隱含馬爾可夫模型（Hidden Markov Model睹簇，HMM）最初是在20世紀(jì)60年代后半期，由Leonard E. Baum和其他一些作者在一系列統(tǒng)計學(xué)論文中描述的械媒。其最初應(yīng)用于語音識別領(lǐng)域劲妙。

1980年代后半期，HMM開始應(yīng)用到生物序列本昏，尤其是DNA序列的分析中。隨后枪汪，在生物信息學(xué)領(lǐng)域涌穆，HMM逐漸成為一項不可或缺的技術(shù)。

本文內(nèi)容包含來自：
[1] 用hmmlearn學(xué)習(xí)隱馬爾科夫模型HMM
[2] 官方文檔

hmmlearn

hmmlearn曾經(jīng)是scikit-learn項目的一部分雀久，現(xiàn)已獨立成單獨的Python包宿稀，可直接通過pip進行安裝，為無監(jiān)督隱馬爾可夫模型赖捌。其官方文檔網(wǎng)址為https://hmmlearn.readthedocs.io/en/stable/祝沸。其有監(jiān)督的版本為seqlearn。

pip3 install hmmlearn

hmmlearn提供三種模型：

MultinomialHMM

方法聲明為

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')

其中巡蘸，較為常用（或?qū)⒏拢┑膮?shù)為：

• n_components：（int）隱含狀態(tài)個數(shù)
• n_iter：（int, optional）訓(xùn)練時循環(huán)（迭代）最大次數(shù)
• tol：（float, optional）Convergence threshold. EM will stop if the gain in log-likelihood is below this value.
• verbose：（bool, optional)賦值為True時奋隶，會向標(biāo)準(zhǔn)輸出輸出每次迭代的概率（score）與本次
• init_params：（string, optional）決定哪些參數(shù)會在訓(xùn)練時被初始化。‘s’ for startprob, ‘t’ for transmat, ‘e’ for emissionprob悦荒。空字符串""代表全部使用用戶提供的參數(shù)進行訓(xùn)練嘹吨。

定義搬味、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

維特比算法預(yù)測狀態(tài)

有說法稱，其返回結(jié)果為ln(prob)蟀拷，文檔原文為“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)))

輸出為

('The ball picked:', 'red, white, red')
('The hidden box', 'box3, box3, box3')

計算觀測的概率

print model.score(seen)

輸出為

-2.03854530992

訓(xùn)練與數(shù)據(jù)準(zhǔn)備

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)