python-3.x - 在Python中生成马尔可夫转移矩阵

Question

想象一下，我有一系列四个可能的马尔可夫状态（A，B，C，D）：

X = [A, B, B, C, B, A, D, D, A, B, A, D, ....]

如何使用Python生成Markov变换矩阵？矩阵必须为4乘4，显示从每个状态转移到其他3个状态的概率。
我一直在网上查看许多示例，但在所有示例中，都是给出矩阵，而不是根据数据计算得出的。
我也研究了hmmlearn，但是在任何地方都没有读到如何使它吐出过渡矩阵。是否有可以用于此目的的库？

这是我要在Python中尝试执行的确切操作的R代码：
https://stats.stackexchange.com/questions/26722/calculate-transition-matrix-markov-in-r

Answer 1

这可能会给您一些想法：

transitions = ['A', 'B', 'B', 'C', 'B', 'A', 'D', 'D', 'A', 'B', 'A', 'D']

def rank(c):
    return ord(c) - ord('A')

T = [rank(c) for c in transitions]

#create matrix of zeros

M = [[0]*4 for _ in range(4)]

for (i,j) in zip(T,T[1:]):
    M[i][j] += 1

#now convert to probabilities:
for row in M:
    n = sum(row)
    if n > 0:
        row[:] = [f/sum(row) for f in row]

#print M:

for row in M:
    print(row)

输出：

[0.0, 0.5, 0.0, 0.5]
[0.5, 0.25, 0.25, 0.0]
[0.0, 1.0, 0.0, 0.0]
[0.5, 0.0, 0.0, 0.5]

在“编辑”中，此函数实现了以上想法：

#the following code takes a list such as
#[1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1]
#with states labeled as successive integers starting with 0
#and returns a transition matrix, M,
#where M[i][j] is the probability of transitioning from i to j

def transition_matrix(transitions):
    n = 1+ max(transitions) #number of states

    M = [[0]*n for _ in range(n)]

    for (i,j) in zip(transitions,transitions[1:]):
        M[i][j] += 1

    #now convert to probabilities:
    for row in M:
        s = sum(row)
        if s > 0:
            row[:] = [f/s for f in row]
    return M

#test:

t = [1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1]
m = transition_matrix(t)
for row in m: print(' '.join('{0:.2f}'.format(x) for x in row))

输出：

0.67 0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 0.12 0.12 0.25 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.50 0.50 0.00 0.00 0.00 0.00
0.00 0.20 0.00 0.00 0.20 0.60 0.00 0.00 0.00
0.17 0.17 0.00 0.00 0.17 0.33 0.00 0.17 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.33 0.00 0.00 0.00 0.33 0.00 0.00 0.33