5. Initial state distribution π = {πi}
Number of states in the model X : N
Number of observation symbols O : M
Transition matrix A = {aij} , where aij represents the
transition probability from state i to state j
Observation emission matrix B = {bij} , where bij
represent the probability of observation j at state i
幾個骰⼦子 3
觀察到骰出的點數 1-8
D4骰⼦子到D8骰⼦子的機率 1/3
D4骰⼦子出現1的機率 1/4
⾸首次選骰⼦子的機率各 1/3
8. solution
1. The Evaluation Problem - Forward
HMM parameter μ=(π,A,B)
forward probability : αj(t) when time = t，observation sequence
(o1,o2,…,ot)，the probability of hidden state j
when t = 1
[ ]
14. solution
3. The Learning Problem - Baum-Welch(EM algorithm)
forward probability
backward probability
when t = T-1
when t = T
15. solution
3. The Learning Problem - Baum-Welch(EM algorithm)
γj(t) : when time = t，the probability of hidden state j
HMM parameter μ=(π,A,B) and observation sequence O
ξij(t) : the probability of when time = t，the probability of hidden
state i,when time = t+1，the probability of hidden state j
17. Initial state distribution π = {πi}
Number of states in the model: N
Number of observation symbols: M
Transition matrix A = {aij} , where aij represents the
transition probability from state i to state j
Observation emission matrix B = {bj(Ot)} , where bj(Ot)
represent the probability of observing Ot at state j
幾個骰⼦子 3
觀察到骰出的點數 1-8
D4骰⼦子到D8骰⼦子的機率 1/3
D4骰⼦子出現1的機率 1/4
⾸首次選骰⼦子的機率各 1/3
18. The Evaluation Problem - Forward
The Decoding Problem - Viterbi
The Learning Problem - Baum-Welch
已知骰⼦子有幾種，每種骰⼦子是什麼，想知道擲出來
想知道此結果的機率？
已知骰⼦子有幾種，每種骰⼦子是什麼，根據骰⼦子擲出
來的結果，想知道擲出來的是哪種骰⼦子？
已知骰⼦子有幾種，不知道骰⼦子是什麼，觀察多次骰
⼦子擲出來的結果，想反推每種骰⼦子是什麼？
21. The Decoding Problem - Viterbi
中⽂文分詞 (jieba)
states set : {B:begin, M:middle, E:end, S:single}
我天天去實驗室 SBESBME
我/天天/去/實驗室 S/BE/S/BME
initiaState
B 0.15
M 0.005
E 0.005
S 0.84
B M E S
B 0 0.3 0.7 0
M 0 0.2 0.8 0
E 0.4 0 0 0.6
S 0.5 0 0 0.5
國 ⺠民 我 挺 柱 …
B -8 -7 -6 -8 -7 …
M -10 -9 -8 -10 -7 …
E -8 -8 -6 -9 -7 …
S -9 -8 -5 -7 -8 …
經驗法則，⽤用現有收集詞庫統計詞頻即可得知
S
O
Discrete
Discrete
數字太⼩小經過log處理
22. The Learning Problem - Baum-Welch
S
O
Discrete
Continuous
Gaussian HMM of stock data
27. Gaussian Mixture Model GMM
S -> O ⼀一個狀態S噴出的O對應⼀一個Gaussian
S -> k -> O
⼀一個狀態S有k個管道，每個管道
噴出的O對應⼀一個Gaussian
1
2
3
ck × N( v , μ k , σ2
k )
N( v , μ , σ2 )
多個Gaussian組成⼀一個GMM
⼀一個狀態S噴出的O 常態分佈
符合
不符合
Gaussian HMM
GMM HMM
29. g ng b nb
g 0.6 0.1 0.2 0.1
ng 0.2 ? 0.3 0.2
b ? ?
nb ? ?
定義 status
gamer的層級
diff wifi
S1 S1-diff(μ, σ2) 0.2
S2 S2-diff(μ, σ2) 0.4
S3 S3-diff(μ, σ2) 0.6
DiscreteContinuous
收集 O 觀察特徵
決定模型
S
O
Discrete
Continuous
MultinomialHMM
S
O
Discrete
Continuous
GaussianHMM GMMHMM
n_mix (注意 overfitting)
boring的層級
