Consider a two-category classification problem in two dimensions with: p(x|w_1) ~ N(0,I), p(x|w_2) ~ N([1 1],I) and P(w_1) = P(w_2) = 1/2. Calculate the Bayes' decision boundary.
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In this case, we have two classes w1 and w2, and we are given that the prior probabilities P(w1) and P(w2) are equal. This means that the decision will be based solely on the likelihoods p(x|w1) and p(x|w2). We are also given that the likelihoods p(x|w1) and Show more…
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Consider a two-category classification problem with a two-dimensional feature vector X (X1, X2). The two categories are W1 and W2. P(X|W1) ~ N(mu1, sigma1) and P(X|W2) ~ N(mu2, sigma2), where mu1 = (0,0), sigma1 = [[1,0],[0,1]], mu2 = (0,0), and sigma2 = [[1,0],[0,1]]. Calculate the Bayes decision boundary: Randomly draw 50 patterns from each of the two class-conditional densities and plot them in the two-dimensional feature space. Also, draw the decision boundary on this plot. Calculate the Bhattacharya error bound. Generate 1000 additional test patterns from each class and determine the empirical error rate based on the decision boundary in (3a). Compare the empirical error with the bound in part (3c).
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