I came across an earlier post that was resolved and had a follow up to it but I couldn't comment because my reputation is under 50. Essentially I am interested in calculating the denominator in Naive Bayes.
Now I understand that the features in Naive Bayes are assumed to be independent so could we calculate $p(x) = p(x_{1})p(x_{2})...p(x_{n})$ or would we have to use this formula $$p(\mathbf{x}) = \sum_k p(C_k) \ p(\mathbf{x} \mid C_k)$$ with the conditional independence assumption that$$ p(\mathbf{x} \mid C_k) = \Pi_{i} \, p(x_i \mid C_k) $$
My question is would both ways of calculating give the same p(x)?
Link to the original question : https://datascience.stackexchange.com/posts/69699/edi
Edit** : Sorry I believe the features have conditional independence, rather than complete independence. Therefore it is incorrect to use $p(x) = p(x_{1})p(x_{2})...p(x_{n})$?
Lastly, I understand we don't actually need the denominator to find our probabilities but am asking out of curiosity.