Reestimation of HMM Parameters

The reestimation procedure calculates new estimates of $ \Lambda$ given the observation sequence $ {\bf O}=O_1 O_2\cdots O_T$. We first define

$\displaystyle \xi_t(i,j) = \frac{\displaystyle \alpha_t(i) \; a_{ij} \; b_j(O_{...
...isplaystyle \sum_{j=1}^N} \alpha_t(i) \; a_{ij} \; b_j(O_{t+1})\beta_{t+1}(j) }$ (13.14)

and

$\displaystyle \gamma_t(i) = {\displaystyle \sum_{j=1}^N} \xi_t(i,j).$ (13.15)

The updated state priors are

$\displaystyle \hat{\pi}_i = \gamma_1(i).$ (13.16)

The updated state transition matrix is

$\displaystyle \hat{a}_{ij} = \frac{\displaystyle {\displaystyle \sum_{t=1}^{T-1}} \xi_t(i,j) }{\displaystyle {\displaystyle \sum_{t=1}^{T-1}} \gamma_t(i) }.$ (13.17)



Baggenstoss 2017-05-19