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The naïve Bayes' generative algorithm is often represented by the following formula:

$$\text{argmax}_{y} p(y|x) = \text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$$

Why do we have $p(x)=1$ which allows the approximation $\text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$?

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    $\begingroup$ They have eliminated it because in comparing probability for best outcome, it would just introduce additional division and the divisor p(x) is same for all candidates. For example, if I tell you to compare the largest of the following numbers: 3/2, 5/2, 1/2, you will without thinking pick 5/2 since the divisors are same and 5 is greatest of all. $\endgroup$
    – kiner_shah
    Dec 2, 2017 at 16:37

1 Answer 1

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The answer from @kiner_shah in the comments has solved it:

They have eliminated it because in comparing probability for best outcome, it would just introduce additional division and the divisor p(x) is same for all candidates. For example, if I tell you to compare the largest of the following numbers: 3/2, 5/2, 1/2, you will without thinking pick 5/2 since the divisors are same and 5 is greatest of all.

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