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Merge pull request SmirkCao#7 from SmirkCao/hmm
HMM 书中正文部分, 后续单独补充习题部分.
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| #! /usr/bin/env python | ||
| #! -*- coding=utf-8 -*- | ||
| # Project: Lihang | ||
| # Filename: hmm | ||
| # Date: 9/17/18 | ||
| # Author: 😏 <smirk dot cao at gmail dot com> | ||
| import numpy as np | ||
| import argparse | ||
| import logging | ||
| import warnings | ||
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| class HMM(object): | ||
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| def __init__(self, n_component=0, | ||
| Q=None, | ||
| V=None, | ||
| n_iters=5): | ||
| self.A = None | ||
| self.B = None | ||
| self.p = None | ||
| self.M = 0 | ||
| self.N = n_component | ||
| self.T = 0 | ||
| self.Q = Q | ||
| self.V = V | ||
| self.n_iters = n_iters | ||
| self.alpha = None | ||
| self.beta = None | ||
| self.gamma = None | ||
| self.xi = None | ||
| self.Ei = None | ||
| self.Ei_ = None | ||
| self.Ei_j = None | ||
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| def init_param(self, X): | ||
| # 最简单的初始化应该是均匀分布 | ||
| # 另外的方法是Dirichlet Distribution | ||
| # todo: update Dirchlet Distribution | ||
| if self.V is not None: | ||
| self.M = len(self.V) | ||
| else: | ||
| warnings.warn("M warning") | ||
| self.A = np.ones((self.N, self.N))/self.N | ||
| self.B = np.ones((self.N, self.M))/self.M | ||
| self.p = np.ones(self.N)/self.N | ||
| self.T = len(X) | ||
| return self | ||
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| def _do_forward(self, X): | ||
| # todo: logsumexp trick | ||
| alpha = np.zeros((self.N, self.T)) | ||
| # A: NxM | ||
| # B: NxM | ||
| # alpha: NxT | ||
| t = 0 | ||
| o = X[t] | ||
| alpha[:, t] = self.p * self.B[:, o] | ||
| t_rest = np.arange(1, self.T) | ||
| for t in t_rest: | ||
| o = X[t] | ||
| alpha[:, t] = np.sum(alpha[:, t-1]*self.A.T, axis=1)*self.B[:, o] | ||
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| prob = np.sum(alpha[:, -1]) | ||
| return prob, alpha | ||
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| def _do_backward(self, X): | ||
| beta = np.ones((self.N, self.T)) | ||
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| t = -1 | ||
| beta[:, t] = 1 | ||
| # print(self.A, self.B, self.p, X) | ||
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| t_rest = np.arange(self.T-1)[::-1] | ||
| for t in t_rest: | ||
| o = X[t+1] | ||
| beta[:, t] = np.sum(self.A*self.B[:, o]*beta[:, t+1], axis=1) | ||
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| prob = np.sum(self.p*self.B[:, X[0]]*beta[:, 0]) | ||
| # print(beta, prob, prob, "new") | ||
| return prob, beta | ||
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| # 后面这两个主要是为了验证前向后向的结果 | ||
| def forward(self, obs_seq): | ||
| """前向算法""" | ||
| # 来源: https://applenob.github.io/hmm.html | ||
| # F保存前向概率矩阵 | ||
| F = np.zeros((self.N, self.T)) | ||
| F[:, 0] = self.p * self.B[:, obs_seq[0]] | ||
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| for t in range(1, self.T): | ||
| for n in range(self.N): | ||
| F[n, t] = np.dot(F[:, t - 1], (self.A[:, n])) * self.B[n, obs_seq[t]] | ||
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| return F | ||
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| def backward(self, obs_seq): | ||
| """后向算法""" | ||
| # X保存后向概率矩阵 | ||
| # 来源: https://applenob.github.io/hmm.html | ||
| X = np.zeros((self.N, self.T)) | ||
| X[:, -1:] = 1 | ||
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| for t in reversed(range(self.T - 1)): | ||
| X[:, t] = np.sum(self.A * self.B[:, obs_seq[t + 1]]*X[:, t + 1], axis=1) | ||
| prob = np.sum(self.p * self.B[:, 0] * X[:, 0]) | ||
| # print(prob) | ||
| return X | ||
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| def _do_estep(self, X): | ||
| # 在hmmlearn里面是会没有专门的estep的 | ||
| _, self.alpha = self._do_forward(X) | ||
| _, self.beta = self._do_backward(X) | ||
| post_prior = self.alpha*self.beta | ||
| # Eq. 10.24 | ||
| self.gamma = post_prior/np.sum(post_prior) | ||
| # Eq. 10.26 | ||
| left_a = self.alpha | ||
| right_a = np.dot(self.B, np.eye(len(X))[X, :len(set(X))].T)*self.beta | ||
| trans_post_prior = np.array([x*self.A*y for x, y in zip(left_a[:, :-1].T, right_a[:, 1:].T)]) | ||
| self.xi = trans_post_prior/np.sum(trans_post_prior) | ||
| # Eq. 10.27 | ||
| self.Ei = np.sum(self.gamma, axis=1) | ||
| # Eq. 10.28 | ||
| self.Ei_ = np.sum(self.gamma[:, :-1], axis=1) | ||
| # Eq. 10.29 | ||
| self.Ei_j = np.sum(self.xi[:, :, :-1], axis=2) | ||
| return self | ||
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| def _do_mstep(self, X): | ||
| # Eq. 10.39 | ||
| self.A = self.Ei_j/self.Ei | ||
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| # Eq. 10.40 | ||
| gamma_o = np.array([np.outer(x, y) for x, y in zip(self.gamma.T, np.eye(len(X))[X, :len(set(X))].T)]) | ||
| self.B = np.sum(gamma_o, axis=2).T/self.Ei.reshape(-1, 1) | ||
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| # Eq. 10.41 | ||
| self.p = self.gamma[:, 0] | ||
| return self | ||
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| def fit(self, X): | ||
| # 估计模型参数 | ||
| self.init_param(X) | ||
| for n_iter in range(self.n_iters): | ||
| self._do_estep(X) | ||
| self._do_mstep(X) | ||
| # convergence check | ||
| if False: | ||
| return rst | ||
| return self | ||
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| def decode(self, X): | ||
| """ | ||
| Find most likely state sequence corresponding to ``X``. | ||
| """ | ||
| if self.T == 0: | ||
| warnings.warn("T warning") | ||
| if self.N == 0: | ||
| warnings.warn("N warning") | ||
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| hidden_states = np.zeros(self.T) | ||
| delta = np.ones((self.N, self.T)) | ||
| psi = np.zeros((self.N, self.T)) | ||
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| t = 0 | ||
| o = X[t] | ||
| delta[:, t] = self.p*self.B[:, o] | ||
| psi[:, t] = 0 | ||
| t_rest = np.arange(1, self.T) | ||
| for t in t_rest: | ||
| o = X[t] | ||
| delta[:, t] = np.max(delta[:, t-1]*self.A.T, axis=1)*self.B[:, o] | ||
| psi[:, t] = np.argmax(delta[:, t-1]*self.A.T, axis=1) | ||
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| # print("参考答案") | ||
| # print(np.array([[0.1, 0.028, 0.00756], | ||
| # [0.016, 0.0504, 0.01008], | ||
| # [0.28, 0.042, 0.0147]])) | ||
| # print("程序结果") | ||
| # print(delta) | ||
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| prob = np.max(delta[:, -1]) | ||
| hidden_states[-1] = np.argmax(delta[:, -1]) | ||
| # T in 1,...,T-1 | ||
| t_rest = np.arange(self.T)[self.T - 1:0:-1] | ||
| for t in t_rest: | ||
| hidden_states[t-1] = np.argmax(delta[:, t]*self.A[:, int(hidden_states[t])], axis=0) | ||
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| return prob, hidden_states | ||
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| def predict(self, X): | ||
| """ | ||
| Find most likely state sequence corresponding to ``X``. | ||
| """ | ||
| rst = self.decode(X) | ||
| return rst | ||
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| def predict_proba(self): | ||
| post_prior = 0 | ||
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| return post_prior | ||
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| def sample(self): | ||
| rst = None | ||
| return rst | ||
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| def score(self): | ||
| rst = None | ||
| return rst | ||
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| if __name__ == '__main__': | ||
| logging.basicConfig(level=logging.INFO, format='%(asctime)s - %(name)s - %(levelname)s - %(message)s') | ||
| logger = logging.getLogger(__name__) | ||
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| ap = argparse.ArgumentParser() | ||
| ap.add_argument("-p", "--path", required=False, help="path to input data file") | ||
| args = vars(ap.parse_args()) | ||
|
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