隐含马尔可夫模型(Hidden Markov Model,HMM)最初是在20世纪60年代后半期,由Leonard E. Baum和其他一些作者在一系列统计学论文中描述的。其最初应用于语音识别领域。
1980年代后半期,HMM开始应用到生物序列,尤其是DNA序列的分析中。随后,在生物信息学领域,HMM逐渐成为一项不可或缺的技术。
本文内容包含来自:
[1] 用hmmlearn学习隐马尔科夫模型HMM
[2] 官方文档
0. 目录
目录
1. hmmlearn
hmmlearn曾经是scikit-learn项目的一部分,现已独立成单独的Python包,可直接通过pip进行安装,为无监督隐马尔可夫模型。其官方文档网址为https://hmmlearn.readthedocs.io/en/stable/。其有监督的版本为seqlearn。
pip3 install hmmlearn
hmmlearn提供三种模型:
名称 | 简介 | 观测状态 |
---|---|---|
hmm.GaussianHMM |
Hidden Markov Model with Gaussian emissions. | 连续 |
hmm.GMMHMM |
Hidden Markov Model with Gaussian mixture emissions. | 连续 |
hmm.MultinomialHMM |
Hidden Markov Model with multinomial (discrete) emissions | 离散 |
2. MultinomialHMM
方法声明为
class hmmlearn.hmm.MultinomialHMM(n_components=1, startprob_prior=1.0, transmat_prior=1.0,
algorithm='viterbi', random_state=None, n_iter=10, tol=0.01, verbose=False, params='ste', init_params='ste')
其中,较为常用(或将更新)的参数为:
- n_components:(int)隐含状态个数
- n_iter:(int, optional)训练时循环(迭代)最大次数
- tol:(float, optional)Convergence threshold. EM will stop if the gain in log-likelihood is below this value.
- verbose:(bool, optional)赋值为
True
时,会向标准输出输出每次迭代的概率(score)与本次 - init_params:(string, optional)决定哪些参数会在训练时被初始化。
‘s’
for startprob,‘t’
for transmat,‘e’
for emissionprob。空字符串""
代表全部使用用户提供的参数进行训练。
2.1 定义、使用:
import numpy as np
from hmmlearn import hmm
states = ["box 1", "box 2", "box3"]
n_states = len(states)
observations = ["red", "white"]
n_observations = len(observations)
start_probability = np.array([0.2, 0.4, 0.4])
transition_probability = np.array([
[0.5, 0.2, 0.3],
[0.3, 0.5, 0.2],
[0.2, 0.3, 0.5]
])
emission_probability = np.array([
[0.5, 0.5],
[0.4, 0.6],
[0.7, 0.3]
])
model = hmm.MultinomialHMM(n_components=n_states, n_iter=20, tol=0.001)
model.startprob_=start_probability
model.transmat_=transition_probability
model.emissionprob_=emission_probability
2.2 维特比算法预测状态
有说法称,其返回结果为ln(prob)
,文档原文为“the log probability”
seen = np.array([[0,1,0]]).T
logprob, box = model.decode(seen, algorithm="viterbi")
print("The ball picked:", ", ".join(map(lambda x: observations[x], seen)))
print("The hidden box", ", ".join(map(lambda x: states[x], box)))
输出为
('The ball picked:', 'red, white, red')
('The hidden box', 'box3, box3, box3')
2.3 计算观测的概率
print model.score(seen)
输出为
-2.03854530992
3. 训练与数据准备
import numpy as np
from hmmlearn import hmm
states = ["box 1", "box 2", "box3"]
n_states = len(states)
observations = ["red", "white"]
n_observations = len(observations)
model = hmm.MultinomialHMM(n_components=n_states, n_iter=20, tol=0.01)
D1 = [[1], [0], [0], [0], [1], [1], [1]]
D2 = [[1], [0], [0], [0], [1], [1], [1], [0], [1], [1]]
D3 = [[1], [0], [0]]
X = numpy.concatenate([D1, D2, D3])
model.fit(X)
print model.startprob_
print model.transmat_
print model.emissionprob_
print model.score(X)
4.GaussianHMM 参数介绍
http://reader.epubee.com/books/mobile/24/240fbe312d9e3a78b5fe3f238df50e87/text00010.html
原书为《从机器学习到深度学习:基于scikit-learn与TensorFlow的高效开发实战(刘长龙 著)》