. 13 Wednesday at class meeting. Policy : You are supposed to finish the homework by yourself. Do not discuss homework with your classmate or friends who took this course before. People who violate this policy, once caught, will be dismissed from the class. You must turn in the homework at class meeting. If you hand in homework in the afternoon, then it will be counted as being late for 1 day. Total 3 late days for the entire class. Questions : My office hour is M 3-4:30pm, BH 9404. Problem 1 : 2 points, (Bayesian classification boundary). For a two-class recognition problem: salmon ( w = 1) and sea bass ( w = 2), suppose we uses two features x = ( x 1 , x 2 ) (e.g. length and brightness) and the two class models (also called likelihood models) p ( x | w = 1) and p ( x | w = 2) are supposed to be 2D Gaussian distributions centered at points (3 , 6) and (6 , 3) respectively with the same covariance matrix Σ = 3 I ( I is the identity matrix). Suppose the prior probability for salmon and sea bass is p ( w = 1) = 0 . 4 , p ( w = 2) = 0 . 6. 1. Suppose we use a Bayes decision rule, write the two discriminant functions g 1 ( x ) and g 2 ( x ). 2. Derive the equation for the decision boundary g 1 ( x ) = g 2 ( x ). Draw the boundary on the feature space ( in this case, it is the 2D plane).

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