前向算法定义(Forward Algorithm)

  数据挖掘研究院

that is, the product of the appropriate observation probability and the sum over all possible routes to that state, exploiting recursion by knowing these values already for the previous time step.

Finally the sum of all partial probabilities gives the probability of the observation, given the HMM, .

To recap, each partial probability (at time t > 2) is calculated from all the previous states.

数据挖掘研究院

Using the `weather′ example, the diagram below shows the calculation for at t = 2 for the cloudy state. This is the product of the appropriate observation probability b and the sum of the previous partial probabilities multiplied by the transition probabilities .