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For the Data Mining - Naïve Bayes Classifier for the case of "Numberless values for an attribute", the conditional probability is modeled with the normal distribution (see below).

Probability Density Function for the Normal Distribution

Suppose I have many values 0.3, 0.7, 0.6, 0.8..., I can calculate the mean and the standard deviation. For a new value x, I can make use of the formula (see above) to calculate the P(x), however, I need to find the associated probability for that P(x). The final classification can be done by choosing the label with the largest value of the product of these probabilities.

How can I calculate this probability?

Thank you very much!

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1 Answer 1

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Hint: Naive Bayes link requires you to calculate the posterior to estimate the class-conditional probabilities. For that you need, prior, likelihood and evidence. (see Gaussian Naive Bayes in the link above).

Hope that helps!

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  • $\begingroup$ Is the probability equal to P(x = v | c) P(c)? If I have n sets of values, is the final probability equal to P(x = v1 | c) P(c) P(x = v2 | c) P(c) ... P(x = vn | c) P(c) P(c) = P(x = v1 | c) P(x = v2 | c) ... P(x = vn | c) P(c)^n? $\endgroup$
    – chrisych
    Oct 19, 2016 at 16:53
  • $\begingroup$ I figured out what the problem was. I don't need to calculate the probability and need to calculate the posterior numerator only for classification. Thank you for providing me a helpful link! $\endgroup$
    – chrisych
    Oct 19, 2016 at 17:22
  • $\begingroup$ Glad I could help! Accept the answer by clicking the accept button on the left of the ans. $\endgroup$
    – CKM
    Oct 20, 2016 at 4:54

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