✏️
LiHang-TongJiXueXiFangFa
More
Search
Ctrl + K
学习问题 - 非监督学习
已知O，求
λ
\lambda
λ
，使O的似然估计最大
输入：
观测数据O
输出：
隐马尔可夫模型参数
过程：
1. 初始化：
λ
(
0
)
=
(
A
(
0
)
,
B
(
0
)
,
π
(
0
)
)
\lambda(0) = (A(0), B(0), \pi(0))
λ
(
0
)
=
(
A
(
0
)
,
B
(
0
)
,
π
(
0
))
递推
a
i
j
(
n
+
1
)
=
∑
t
=
1
T
−
1
ξ
t
(
i
,
j
)
∑
t
=
1
T
−
1
γ
t
(
i
)
b
j
(
k
)
(
n
+
1
)
=
∑
t
=
1
,
O
t
=
v
k
T
γ
t
(
j
)
∑
t
=
1
T
γ
t
(
j
)
π
i
(
n
+
1
)
=
γ
1
(
i
)
\begin{aligned} a_{ij}^{(n+1)} = \frac{\sum_{t=1}^{T-1}\xi_t(i,j)}{\sum_{t=1}^{T-1}\gamma_t(i)} \\ b_j(k)^{(n+1)} = \frac{\sum_{t=1,O_t=v_k}^T\gamma_t(j)}{\sum_{t=1}^T\gamma_t(j)} \\ \pi_i^{(n+1)} = \gamma_1(i) \end{aligned}
a
ij
(
n
+
1
)
=
∑
t
=
1
T
−
1
γ
t
(
i
)
∑
t
=
1
T
−
1
ξ
t
(
i
,
j
)
b
j
(
k
)
(
n
+
1
)
=
∑
t
=
1
T
γ
t
(
j
)
∑
t
=
1
,
O
t
=
v
k
T
γ
t
(
j
)
π
i
(
n
+
1
)
=
γ
1
(
i
)
其中：
γ
t
(
i
)
=
α
t
(
i
)
β
t
(
i
)
∑
j
=
1
N
α
t
(
i
)
β
t
(
i
)
ξ
t
(
i
,
j
)
=
α
t
(
i
)
a
i
j
b
j
(
o
t
+
1
)
β
t
+
1
(
j
)
∑
i
=
1
N
∑
j
=
1
N
α
t
(
i
)
a
i
j
b
j
(
o
t
+
1
)
β
t
+
1
(
j
)
\begin{aligned} \gamma_t(i) = \frac{\alpha_t(i)\beta_t(i)}{\sum_{j=1}^N\alpha_t(i)\beta_t(i)} \\ \xi_t(i,j) = \frac{\alpha_t(i)a_{ij}b_j(o_{t+1})\beta_{t+1}(j)}{\sum_{i=1}^N\sum_{j=1}^N\alpha_t(i)a_{ij}b_j(o_{t+1})\beta_{t+1}(j)} \end{aligned}
γ
t
(
i
)
=
∑
j
=
1
N
α
t
(
i
)
β
t
(
i
)
α
t
(
i
)
β
t
(
i
)
ξ
t
(
i
,
j
)
=
∑
i
=
1
N
∑
j
=
1
N
α
t
(
i
)
a
ij
b
j
(
o
t
+
1
)
β
t
+
1
(
j
)
α
t
(
i
)
a
ij
b
j
(
o
t
+
1
)
β
t
+
1
(
j
)
终止：
λ
(
N
+
1
)
=
(
A
(
N
+
1
)
,
B
(
N
+
1
)
,
π
(
N
+
1
)
)
\lambda(N+1) = (A(N+1), B(N+1), \pi(N+1))
λ
(
N
+
1
)
=
(
A
(
N
+
1
)
,
B
(
N
+
1
)
,
π
(
N
+
1
))
Previous
学习问题 - 监督学习
Next
Baum - Welch算法推导
Last updated
4 years ago