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@ -8,9 +8,6 @@ Bayes Theorem finds the probability of an event occurring given the probabili
$$ P(C|X) = \frac{P(X|C) \cdot P(C)}{P(X)} $$ $$ P(C|X) = \frac{P(X|C) \cdot P(C)}{P(X)} $$
![img.png](img.png)
where A and B are events and P(B) ≠ 0 where A and B are events and P(B) ≠ 0
* We are trying to find probability of event A, given the event B is true. * We are trying to find probability of event A, given the event B is true.
@ -78,6 +75,10 @@ In Gaussian Naive Bayes, continuous values associated with each feature are assu
* Assumption: Each feature follows a Gaussian distribution. * Assumption: Each feature follows a Gaussian distribution.
* Formula: The likelihood of the features given the class is computed using the Gaussian (normal) distribution formula: * Formula: The likelihood of the features given the class is computed using the Gaussian (normal) distribution formula:
$$
P(C_k | x) = \frac{P(C_k) \cdot \prod_{i=1}^{n} \frac{1}{\sqrt{2 \pi \sigma_{k,i}^2}} \exp \left( -\frac{(x_i - \mu_{k,i})^2}{2 \sigma_{k,i}^2} \right)}{P(x)}
$$
![img_3.png](img_3.png) ![img_3.png](img_3.png)
where 𝜇𝐶 and 𝜎𝐶 are the mean and standard deviation of the feature 𝑥𝑖 for class C. where 𝜇𝐶 and 𝜎𝐶 are the mean and standard deviation of the feature 𝑥𝑖 for class C.