HMM notes

You need to know three elements ：

 

1、 Hidden state probability of the first day , The first day was far away Sunny probability 0.67, The probability of rainy days far away on the first day 0.33.

2、 The emission probability of the hidden state , a sunny day 0.8 Happy , a sunny day 0.2 angry . rain 0.4 Happy , rain 0.6 angry .

3、 State transition matrix , Sunny to sunny 0.8, Sunny to rainy 0.2. Rainy days to sunny days 0.4, Rainy days to rainy days 0.6.

viterbi algorithm ： According to the dominant state sequence mood -> Invisible state sequence The weather

consider     Max( The weather sequence is in 6 Probability of sunny days , The weather sequence is in 6 Probability of rainy days )

Dependent on the weather sequence in the 5 Probability of sunny days , The weather sequence is in 5 Probability of rainy days

The weather sequence is in 5 Probability of sunny days from Max（ The weather sequence is in 4 Probability of sunny days To The weather sequence is in 5 Probability of sunny days

                                                    The weather sequence is in 4 Probability of rainy days To The weather sequence is in 5 Probability of sunny days )            Select the maximum probability route by   The weather sequence is in 5 Probability of sunny days , Other low probability routes are not considered ）

The weather sequence is in 5 Probability of rainy days from Max（ The weather sequence is in 4 Probability of sunny days To The weather sequence is in 5 Probability of rainy days

                                                    The weather sequence is in 4 Probability of rainy days To The weather sequence is in 5 Probability of rainy days )            Select the maximum probability route by   The weather sequence is in 5 Probability of sunny days , Other low probability routes are not considered ）

Do this from the next day to the last day .

Because the first day is known .