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hmm code.
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‎charpter23_hmm/charpter_23.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"\n",
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"class HMM(object):\n",
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" def __init__(self, N, M, pi=None, A=None, B=None):\n",
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" # 可能的状态数\n",
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" self.N = N\n",
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" # 可能的观测数\n",
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" self.M = M\n",
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" # 初始状态概率向量\n",
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" self.pi = pi\n",
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" # 状态转移概率矩阵\n",
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" self.A = A\n",
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" # 观测概率矩阵\n",
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" self.B = B\n",
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"\n",
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" # 根据给定的概率分布随机返回数据\n",
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" def rdistribution(self, dist): \n",
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" r = np.random.rand()\n",
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" for ix, p in enumerate(dist):\n",
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" if r < p: \n",
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" return ix\n",
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" r -= p\n",
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"\n",
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" # 生成HMM观测序列\n",
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" def generate(self, T):\n",
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" # 根据初始概率分布生成第一个状态\n",
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" i = self.rdistribution(self.pi) \n",
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" # 生成第一个观测数据\n",
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" o = self.rdistribution(self.B[i]) \n",
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" observed_data = [o]\n",
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" # 遍历生成剩下的状态和观测数据\n",
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" for _ in range(T-1): \n",
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" i = self.rdistribution(self.A[i])\n",
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" o = self.rdistribution(self.B[i])\n",
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" observed_data.append(o)\n",
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" return observed_data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[1, 0, 0, 1, 0]\n"
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]
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}
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],
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"source": [
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"pi = np.array([0.25, 0.25, 0.25, 0.25])\n",
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"A = np.array([\n",
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" [0, 1, 0, 0],\n",
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" [0.4, 0, 0.6, 0],\n",
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" [0, 0.4, 0, 0.6],\n",
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" [0, 0, 0.5, 0.5]])\n",
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"B = np.array([\n",
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" [0.5, 0.5],\n",
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" [0.6, 0.4],\n",
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" [0.2, 0.8],\n",
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" [0.3, 0.7]])\n",
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"hmm = HMM(4, 2, pi, A, B)\n",
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"print(hmm.generate(5))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.01983169125\n"
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]
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}
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],
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"source": [
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"### 前向算法计算条件概率\n",
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"def prob_calc(O):\n",
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" '''\n",
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" 输入：\n",
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" O：观测序列\n",
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" 输出：\n",
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" alpha.sum()：条件概率\n",
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" '''\n",
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" # 初值\n",
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" alpha = pi * B[:, O[0]]\n",
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" # 递推\n",
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" for o in O[1:]:\n",
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" alpha = np.sum(A * alpha.reshape(-1,1) * B[:,o].reshape(1,-1), axis=0)\n",
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" return alpha.sum()\n",
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"\n",
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"# 给定观测\n",
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"O = [1,0,1,0,0]\n",
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"print(prob_calc(O))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.01983169125\n"
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]
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}
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],
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"source": [
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"### 前向算法计算条件概率\n",
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"def prob_calc(O):\n",
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" '''\n",
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" 输入：\n",
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" O：观测序列\n",
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" 输出：\n",
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" alpha.sum()：条件概率\n",
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" '''\n",
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" # 初值\n",
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" alpha = pi * B[:, O[0]]\n",
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" # 递推\n",
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" for o in O[1:]:\n",
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" alpha_next = np.empty(4)\n",
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" for j in range(4):\n",
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" alpha_next[j] = np.sum(A[:,j] * alpha * B[j,o])\n",
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" alpha = alpha_next\n",
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" return alpha.sum()\n",
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"\n",
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"# 给定观测\n",
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"O = [1,0,1,0,0]\n",
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"print(prob_calc(O))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[0, 1, 2, 3, 3]\n"
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]
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}
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],
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"source": [
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"### 序列标注问题和维特比算法\n",
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"def viterbi_decode(O):\n",
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" '''\n",
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" 输入：\n",
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" O：观测序列\n",
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" 输出：\n",
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" path：最优隐状态路径\n",
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" ''' \n",
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" # 序列长度和初始观测\n",
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" T, o = len(O), O[0]\n",
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" # 初始化delta变量\n",
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" delta = pi * B[:, o]\n",
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" # 初始化varphi变量\n",
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" varphi = np.zeros((T, 4), dtype=int)\n",
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" path = [0] * T\n",
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" # 递推\n",
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" for i in range(1, T):\n",
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" delta = delta.reshape(-1, 1) \n",
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" tmp = delta * A\n",
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" varphi[i, :] = np.argmax(tmp, axis=0)\n",
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" delta = np.max(tmp, axis=0) * B[:, O[i]]\n",
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" # 终止\n",
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" path[-1] = np.argmax(delta)\n",
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" # 回溯最优路径\n",
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" for i in range(T-1, 0, -1):\n",
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" path[i-1] = varphi[i, path[i]]\n",
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" return path\n",
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"\n",
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"# 给定观测序列\n",
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"O = [1,0,1,1,0]\n",
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"print(viterbi_decode(O))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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},
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"toc": {
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"base_numbering": 1,
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"nav_menu": {},
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"number_sections": true,
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"sideBar": true,
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"skip_h1_title": false,
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"title_cell": "Table of Contents",
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"title_sidebar": "Contents",
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"toc_cell": false,
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"toc_position": {},
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"toc_section_display": true,
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"toc_window_display": false
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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