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hmm.py
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hmm.py
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import numpy as np
from abc import ABCMeta, abstractmethod
class _BaseHMM:
"""
n_state : number of hidden states
n_iter :
x_size : dimension of obs
start_prob : initial prob
transmat_prob : transition prob
"""
__metaclass__ = ABCMeta
def __init__(self, n_state=1, x_size=1, iter=20):
self.n_state = n_state
self.x_size = x_size
# initialize
self.start_prob = np.ones(n_state) * (1.0 / n_state)
self.transmat_prob = np.ones((n_state, n_state)) * (1.0 / n_state)
self.trained = False
self.n_iter = iter
@abstractmethod
def _init(self, X):
pass
@abstractmethod
def emit_prob(self, x): # emission prob
return np.array([0])
# 虚函数
@abstractmethod
def generate_x(self, z): # generate x according to p(x|z)
return np.array([0])
# 虚函数：发射概率的更新
@abstractmethod
def emit_prob_updated(self, X, post_state):
pass
# 通过HMM生成序列
def generate_seq(self, seq_length):
X = np.zeros((seq_length, self.x_size))
Z = np.zeros(seq_length)
Z_pre = np.random.choice(self.n_state, 1, p=self.start_prob)
X[0] = self.generate_x(Z_pre)
Z[0] = Z_pre
for i in range(seq_length):
if i == 0:
continue
# P(Zn+1)=P(Zn+1|Zn)P(Zn)
Z_next = np.random.choice(
self.n_state, 1, p=self.transmat_prob[Z_pre, :][0]
)
Z_pre = Z_next
# P(Xn+1|Zn+1)
X[i] = self.generate_x(Z_pre)
Z[i] = Z_pre
return X, Z
# Evaluation
def X_prob(self, X, Z_seq=np.array([])):
X_length = len(X)
if Z_seq.any():
Z = np.zeros((X_length, self.n_state))
for i in range(X_length):
Z[i][int(Z_seq[i])] = 1
else:
Z = np.ones((X_length, self.n_state))
_, c = self.forward(X, Z) # P(x,z)
prob_X = np.sum(np.log(c)) # P(X)
return prob_X
# def predict_next_prob(self, X, x_next, Z_seq=np.array([]), istrain=True):
# if self.trained == False or istrain == False:
# self.train(X)
# X_length = len(X)
# if Z_seq.any():
# Z = np.zeros((X_length, self.n_state))
# for i in range(X_length):
# Z[i][int(Z_seq[i])] = 1
# else:
# Z = np.ones((X_length, self.n_state))
# alpha, _ = self.forward(X, Z) # P(x,z)
# prob_x_next = self.emit_prob(np.array([x_next])) * np.dot(
# alpha[X_length - 1], self.transmat_prob
# )
# return prob_x_next
def decode(self, X, istrain=True):
"""
Viterbi
:param X: observations
:param istrain:
:return: hidden states
"""
if self.trained == False or istrain == False:
self.train(X)
X_length = len(X)
state = np.zeros(X_length)
pre_state = np.zeros((X_length, self.n_state))
max_pro_state = np.zeros((X_length, self.n_state))
_, c = self.forward(X, np.ones((X_length, self.n_state)))
max_pro_state[0] = self.emit_prob(X[0]) * self.start_prob * (1 / c[0])
# forward
for i in range(X_length):
if i == 0:
continue
for k in range(self.n_state):
prob_state = (
self.emit_prob(X[i])[k]
* self.transmat_prob[:, k]
* max_pro_state[i - 1]
)
max_pro_state[i][k] = np.max(prob_state) * (1 / c[i])
pre_state[i][k] = np.argmax(prob_state)
# backward
state[X_length - 1] = np.argmax(max_pro_state[X_length - 1, :])
for i in reversed(range(X_length)):
if i == X_length - 1:
continue
state[i] = pre_state[i + 1][int(state[i + 1])]
return state
#
# def train_batch(self, X, Z_seq=list()):
#
# self.trained = True
# X_num = len(X)
# self._init(self.expand_list(X))
# if Z_seq == list():
# Z = []
# for n in range(X_num):
# Z.append(list(np.ones((len(X[n]), self.n_state))))
# else:
# Z = []
# for n in range(X_num):
# Z.append(np.zeros((len(X[n]), self.n_state)))
# for i in range(len(Z[n])):
# Z[n][i][int(Z_seq[n][i])] = 1
# for e in range(self.n_iter): # EM
# # E
# print("iter: ", e)
# b_post_state = []
# b_post_adj_state = np.zeros(
# (self.n_state, self.n_state)
# )
# b_start_prob = np.zeros(self.n_state)
# for n in range(X_num):
# X_length = len(X[n])
# alpha, c = self.forward(X[n], Z[n]) # P(x,z)
# beta = self.backward(X[n], Z[n], c) # P(x|z)
# post_state = alpha * beta / np.sum(alpha * beta) # Normalize
# b_post_state.append(post_state)
# post_adj_state = np.zeros((self.n_state, self.n_state))
# for i in range(X_length):
# if i == 0:
# continue
# if c[i] == 0:
# continue
# post_adj_state += (
# (1 / c[i])
# * np.outer(alpha[i - 1], beta[i] * self.emit_prob(X[n][i]))
# * self.transmat_prob
# )
# if np.sum(post_adj_state) != 0:
# post_adj_state = post_adj_state / np.sum(post_adj_state) # Normalize
# b_post_adj_state += post_adj_state
# b_start_prob += b_post_state[n][0]
# # M
# b_start_prob += 0.001 * np.ones(self.n_state)
# self.start_prob = b_start_prob / np.sum(b_start_prob)
# b_post_adj_state += 0.001
# for k in range(self.n_state):
# if np.sum(b_post_adj_state[k]) == 0:
# continue
# self.transmat_prob[k] = b_post_adj_state[k] / np.sum(
# b_post_adj_state[k]
# )
# self.emit_prob_updated(self.expand_list(X), self.expand_list(b_post_state))
def expand_list(self, X):
C = []
for i in range(len(X)):
C += list(X[i])
return np.array(C)
# 针对于单个长序列的训练
def train(self, X, Z_seq=np.array([])):
self.trained = True
X_length = len(X)
self._init(X)
if Z_seq.any():
Z = np.zeros((X_length, self.n_state))
for i in range(X_length):
Z[i][int(Z_seq[i])] = 1
else:
Z = np.ones((X_length, self.n_state))
for e in range(self.n_iter): # EM
print(e, " iter")
# E
alpha, c = self.forward(X, Z) # P(x,z)
beta = self.backward(X, Z, c) # P(x|z)
post_state = alpha * beta
post_adj_state = np.zeros((self.n_state, self.n_state))
for i in range(X_length):
if i == 0:
continue
if c[i] == 0:
continue
post_adj_state += (
(1 / c[i])
* np.outer(alpha[i - 1], beta[i] * self.emit_prob(X[i]))
* self.transmat_prob
)
# M
self.start_prob = post_state[0] / np.sum(post_state[0])
for k in range(self.n_state):
self.transmat_prob[k] = post_adj_state[k] / np.sum(post_adj_state[k])
self.emit_prob_updated(X, post_state)
def forward(self, X, Z):
X_length = len(X)
alpha = np.zeros((X_length, self.n_state)) # P(x,z)
alpha[0] = self.emit_prob(X[0]) * self.start_prob * Z[0]
c = np.zeros(X_length)
c[0] = np.sum(alpha[0])
alpha[0] = alpha[0] / c[0]
for i in range(X_length):
if i == 0:
continue
alpha[i] = (
self.emit_prob(X[i]) * np.dot(alpha[i - 1], self.transmat_prob) * Z[i]
)
c[i] = np.sum(alpha[i])
if c[i] == 0:
continue
alpha[i] = alpha[i] / c[i]
return alpha, c
def backward(self, X, Z, c):
X_length = len(X)
beta = np.zeros((X_length, self.n_state)) # P(x|z)
beta[X_length - 1] = np.ones((self.n_state))
for i in reversed(range(X_length)):
if i == X_length - 1:
continue
beta[i] = (
np.dot(beta[i + 1] * self.emit_prob(X[i + 1]), self.transmat_prob.T)
* Z[i]
)
if c[i + 1] == 0:
continue
beta[i] = beta[i] / c[i + 1]
return beta