07_hmm

Hidden Markov Model

dynamic clustering

生成模式

• generating patterns
  • deterministic patterns
  • non-deterministic patterns
    • 状态量
    • pi向量：初始化概率
    • 状态转移矩阵

隐藏模式

Markov process

未来状态只依赖于当前状态。

• hidden space
• observed space
• start probability
• transition probabilities
• emission probabilities

three main questions

• evaluation:
  • given: an hmm M AND a sequence x
  • find: prob(x|M)
  • forward
• decoding
  • given: an HMM M and a sequence x
  • find: the sequence y of states that maximizes the most probable subsequence of states
  • Viterbi, forward-backward
• learning
  • given: an HMM M with unspecified transition/emission probs, and a sequence x,
  • parameters $\theta=(\pi_i,\alpha_{ij},\eta_{ik})$ that maximize $P(x|\Theta)$
  • Baum-welch

solutions

forward algorithm

1. 穷举搜索(exhausive search for solution)
2. 递归(recursive solution)
   • 假设上一时间概率已知，则通过哥哥状态的概率相加得出这一时刻的概率

reference

1. 我爱自然语言处理