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Is there any relationship between Naive Bayes and Hidden Markov model? Can we derive one from another?

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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.

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If we make the hidden state of HMM fixed, we will have a Naive Bayes model. Suppose we use graphical model's notation. Naive Bayes model can be described as

enter image description here

Where HMM can be described as

enter image description here

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  • $\begingroup$ (+1), I just deleted my answer because yours helped me to realize I had this backwards. NB models do assume the marginal distributions of the latent rvs, and the distributions of data conditional these latent rvs. $\endgroup$ – Taylor Sep 18 '17 at 18:57
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They both use Bayes' rule. That's it though.

Some differences:

  1. a HMM is a time series model, while Naive Baye's isn't
  2. 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.

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