概率计算问题:已知λ\lambda和O,求P(Oλ)P(O|\lambda)
根据概率公式:
P(Oλ)=IP(O,Iλ)=IP(OI,λ)P(Iλ) \begin{aligned} P(O|\lambda) & = \sum_{I}P(O, I | \lambda) \\ & = \sum_IP(O|I,\lambda)P(I|\lambda) \end{aligned} 当序列长度为T时:
P(Iλ)=πi1ai1i2aiT1iTP(OI,λ)=bi1(O1)biT(OT) \begin{aligned} P(I|\lambda) = \pi_{i_1}a_{i_1i_2}\cdots a_{i_{T-1}i_T} \\ P(O|I,\lambda) = b_{i_1}(O_1)\cdots b_{i_T}(O_T) \end{aligned} I为所有可能的长度为T的状态序列的集合。

计算量大,不可行

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