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gradient wrt transition probabilities

Using the chain rule for any of the likelihoods, free or clamped,


Differentiating eqns.1.39 and 1.40 wrt tex2html_wrap_inline2892 , to get two results for free and clamped cases and using the common result in eqn.1.25, we get substitutions for both terms on the right hand side of eqn. 1.41. This substitution yields two separate results for free and clamped cases.


where tex2html_wrap_inline3016 is a Kronecker delta.


Substitution of eqns. 1.42 and 1.43 in the eqn.1.38(keeping in mind that tex2html_wrap_inline2900 in this case) gives the required result,


Narada Warakagoda
Fri May 10 20:35:10 MET DST 1996

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