在Python

Question

生成馬爾科夫轉移矩陣想象我有一系列的4個可能的狀態馬爾可夫（A，B，C，d）：

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

怎樣才能使用Python馬爾可夫變換矩陣？矩陣必須是4乘4，表示從每個狀態移動到其他3個狀態的概率。 我一直在看很多例子，但在所有這些例子中，矩陣是給出的，而不是基於數據計算的。 我也看着hmmlearn，但是我沒有看到如何讓它吐出轉換矩陣。有沒有可以用於此目的的圖書館？

這裏是我想在Python做確切的事情的R代碼： https://stats.stackexchange.com/questions/26722/calculate-transition-matrix-markov-in-r

Answer 1

這可能給你一些想法：

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) 

輸出：

[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] 

On編輯這是一個實現上述想法的功能：

#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)) 

輸出：

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