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!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.