The probabilities $\betai(s)$ satisfy the equations
$$\betam(sF) = 1 \quad (7.6a)$$
$$\betai(s) = \sumt \betai(R(t)) \gamma(t, s, \phi) + \sumt \beta{i+1}(R(t)) \gamma(t, s, bi) \quad i \le m, s \neq sF \quad (7.6b)$$
where $\beta{m+1}(s…falls. It might appear that the convergence of the estimation of the interpolation weights $\lambda(i)$ needs proving since it involves the use of different fixed distributions $q(s, j)$ over different blocks $j = 1, \dots, n$. However, som…[14] L. R. Bahl and F. Jelinek, "Decoding for channels with insertions, deletions, and substitutions with applications to speech recognition," IEEE Trans. Inform. Theory, vol. IT-21, pp. 404-411, July 1975.
[15] F. Jelinek and R. L. Mercer…
Leonard E. Baum
mathematician · 3 mentions across 1 reading
In this course
Leonard E. Baum developed the foundational algorithms for hidden Markov models (HMMs), particularly the forward-backward algorithm and expectation-maximization framework that enable probabilistic inference in sequential data. His work appears in these course readings through the mathematical machinery of dynamic programming and probabilistic estimation, which underlies both classical speech recognition systems and modern sequence modeling in deep learning—making him essential to understanding how machines learn to decode noisy, hidden state sequences.
Mentioned in 1 reading
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