Is there any relationship between Naive Bayes and Hidden Markov model? Can we derive one from another?
The relationship between Naive Bayes and HMM (as well as the relationship between Logistic Regression and CRM) is brilliantly described in the section 2.2 of An Introduction to Conditional Random Fields by Sutton and Mc Callum.
They both use Bayes' rule. That's it though.
- a HMM is a time series model, while Naive Baye's isn't
- a HMM assumes the marginal distributions of the discrete latent variables,
while Naive Bayes assumes the conditional distribution of the discrete latent variables.Edit: I have this backwards. Naive Bayes models do assume the marginal distribution for the hidden portion, and the distributions of the data conditional on the hidden rvs. And this is similar to HMMs, so it should be counted as a similarity. Your picture illustrates this well.
Naive Bayes has a lot in common with Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA), though.