Hidden Markov model HMM

The problem solved has two characteristics ：

1: Our problem is based on sequence , Such as time series , Or a sequence of states .
2: There are two types of data in our problem , A class of sequence data can be observed , That is, the observation sequence ; And another kind of data can't be observed , Hidden state sequence , State sequence for short .

Model definition ：

for example ： Jobs invented Apple mobile phone

HMM The model makes two important assumptions as follows ：
　　1） Homogeneous Markov chain hypothesis . That is, the hidden state at any time only depends on its previous hidden state
　　

　　　　2） Observation independence Hypothesis . That is, the observation state at any time only depends on the hidden state at the current time
　　　　

Initial state at the beginning ：



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That is, according to the given observation sequence 𝑂={ red , white , red }, Predict that each ball is most likely to come out of that box .

So the corresponding observation sequence （ red , white , red ）, The most likely hidden sequence is （ The box 3, The box 3, The box 3）.

https://www.cnblogs.com/pinard/p/6991852.html