Difference between a mixture model and HHM
- If we examine a single time slice of the model, it can be seen as a mixture distribution with component densities given by
- It can be interpreted as an extension of a mixture model where the choice of mixture component for each observation is not independent but depends on the choice of component for the previous observations (
)
Applications
- Speech recognition
- Natural language modeling
- On-line handwriting recognition
- analysis of biological sequences such as protein and DNA
Transition probability
- Latent variables; discrete multinomial variables
= describe which component of the mixture is responsible for generating the corresponding observation
- The probability distribution of
depends on the previous latent variable
through conditional distribution
- Conditional distribution
- Inital latent node
does not have a parent node, so it has a marginal distribution
- Lattice or trellis diagram
Emission probability
Example;
- Three Gaussian distribution/ two dice problem
- Handwriting