What are the different independence assumptions in hMM & Naive Bayes ?

Both the hMM and Naive Bayes have conditional independence assumption.

hMM can be expressed by the equation below :

Second equation implies a conditional independence assumption: Given the state observed variable is conditionally independent of previous observed variables, i.e. and

Naive Bayes Model is expressed as:

is the feature for the data sample and is the label for class problem.

The above equation can be written as

This implies a conditional independence assumption: given the class label, data features are independent of each other.