Python如何实现隐马尔可夫模型的前向后向算法-创新互联
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创新互联是一家以重庆网站建设、网页设计、品牌设计、软件运维、seo优化、小程序App开发等移动开发为一体互联网公司。已累计为不锈钢雕塑等众行业中小客户提供优质的互联网建站和软件开发服务。前向算法Python实现循环方式
import numpy as np def hmm_forward(Q, V, A, B, pi, T, O, p): """ :param Q: 状态集合 :param V: 观测集合 :param A: 状态转移概率矩阵 :param B: 观测概率矩阵 :param pi: 初始概率分布 :param T: 观测序列和状态序列的长度 :param O: 观测序列 :param p: 存储各个状态的前向概率的列表,初始为空 """ for t in range(T): # 计算初值 if t == 0: for i in range(len(Q)): p.append(pi[i] * B[i, V[O[0]]]) # 初值计算完毕后,进行下一时刻的递推运算 else: alpha_t_ = 0 alpha_t_t = [] for i in range(len(Q)): for j in range(len(Q)): alpha_t_ += p[j] * A[j, i] alpha_t_t.append(alpha_t_ * B[i, V[O[t]]]) alpha_t_ = 0 p = alpha_t_t return sum(p) # 《统计学习方法》书上例10.2 Q = [1, 2, 3] V = {'红':0, '白':1} A = np.array([[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]]) B = np.array([[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]]) pi = [0.2, 0.4, 0.4] T = 3 O = ['红', '白', '红'] p = [] print(hmm_forward(Q, V, A, B, pi, T, O, p)) # 0.130218
递归方式
import numpy as np def hmm_forward_(Q, V, A, B, pi, T, O, p, T_final): """ :param T_final:递归的终止条件 """ if T == 0: for i in range(len(Q)): p.append(pi[i] * B[i, V[O[0]]]) else: alpha_t_ = 0 alpha_t_t = [] for i in range(len(Q)): for j in range(len(Q)): alpha_t_ += p[j] * A[j, i] alpha_t_t.append(alpha_t_ * B[i, V[O[T]]]) alpha_t_ = 0 p = alpha_t_t if T >= T_final: return sum(p) return hmm_forward_(Q, V, A, B, pi, T+1, O, p, T_final) Q = [1, 2, 3] V = {'红':0, '白':1} A = np.array([[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]]) B = np.array([[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]]) pi = [0.2, 0.4, 0.4] T = 0 O = ['红', '白', '红'] p = [] T_final = 2 # T的长度是3,T的取值是(0时刻, 1时刻, 2时刻) print(hmm_forward_(Q, V, A, B, pi, T, O, p, T_final))后向算法Python实现
循环方式
import numpy as np def hmm_backward(Q, V, A, B, pi, T, O, beta_t, T_final): for t in range(T, -1, -1): if t == T_final: beta_t = beta_t else: beta_t_ = 0 beta_t_t = [] for i in range(len(Q)): for j in range(len(Q)): beta_t_ += A[i, j] * B[j, V[O[t + 1]]] * beta_t[j] beta_t_t.append(beta_t_) beta_t_ = 0 beta_t = beta_t_t if t == 0: p=[] for i in range(len(Q)): p.append(pi[i] * B[i, V[O[0]]] * beta_t[i]) beta_t = p return sum(beta_t) # 《统计学习方法》课后题10.1 Q = [1, 2, 3] V = {'红':0, '白':1} A = np.array([[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]]) B = np.array([[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]]) pi = [0.2, 0.4, 0.4] T = 3 O = ['红', '白', '红', '白'] beta_t = [1, 1, 1] T_final = 3 print(hmm_backward_(Q, V, A, B, pi, T, O, beta_t, T_final)) # 0.06009
递归方式
import numpy as np def hmm_backward(Q, V, A, B, pi, T, O, beta_t, T_final): if T == T_final: beta_t = beta_t else: beta_t_ = 0 beta_t_t = [] for i in range(len(Q)): for j in range(len(Q)): beta_t_ += A[i, j] * B[j, V[O[T+1]]] * beta_t[j] beta_t_t.append(beta_t_) beta_t_ = 0 beta_t = beta_t_t if T == 0: p=[] for i in range(len(Q)): p.append(pi[i] * B[i, V[O[0]]] * beta_t[i]) beta_t = p return sum(beta_t) return hmm_backward(Q, V, A, B, pi, T-1, O, beta_t, T_final) jpgQ = [1, 2, 3] V = {'红':0, '白':1} A = np.array([[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]]) B = np.array([[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]]) pi = [0.2, 0.4, 0.4] T = 3 O = ['红', '白', '红', '白'] beta_t = [1, 1, 1] T_final = 3 print(hmm_backward_(Q, V, A, B, pi, T, O, beta_t, T_final)) # 0.06009
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文章标题:Python如何实现隐马尔可夫模型的前向后向算法-创新互联
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