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Just for the practice of it, I'm trying to do a naive Bayes classifier for data which has exponential distribution for the likelihood function, i.e. $X_k=x|Y=1 \in Exp(\lambda_k)$ where $k = 1,..., p$ and p is the number of predictor\independent variables.

Now I'm facing an issue of my predictor variables being exponentially distributed with really big lambdas which I got from an MLE of the parameters with $\hat{\lambda_k} = \bar{x_k}^{-1}$. One of them is as big as 1451000. This gives me a lot of really small numbers of the predictors and when I calculate the product of $P(X_k=x|Y=c)$ I always get 0.

This is my dataset, it's basically a spam classification algorithm.

How can I tackle this issue, is this what is called the zero frequency problem? I read something about Laplace smoothing, but couldn't find how I can incorporate it in my scenario.

Thanks in advance!

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