Markov Chain: discrete-time Markov chain is a stochastic process through this transition from a state to another state space.
This process is required to have properties of "no memory": the probability distribution of the next state can only be determined by the current state of its preceding time are irrelevant in a time series. This particular type of "no memory" referred to the Markov property.
The next moment is determined by the state only if the current state, called the first-order Markov, if by the current and former moment, it is called the second order, empathy. Therefore, there are m-order Markov chain.
Hidden Markov examples:
A friend in Tokyo according to the weather {rain, sunny day decide the day's activities} {walk in the park, shopping, cleaning the room} of a medium, I could only see her hair pushed on twitter every day, "ah, I was the day before yesterday walk in the park, shopping yesterday, today, to clean the room! ", then I can infer tokyo three days according to the weather she made a special push. In this case, substantial state is active, hidden state is the weather.
Corresponding to the above three issues:
- Known throughout the model, I observed three consecutive days to do are: walking, shopping, pick up, I want to guess, this three-day weather is kind of how.
- Known throughout the model, I observed three consecutive days to do are: walking, shopping, pick up. So according to the model, the calculated probability produce these behaviors is.
- The most complex, I only know three days to do these three things children, and what other information did not. I have to build a model, rain or shine transition probability, probability distribution of the first day of weather conditions, choose to do something depending on the weather probability distribution.
Hidden Markov Chain Solution:
One problem: Viterbi Algo, the Viterbi algorithm.
Second problem: Forword Algorithm, forward algorithm, or Backward Algorithm, backward algorithm.
Question three: Baum-Welch Algo, Baum - Welch algorithm