# What is the meaning of generating data from a probabilistic model such as a naive bayes classifier?

I am studying probabilistic modeling but I am stuck with the concept of generating data from the probabilistic model. Say I have built a naive bayes classification model, what is the point of generating data from it? Generating data doesn't make sense to me. Hope somebody make me understand.

• What doesn't make sense about "generating data"? You should view this as simulating artificial data. There are many reasons you might want to do this; one is to check if these artificial outcomes are somehow similar to real data - i.e. to test the quality of your model. – Maurits M Jul 17 at 15:15
• Thank you for the comment. What do you mean by "to test the quality of my model by checking f theses articial outcomes are somehow si.ilar to real data? If it is a long story, some links will be appreciated. – Changhee Kang Jul 17 at 16:40
• A link with lots of references to fake data simulation, in general, is statmodeling.stat.columbia.edu/2019/03/23/… . A simple example of what I mean is as follows. Suppose you have some data and your probabilistic model is that it comes from a normal distribution with parameters $\mu$ and $\sigma^2$. After fitting the model (and thus finding the best estimates for $\mu$ and $\sigma^2$) you simulate 1000 new observations from the model and compare with your actual data, looking for any differences. – Maurits M Jul 17 at 20:03
• Thank you, Maurits. Can I assume a probability distribution for a generative model like Naive Bayes? I have never thought about generating data from this probabilistic model. But I know I can generate data because each variables value has probability. However, the problem I don't know what probability distribution it is from. This case, can I just assume it has a normal probability distribution with a mean and a variance? I am trying to learn it, forgive my ignorance if I sound like I am not making sense. – Changhee Kang Jul 18 at 8:32
• So this depends on the structure you assume in the first place. See for instance en.wikipedia.org/wiki/… for several examples of probability distributions used in Naive Bayes. – Maurits M Jul 18 at 10:47

[Naive] bayes is a generative model, which means we can generate data using it if we wanted. In NB, we estimate $$p(\mathbf{x}|y)$$, where $$\mathbf{x}$$ is our feature vector and $$y$$ is the class variable. For example, we first pick a $$y$$, indicating the class, and then pick word(s) according to the probability distribution, $$p(\mathbf{x}|y)$$.