# Why is the denominator ignored in the Bayes' rule?

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

• 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. – kiner_shah Dec 2 '17 at 16:37

## 1 Answer

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.