hmm实践.ipynb

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   "source": [
    "import numpy as np\n",
    "from hmmlearn import hmm\n",
    "#http://hmmlearn.readthedocs.io/en/latest/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "隐藏状态：3个盒子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "states = [\"box 1\", \"box 2\", \"box3\"]\n",
    "n_states = len(states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "观测状态：2种球"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "observations = [\"red\", \"white\"]\n",
    "n_observations = len(observations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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   "outputs": [],
   "source": [
    "start_probability = np.array([0.2, 0.4, 0.4])\n",
    "\n",
    "transition_probability = np.array([\n",
    "  [0.5, 0.2, 0.3],\n",
    "  [0.3, 0.5, 0.2],\n",
    "  [0.2, 0.3, 0.5]\n",
    "])\n",
    "\n",
    "emission_probability = np.array([\n",
    "  [0.5, 0.5],\n",
    "  [0.4, 0.6],\n",
    "  [0.7, 0.3]\n",
    "])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#用于离散观测状态\n",
    "model = hmm.MultinomialHMM(n_components=n_states)\n",
    "\n",
    "model.startprob_=start_probability\n",
    "model.transmat_=transition_probability\n",
    "model.emissionprob_=emission_probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 维特比算法，看到的是[0,1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seen = np.array([[0,1,0]]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "logprob, box = model.decode(seen, algorithm=\"viterbi\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到的结果跟我们算的是一样的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['box3' 'box3' 'box3']\n"
     ]
    }
   ],
   "source": [
    "print (np.array(states)[box])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "predict也可以"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['box3' 'box3' 'box3']\n"
     ]
    }
   ],
   "source": [
    "box2 = model.predict(seen)\n",
    "print (np.array(states)[box2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到观测序列的概率 ln0.13022≈−2.0385"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.03854530992\n"
     ]
    }
   ],
   "source": [
    "print (model.score(seen))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### EM算法求解模型参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "tol : 停机阈值\n",
    "n_iter : 最大迭代次数 \n",
    "n_components : 隐藏状态数目 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "startprob_ [  1.00830546e-21   9.99155974e-01   8.44026026e-04]\n",
      "-----------------------------------------\n",
      "transmat_ [[  3.54305307e-01   4.25087407e-01   2.20607286e-01]\n",
      " [  9.66579437e-01   1.41083293e-04   3.32794799e-02]\n",
      " [  4.18739654e-01   1.17370397e-01   4.63889949e-01]]\n",
      "-----------------------------------------\n",
      "emissionprob_ [[ 0.10352942  0.89647058]\n",
      " [ 0.99860862  0.00139138]\n",
      " [ 0.80494989  0.19505011]]\n",
      "-----------------------------------------\n",
      "score -6.69039955756\n"
     ]
    }
   ],
   "source": [
    "model2 = hmm.MultinomialHMM(n_components=n_states, n_iter=20, tol=0.01)\n",
    "X2 = np.array([[0,1,0,1],[0,0,0,1],[1,0,1,1]])\n",
    "model2.fit(X2)\n",
    "\n",
    "print ('startprob_',model2.startprob_)\n",
    "print ('-----------------------------------------')\n",
    "print ('transmat_',model2.transmat_)\n",
    "print ('-----------------------------------------')\n",
    "print ('emissionprob_',model2.emissionprob_)\n",
    "print ('-----------------------------------------')\n",
    "print ('score',model2.score(X2))"
   ]
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