What attributes does Laplace Smoothing apply on in Naive Bayes Consider the dataset:




Outlook
Temperature
Humidity
Play Golf?




Overcast
Cool
Low
Yes


Sunny
Hot
Low
Yes


Rainy
Cool
High
No


Sunny
Hot
High
No


Rainy
Cool
Low
Yes




There are 3 possible values for the feature "Outlook":

*

*Overcast

*Sunny

*Rainy

P(Yes) = 3/5 and P(No) = 2/5.
The probability of Overcast given No is P(Overcast | No) = 0. I do know to solve this issue, we use Laplace Smoothing with the formula, α/(N + α⋅k). In this case if α = 1, 0 + 1/(2 + 1⋅k). What I'm unsure about is what does k here means.
So my questions are:

*

*Does k refer to the number of features (Outlook, Temperature, Humidity) or the number of possible values for Outlook?

*Do we apply Laplace Smoothing for the feature Outlook or to all other features too?

*Do we normally check if conditional probability is 0 before applying Laplace Smoothing or do we just apply it straight?


$k$ refers to the possible values for Outlook, because you'll need the sum of all Outlook probabilities be $1$. It's up to you to apply this to all features or not. The smoothing is useful for remedying zero probability cases, but it's also for applying regularization. The degree/strength of regularization depends on the value of $\alpha$ and can be chosen by validation. So, zero probability is not the sole driver behind it.
