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Violation of NB Assumptions

Violation of NB Assumptions. Positional I ndependence Conditional I ndependence. Examples?. Posterior Probabilities in NB. Classification results of N aïve Bayes (the class with maximum posterior probability) are usually fairly accurate.

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Violation of NB Assumptions

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  1. Violation of NB Assumptions Positional Independence Conditional Independence Examples?

  2. Posterior Probabilities in NB Classification results of Naïve Bayes (the class with maximum posterior probability) are usually fairly accurate. However, due to the inadequacy of the conditional independence assumption, the actual posterior-probability numerical estimates are not. Output probabilities are commonly very close to 0 or 1. Correct estimation  accurate prediction, but correct probability estimation is NOTnecessary for accurate prediction (just need right ordering of probabilities)

  3. Example: Sensors NB FACTORS: P(r) = 1/2 P(s) = 1/2 P(+|s) = 1/4 P(+|r) = 3/4 Reality Raining Sunny P(+,+,r) = 3/8 P(-,-,r) = 1/8 P(+,+,s) = 1/8 P(-,-,s) = 3/8 NB Model PREDICTIONS: • P(r,+,+) = (½)(¾)(¾) • P(s,+,+) = (½)(¼)(¼) • P(r|+,+) = 9/10 • P(s|+,+) = 1/10 Raining? M1 M2

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