Introduction to Machine Learning by Alex Smola, S.V.N. Vishwanathan

By Alex Smola, S.V.N. Vishwanathan

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1 Naive Bayes Train(X, Y) {reads documents X and labels Y} Compute dictionary D of X with n words. Compute m, mham and mspam . Initialize b := log c + log mham − log mspam to offset the rejection threshold Initialize p ∈ R2×n with pij = 1, wspam = n, wham = n. 2 Nearest Neighbor Estimators An even simpler estimator than Naive Bayes is nearest neighbors. 17). Hence, all we need to implement it is a distance measure d(x, x ) between pairs of observations. Note that this distance need not even be symmetric.

Since we know process ’A’ exactly we only need to concern ourselves with ’B’. We associate the random variable Xi with wafer i. A reasonable (and somewhat simplifying) assumption is to posit that all Xi are independent and identically distributed where all Xi have the mean µB . Obviously we do not know µB — otherwise there would ¯ m the average of the yields of m be no reason for testing! We denote by X wafers using process ’B’. 05. δ = Pr(|X Let us now discuss how the various bounds behave. e.

Obviously, we may apply it to problems other than document categorization, too. 1 Naive Bayes Train(X, Y) {reads documents X and labels Y} Compute dictionary D of X with n words. Compute m, mham and mspam . Initialize b := log c + log mham − log mspam to offset the rejection threshold Initialize p ∈ R2×n with pij = 1, wspam = n, wham = n. 2 Nearest Neighbor Estimators An even simpler estimator than Naive Bayes is nearest neighbors. 17). Hence, all we need to implement it is a distance measure d(x, x ) between pairs of observations.

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