Suppose we have class C_k and input feature vector x in dataset enter image description here

How to calculate probability p(x)?

  • $\begingroup$ Do you need p(x)?, note that for classification with Naive Bayes one doesnt need it. $\endgroup$ Mar 14 '20 at 15:17
  • $\begingroup$ Your correct Naive Bayes doesn't need it, therefore, it's a more theoretical question $\endgroup$
    – Hyphen
    Mar 14 '20 at 16:15

in the Examples section of the Wikipedia article there is a nice example. The calculation of $p(\mathbf{x})$ can be done via

$$p(\mathbf{x}) = \sum_k p(C_k) \ p(\mathbf{x} \mid C_k)$$

Note that using the conditional independence assumption of the Naive Bayes one can write

$$ p(\mathbf{x} \mid C_k) = \Pi_{i} \, p(x_i \mid C_k) $$


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