Hidden Markov model is a generative model used to label the problem. Several parameters (π, A, B): the initial state probability vector π, state transition matrix A, the observation probability matrix B. Called a Markov model of the three elements
Examples observation sequence is "dry, wet, wet."
Examples of state sequence "sunny, cloudy, rainy"
A second is a table showing state transition matrix vector:
B is the observation probability matrix vector:
[pi] is hidden initial probability vector:
1, the probability calculation (assessment)
Probability calculation (assessment): given the observation sequence and the model, calculate the probability of the observed sequence of output models, the model that best matches the sequence for evaluating . (Obtained sequence probability and probability of the observed sequence hidden)
2, learning problems
Learning problems: Given the observation sequence, estimate model parameters, which uses maximum likelihood estimation to estimate the parameters. - "Baum-Welch (that is, the EM algorithm) and maximum likelihood estimation.
That observation sequence is known , find π, A, B maximum probability optimal solution three parameters to achieve a certain result of the need to obtain parameters of the model
(1), Baum-Welch Algorithm Description:
(2), the EM algorithm:
Detailed please click: https://blog.csdn.net/quicmous/article/details/52154527
(3), maximum likelihood estimation:
Detailed please click: https://blog.csdn.net/quicmous/article/details/52154628
3, prediction problem
PREDICTION: observation sequence and the model parameters are known, the corresponding sequence of states solved. - "approximation algorithm (a greedy algorithm) and Viterbi algorithm (dynamic programming optimal path)
Finishing Ideas from:
the hidden Markov model analysis to solve three problems examples ( mostly from here ):
https://blog.csdn.net/quicmous/article/details/52208302
hidden Markov model, three basic questions and the corresponding algorithm:
https://blog.csdn.net/xingchenhy/article/details/72847534
