hmms.ipynb

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    "HMMs Library \n",
    "============================\n",
    "#### (Discrete & Continuous hidden markov models )\n",
    "\n",
    "The document contain the tutorial ( usage explained by example ) for the hidden markov models library [link to pip].\n",
    "* [The **first** part](#dthmm) will cover disrete-time hidden markov model (**DtHMM**)\n",
    "* [The **second** part](#cthmm) will be dedicated to continuous-time hidden markov model (**CtHMM**)\n",
    "* [The **third** part](#conv) will compare the convergences of **both** models\n",
    "* [The **fourth** part](#dataset) will explain how to use more complex **datasets** and run **multiple trains** by one function call\n",
    "\n",
    "The all of the part are independent, so you do not need to run all notebook, if you are interested only in one of them. \n",
    "\n",
    "\n",
    "If you are not familiar with the hidden markov model theory, We recommend ...\n",
    "%todo: refer to DP theory, (simple guide to cthmm?), github, sources\n"
   ]
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   "source": [
    "<a id='dthmm'></a>\n",
    "Part 1: Discrete Time Hidden Markov Model\n",
    "---------------------------------------------------"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
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   "source": [
    "### Construct DtHMM \n",
    "You can directly initialize the DtHMM by passing the **model parameters**.  \n",
    "\n",
    "We will create simple DtHMM of two hidden states and three output variables."
   ]
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   "cell_type": "code",
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   "source": [
    "# A is the matrix of transition probabilities from state [row] to state [column].\n",
    "A = np.array([[0.9,0.1],[0.4,0.6]])\n",
    "# B is the matrix of probabilities that the state [row] will emmit output variable [column].\n",
    "B = np.array([[0.9,0.08,0.02],[0.2,0.5,0.3]])\n",
    "# Pi is the vector of initial state probabilities.   \n",
    "Pi = np.array( [0.8,0.2] )\n",
    "\n",
    "# Create DtHMM by given parameters.\n",
    "dhmm = hmms.DtHMM(A,B,Pi)"
   ]
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   "source": [
    "Or you can initialize it by **random parameters**. Passing the number of hidden states and output variables. "
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [],
   "source": [
    "dhmm_random = hmms.DtHMM.random(2,3)"
   ]
  },
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   "source": [
    "### Save & Read from File\n",
    "Once you have created the model you can **save** its parameters in file simply by calling *save_params* method.  "
   ]
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   "execution_count": 4,
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   "outputs": [],
   "source": [
    "dhmm.save_params(\"hello_dthmm\") "
   ]
  },
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   "source": [
    "The method stored the parameters in *.npz* format.  \n",
    "\n",
    "The saved file can be later used to **read** parametrs for model initialization."
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [],
   "source": [
    "dhmm_from_file = hmms.DtHMM.from_file( \"hello_dthmm.npz\" )"
   ]
  },
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   "source": [
    "### Set & Get Parameters\n",
    "Later you can always **set** parameters with triple of methods corresponding to the constructors."
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [],
   "source": [
    "dhmm.set_params(A,B,Pi)\n",
    "dhmm.set_params_random(2,3)\n",
    "dhmm.set_params_from_file( \"hello_dthmm.npz\" )"
   ]
  },
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   "source": [
    "You can **get** parameters by calling them separately,"
   ]
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   "cell_type": "code",
   "execution_count": 7,
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    {
     "data": {
      "text/plain": [
       "(array([[ 0.9,  0.1],\n",
       "        [ 0.4,  0.6]]), array([[ 0.9 ,  0.08,  0.02],\n",
       "        [ 0.2 ,  0.5 ,  0.3 ]]), array([ 0.8,  0.2]))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dhmm.a, dhmm.b, dhmm.pi"
   ]
  },
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   "source": [
    "or **get** them **all** together as the triple."
   ]
  },
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   "cell_type": "code",
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   "source": [
    "(A,B,Pi) = dhmm.params"
   ]
  },
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   "source": [
    "### Generate Random State and Emission Sequence\n",
    " Now we can use our model to generate state and emission sequence.   \n",
    " The model will randomly choose which transition or emission will happen, taking into consideration the parameters we have previously defined.\n"
   ]
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   "execution_count": 9,
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HzufzDdlFt9vtCd/rLMuyJq/9i/H7/fjbv/3bhLcWalkTAM264sDA3L797W8j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\nIiIP+P+RBazifjuq9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14c5e41748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq_len = 20\n",
    "s_seq, e_seq = dhmm.generate( seq_len )\n",
    "\n",
    "#resize plot\n",
    "plt.rcParams['figure.figsize'] = [20,20]\n",
    "\n",
    "hmms.plot_hmm( s_seq, e_seq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Find Most Likely State Sequence\n",
    "If we have the model parameters and emission sequence, we can find the most probable state sequence that would generate it. Notice, that it can be different, than the actual sequence that has generated the emissions.  \n",
    "We will use Viterbi algorithm for the calculation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qlKqxcnNzsXLlSlV33z/f1KlTL+j2GwwGzJ49G2PHjlU1jpY1Wa1WPPvss5gw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\n2bKPUZgoqvWs9sCfOY/PWOL72fzbvvOcHtjZrQ+9YZHqE46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H1H/v7crs3y6nvkV20l9u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\nnGthNxt0TFAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14c5e416d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "( log_prob, s_seq ) =  dhmm.viterbi( e_seq )\n",
    "# Let's print the most likely state sequence, it can be same or differ from the sequence above.\n",
    "hmms.plot_hmm( s_seq, e_seq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "The *log_prob* parameter store the probability of the sequence.  \n",
    "All the probabilities in the library are stored in the logarithm of their actual value. As the number of possible sequences grows exponentialy by it length, it could easily lead to float underflow.  \n",
    "You can easily transform it to the normal scale value applying *exp* function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5822415043907858e-07"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp( log_prob )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### State Confidence "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We may want to know what is the probability that the emission was generated by some concrete state. You can get the result for every state in every time by calling the method *states_confidence*. **Notice** that the viterbi most probable sequence,  presented above, doesn't neccessery contain the most probable states from this method as here is not important the consecutive states transition probability. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.97222557,  0.02777443],\n",
       "       [ 0.98371853,  0.01628147],\n",
       "       [ 0.98506713,  0.01493287],\n",
       "       [ 0.98383707,  0.01616293],\n",
       "       [ 0.97312765,  0.02687235],\n",
       "       [ 0.8928591 ,  0.1071409 ],\n",
       "       [ 0.29272483,  0.70727517],\n",
       "       [ 0.21393163,  0.78606837],\n",
       "       [ 0.88232335,  0.11767665],\n",
       "       [ 0.97172518,  0.02827482],\n",
       "       [ 0.9836814 ,  0.0163186 ],\n",
       "       [ 0.9852664 ,  0.0147336 ],\n",
       "       [ 0.98537202,  0.01462798],\n",
       "       [ 0.98459082,  0.01540918],\n",
       "       [ 0.97854026,  0.02145974],\n",
       "       [ 0.93327669,  0.06672331],\n",
       "       [ 0.59487146,  0.40512854],\n",
       "       [ 0.748624  ,  0.251376  ],\n",
       "       [ 0.39914117,  0.60085883],\n",
       "       [ 0.84016743,  0.15983257]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_prob_table = dhmm.states_confidence( e_seq )\n",
    "np.exp( log_prob_table )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='dtest'></a>\n",
    "### The Probability of the Emission Sequence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can compute the probability, that the model will generate the emission sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4317925829470709e-06"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp( dhmm.emission_estimate( e_seq ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### The Probability of the State and Emission Sequences "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Similary we can compute the probabilty of the state and emission sequences given the model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5822415043907858e-07"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp( dhmm.estimate( s_seq, e_seq ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Notice!**  - You can simply count the probability estimations for whole dataset by one command, watch [The chapter 4](#dsest)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Generate Artificial Dataset\n",
    "\n",
    "You can easily generate many sequences in once by using the generate_data function.\n",
    "The generated emission sequences are in the form that is suitable for training of parameters. You can switch times=True, if you want to generate also the corresponding equidistant time sequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]]),\n",
       " array([[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 2, 2, 2, 0, 0, 0, 0]]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seq_num= 3   #number of data sequences\n",
    "seq_len= 10  #length of each sequence\n",
    "\n",
    "dhmm.generate_data( (seq_num,seq_len) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Parameters Estimation - Baum Welch Algorithm\n",
    "We usually do not know the real parameters of the model. But, if we have sufficient data, we can estimate them by EM algorithm.  \n",
    "Here we will have several output variables (emissions) sequences and we will show, how to use them to train the model parameters\n",
    "\n",
    "Let's start by creating some artifficial data. We will use the previously defined *dhmm* model for it.\n",
    "\n",
    "**Notice!**  - For more detail information about possible datasets watch  [The chapter 4](#datasets).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0,\n",
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       "        0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
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       "        0, 0, 0, 0, 0, 0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seq_num = 5\n",
    "seq_len = 50\n",
    "\n",
    "_ , data = dhmm.generate_data( (seq_num,seq_len) )\n",
    "\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now, we will create the model with random parameters, that will be eventually trained to match the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial probabilities (π) :\n"
     ]
    },
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     "text": [
      "Transition probabilities matrix (A):\n"
     ]
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     "name": "stdout",
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     "text": [
      "Emission probabilities matrix (B):\n"
     ]
    },
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   ],
   "source": [
    "dhmm_r = hmms.DtHMM.random( 2,3 )\n",
    "# We can print all the parameters.\n",
    "hmms.print_parameters( dhmm_r )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's compare the dataset likelihood estimation of model used for generating the data and the random parameters model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generator model: 7.99358091973e-65\n",
      "Random model:    5.74532109077e-162\n"
     ]
    }
   ],
   "source": [
    "print( \"Generator model:\" , np.exp( dhmm.data_estimate(data)   ) )\n",
    "print( \"Random model:   \" ,np.exp( dhmm_r.data_estimate(data) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Most likely the probability that the data was generated by random model is extremly low.\n",
    "\n",
    "Now we can take the random model and reestimate it to fit the data better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration  4351609 / 10\n",
      "iteration  2 / 10\n",
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      "iteration  2 / 10\n",
      "Reestimated model after 10 iterations:    8.42721211172e-67\n"
     ]
    }
   ],
   "source": [
    "dhmm_r.baum_welch( data, 10 )\n",
    "print( \"Reestimated model after 10 iterations:   \" ,np.exp( dhmm_r.data_estimate(data) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The probability of the reestimated model should now be similiar (possibly even higher) that the generator's model. If it is not, you can try to run the estimation procedure more time at different randomly generated models. It could happen that the estimation fall in the local optima.\n",
    "\n",
    "If you are satisfied with the results, you can run some more iteration to fine-tune it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Reestimated model after 110 iterations:    1.56505367922e-66\n"
     ]
    }
   ],
   "source": [
    "dhmm_r.baum_welch( data, 100 )\n",
    "print( \"Reestimated model after 110 iterations:   \" ,np.exp( dhmm_r.data_estimate(data) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can compare the parameters of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial probabilities (π) :\n"
     ]
    },
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2\n",
       "0  0.9  0.08  0.02\n",
       "1  0.2  0.50  0.30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hmms.print_parameters( dhmm_r )\n",
    "hmms.print_parameters( dhmm )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "source": [
    "Alternatively, we can run *baum_welch_graph* method to get learning curve of estimated probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration  -965849439 / 50\n",
      "iteration  2 / 50\n",
      "iteration  2 / 50\n",
      "iteration  2 / 50\n",
      "iteration  2 / 50\n",
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      "iteration  2 / 50\n",
      "iteration  2 / 50\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([  3.96183691e-97,   9.13140377e-67,   9.24469419e-67,\n",
       "         9.35457728e-67,   9.46195517e-67,   9.56755384e-67,\n",
       "         9.67195352e-67,   9.77561238e-67,   9.87888500e-67,\n",
       "         9.98203732e-67,   1.00852587e-66,   1.01886720e-66,\n",
       "         1.02923422e-66,   1.03962842e-66,   1.05004692e-66,\n",
       "         1.06048317e-66,   1.07092749e-66,   1.08136764e-66,\n",
       "         1.09178939e-66,   1.10217702e-66,   1.11251383e-66,\n",
       "         1.12278254e-66,   1.13296581e-66,   1.14304654e-66,\n",
       "         1.15300828e-66,   1.16283549e-66,   1.17251379e-66,\n",
       "         1.18203015e-66,   1.19137306e-66,   1.20053258e-66,\n",
       "         1.20950041e-66,   1.21826988e-66,   1.22683593e-66,\n",
       "         1.23519503e-66,   1.24334509e-66,   1.25128534e-66,\n",
       "         1.25901622e-66,   1.26653925e-66,   1.27385687e-66,\n",
       "         1.28097233e-66,   1.28788954e-66,   1.29461295e-66,\n",
       "         1.30114746e-66,   1.30749828e-66,   1.31367085e-66,\n",
       "         1.31967078e-66,   1.32550375e-66,   1.33117548e-66,\n",
       "         1.33669165e-66,   1.34205792e-66,   1.34727982e-66])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dhmm_r = hmms.DtHMM.random(2,3) \n",
    "out = dhmm_r.baum_welch( data, 50, est=True )\n",
    "\n",
    "np.exp(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's plot it in the graph, comparing the results in ratio with *real* data-generator model. ( Notice, it is the ratio of logaritmic probability values. )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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JlUplwps9b5sf6A1vpLqqyOXHjEnbmqqccevUbNxSW/YkAAAA4C0Qlyhd364d8h+Hj8qs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14c5c890b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "real = dhmm.data_estimate(data)\n",
    "#For better visibility of the graph, we cut first two values.\n",
    "plt.plot( out[2:] / real  )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Maximum Likelihood Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sometimes, we can have a dataset of full observations (i.e. both emission and hidden states sequences). We can use method *maximum_likelihood estimation* to estimate most likely parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of the dataset being generated by the original model is: 9.59995696965e-97 .\n",
      "The probability of the dataset being generated by the MLE model is: 6.54309210608e-95 .\n"
     ]
    }
   ],
   "source": [
    "seq_num = 5\n",
    "seq_len = 50\n",
    "\n",
    "#generate artificial dataset of both hidden states and emissions sequences\n",
    "s_seqs , e_seqs = dhmm.generate_data( (seq_num,seq_len) )\n",
    "\n",
    "dhmm_r = hmms.DtHMM.random(2,3) \n",
    "dhmm_r.maximum_likelihood_estimation(s_seqs,e_seqs)\n",
    "\n",
    "log_est =     dhmm.full_data_estimate  ( s_seqs, e_seqs )\n",
    "log_est_mle = dhmm_r.full_data_estimate( s_seqs, e_seqs )\n",
    "\n",
    "print(\"The probability of the dataset being generated by the original model is:\", \\\n",
    "np.exp(log_est), \".\" )\n",
    "print(\"The probability of the dataset being generated by the MLE model is:\", \\\n",
    "np.exp(log_est_mle), \".\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "For the discrete-time model will be the probability of dataset estimated by parameters from *maximum_likelihood_estimation* always higher equal to probability of being generated by original model. It is the consequence of statistical inaccuracy of dataset. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='cthmm'></a>\n",
    "Part 2: Continuous Time Hidden Markov Model\n",
    "-----------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Construct CtHMM \n",
    "Construction of CtHMM is similar to the discrete model. \n",
    "\n",
    "You can directly initialize the CtHMM by passing the **model parameters**.  \n",
    "We will create simple CtHMM of three hidden states and three output variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Q is the matrix of transition rates from state [row] to state [column].\n",
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "# B is the matrix of probabilities that the state [row] will emmit output variable [column].\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "# Pi is the vector of initial state probabilities.   \n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "# Create CtHMM by given parameters.\n",
    "chmm = hmms.CtHMM(Q,B,Pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Or you can initialize it by **random parameters**. Passing the number of hidden states and output variables.  \n",
    "By default are the parameters generated by exponential distribution and than normalized to sum to one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_random = hmms.CtHMM.random(3,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "You can choose generating by uniform distribution passing the parameter *method*. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_random = hmms.CtHMM.random(3,3,method=\"unif\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Save & Read from File\n",
    "\n",
    "Once you have created the model you can save its parameters in file simply by calling save_params method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm.save_params(\"hello_cthmm\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The method stored the parameters in .npz format.\n",
    "The saved file can be later used to read parametrs for model initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_from_file = hmms.CtHMM.from_file( \"hello_cthmm.npz\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Set & Get Parameters\n",
    "Later you can always set parameters with triple of methods corresponding to the constructors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm.set_params(Q,B,Pi)\n",
    "chmm.set_params_random(3,3)\n",
    "chmm.set_params_from_file( \"hello_cthmm.npz\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "You can **get** parameters by calling them separately,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm.q, chmm.b, chmm.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "or get them all together as the triple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "(A,B,Pi) = chmm.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Generate Random Sequence\n",
    "Now we can use our model to **generate** time, state and emission sequence.\n",
    "The model will **randomly** choose which transition or emission will happen, taking into consideration the parameters we have previously defined.\n",
    "\n",
    "The times are generated with **exponencial** waiting times, you can define the parameter of exponencial distribution as second optional parameter. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "seq_len = 10\n",
    "t_seq, s_seq, e_seq = chmm.generate( seq_len, 0.5)\n",
    "\n",
    "#resize plot\n",
    "plt.rcParams['figure.figsize'] = [20,20]\n",
    "\n",
    "hmms.plot_hmm( s_seq, e_seq, time=t_seq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Optionally, you can generate the sequences by putting your own time sequence (as list or numpy array ) with wished observation times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t_seq, s_seq, e_seq = chmm.generate( 7, time=[0,3,5,7,8,11,14])\n",
    "\n",
    "#resize plot\n",
    "plt.rcParams['figure.figsize'] = [20,20]\n",
    "\n",
    "hmms.plot_hmm( s_seq, e_seq, time=t_seq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Find Most Likely State Sequence\n",
    "If we have corresponding time and emission sequence, we can find the most probable state sequence that would generate it given the current model parameters. Notice, that it can be different, than the actual sequence that has generated the emissions.  \n",
    "We will use Viterbi algorithm for the calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "( log_prob, s_seq ) =  chmm.viterbi( t_seq, e_seq )\n",
    "# Let's print the most likely state sequence, it can be same or differ from the sequence above.\n",
    "hmms.plot_hmm( s_seq, e_seq, time = t_seq )\n",
    "print( \"Probability of being generated by the found state sequence:\", np.exp( log_prob ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### State Confidence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We may want to know what is the probability that the emission was generated by some concrete state. You can get the result for every state in every time by calling the method *states_confidence*. **Notice** that the viterbi most probable sequence,  presented above, doesn't neccessery contain the most probable states from this method as here is not important the consecutive states transition probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "log_prob_table = chmm.states_confidence( t_seq, e_seq )\n",
    "np.exp( log_prob_table )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### The Probability of the Time and Emission Sequences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can compute the probability, of the emission sequence given model and its time sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm.emission_estimate( t_seq, e_seq ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### The Probability of the State, Time and Emission Sequences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Similary we can compute the probabilty of the state, time and emission sequences given the model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm.estimate( s_seq, t_seq, e_seq ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Notice!**  - You can simply count the probability estimations for whole dataset by one command, watch [The chapter 4](#dsest)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Generate Artificial  Dataset\n",
    "You can easily generate many sequences in once by using the *generate_data* function.  \n",
    "The generated data are in the form that is suitable for training of parameters. \n",
    "You can switch *states=True*, if you want to generate also the corresponding state sequences.\n",
    "\n",
    "The times are generated with **exponencial** waiting times, you can define the parameter of exponencial distribution as second optional parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "seq_num= 5   #number of data sequences\n",
    "seq_len= 30  #length of each sequence\n",
    "\n",
    "t,e = chmm.generate_data( (seq_num,seq_len) )\n",
    "t,e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Parameters Estimation - Continuous Version of Baum Welch Algorithm\n",
    "\n",
    "We will use the previously generated data for the training of randomly generated model.\n",
    "\n",
    "**Notice!**  - Always use the integers in your time points dataset. Floats times are also supported, but it can make the computation significantly slower and you should know, why you are using them. For more detail information watch [The chapter 4](#dataset)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 3,3 )\n",
    "# We can print all the parameters.\n",
    "hmms.print_parameters( chmm_r )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we can compare the probabilities, that the data was generated by the given model. Its ratio is most probably not so big as in the disrete model. It is because the intervals between the observations are the source of many unknown, so it is pushing the probability of real model down. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "print( \"Generator model:\" , np.exp( chmm.data_estimate(t,e)   ) )\n",
    "print( \"Random model:   \" ,np.exp( chmm_r.data_estimate(t,e) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's run the EM algorithm for couple of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "out = chmm_r.baum_welch( t,e, 100, est=True )\n",
    "\n",
    "np.exp(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We will plot its probabilities estimations in ratio with generator model. (Notice, it is the ratio of logarithms of probabilities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t, e )\n",
    "#For better visibility of the graph, we cut first two values.\n",
    "plt.plot( out[2:] / real  )\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Maximum Likelihood Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sometimes, we can have a dataset of full observations (i.e. both emission and hidden states sequences). We can use method *maximum_likelihood_estimation* to estimate most likely parameters. The usage and parameters of the methods are similiar to the *baum_welch method*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "seq_num = 5\n",
    "seq_len = 50\n",
    "\n",
    "#generate artificial dataset of times, hidden states and emissions sequences\n",
    "t_seqs, s_seqs, e_seqs = chmm.generate_data( (seq_num,seq_len), states=True )\n",
    "\n",
    "chmm_r = hmms.CtHMM.random(3,3) \n",
    "graph = chmm_r.maximum_likelihood_estimation(s_seqs,t_seqs,e_seqs,100,est=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "#print the convergence graph\n",
    "log_est =  chmm.full_data_estimate  ( s_seqs,t_seqs,e_seqs )\n",
    "\n",
    "plt.plot( graph / log_est )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='conv'></a>\n",
    "Part 3: Comparison of Models Convergences\n",
    "-----------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this chapter we will compare the convergence rate of discrete and continuous models. It will show some functions usefull for convergence among model parameters.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We will start by defining the continuous time model. For that, who have read the previous section, it will be the familiar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "chmm = hmms.CtHMM( Q,B,Pi )\n",
    "hmms.print_parameters( chmm )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can simply create discrete model with equivalent parameters, using function *get_dthmm_params*.  \n",
    "By default, it will create the model with transition probabilities equal to one time unit probability transition in continuous model. You can pass the optional parameter for different time steps.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm = hmms.DtHMM( *chmm.get_dthmm_params() )\n",
    "hmms.print_parameters( dhmm )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can let the disrete model to generate the data sufficient for both models by passing the *times* parameter as *True*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t,_,e = dhmm.generate_data( (50,50), times=True )   \n",
    "# The free space in the return triple is for the state sequences, \n",
    "# we do not need them for the training "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can compare the estimation of the data, using both of the model. (They should be the same.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "creal = chmm.data_estimate(t,e)\n",
    "dreal = dhmm.data_estimate(e)\n",
    "print(\"Data estimation by continuous model:\", creal)\n",
    "print(\"Data estimation by discrete model:  \", dreal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we will create two equivalent random models. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ct = hmms.CtHMM.random(3,3)\n",
    "dt = hmms.DtHMM( *ct.get_dthmm_params() )\n",
    "    \n",
    "hmms.print_parameters( ct )\n",
    "hmms.print_parameters( dt )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We will train them at our dataset. (It can take a while.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "iter_num = 50\n",
    "outd = dt.baum_welch( e,   iter_num, est=True )\n",
    "outc = ct.baum_welch( t,e, iter_num, est=True )\n",
    "outd,outc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can plot and compare both convergence rates. From the essence of models, the continuous model will probably  converge a bit slower, but finally will reach the similar value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "plt.plot( outd[1:] / dreal  )\n",
    "plt.plot( outc[1:] / dreal, color=\"red\"  )\n",
    "#plt.savefig('my_plot.svg')  #Optional save the figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='dataset'></a>\n",
    "## Part 4: Advance Work with Datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Various Length of Training Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "There are two supported data-structures, that you can pass toward training:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 1. The Numpy Matrix\n",
    "The two dimensional array, where the rows consist of training sequences.  \n",
    "Though, this way is restricted in the way that all the vectors need to have the same size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_n = np.array(  [[0, 0, 0, 1, 1, 1, 1, 1, 1, 1],\n",
    "                     [0, 0, 0, 0, 1, 1, 1, 0, 1, 0],\n",
    "                     [2, 0, 1, 0, 0, 0, 0, 0, 0, 0]] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm_r = hmms.DtHMM.random( 2,3 )\n",
    "graph_n = dhmm_r.baum_welch( data_n, 10, est=True )\n",
    "np.exp( dhmm_r.data_estimate(data_n) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 2. The List of Numpy Vectors\n",
    "The standard Python list, consisting of Numpy vectors.\n",
    "Every vector can have different length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_l = [ np.array( [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1] ) ,\n",
    "           np.array( [0, 1, 0, 0, 1, 0, 1 ] ),\n",
    "           np.array( [2, 0, 1, 0, 0, 0, 0, 0, 0, 0] ) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm_r = hmms.DtHMM.random( 2,3 )\n",
    "graph_l = dhmm_r.baum_welch( data_l, 10, est=True )\n",
    "np.exp( dhmm_r.data_estimate(data_l) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# you can plot the graphs, just for fun.\n",
    "plt.plot( graph_n, color='red' )\n",
    "plt.plot( graph_l )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Continuous-Time HMM\n",
    "The work with datasets in CtHMM is analogous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_n = np.array(  [[0, 0, 0, 1],\n",
    "                     [0, 2, 0, 0],\n",
    "                     [2, 0, 1, 0] ] )\n",
    "time_n = np.array(  [[0, 1, 3, 4],\n",
    "                     [0, 2, 3, 5],\n",
    "                     [0, 2, 4, 6] ] )\n",
    "\n",
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph_n = chmm_r.baum_welch( time_n, data_n, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate(time_n, data_n) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_l = [ np.array( [0, 0, 2, 0 ] ) ,\n",
    "           np.array( [0, 1, 0, 0, 1 ] ),\n",
    "           np.array( [2, 0, 1 ] ) ]\n",
    "time_l = [ np.array( [0, 1, 2, 4 ] ) ,\n",
    "           np.array( [0, 1, 3, 5, 6 ] ),\n",
    "           np.array( [0, 2, 3 ] ) ]\n",
    "\n",
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph_n = chmm_r.baum_welch( time_l, data_l, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate(time_l, data_l) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Time Sequences in Floats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The time sequences datatypes can be **integers** or **floats**.\n",
    "However both datatypes are allowed, it is strongly *adviced* to *use* integers or floats with *integral distance*\n",
    "(be carefull about float operation unprecision here.)  \n",
    "The *non-integral* time intervals among two neigbouring observation are *computationaly costly*, as it doesn't allow to compute matrix power and more complex operations are needed.  \n",
    "Later are showed two examples with the float data and possible *tricks* how to make computation *faster*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Example one:  Change intervals length to integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data = np.array(  [[0, 0, 0, 1],\n",
    "                   [0, 2, 0, 0],\n",
    "                   [2, 0, 1, 0] ] )\n",
    "time = np.array(  [[0, 1.5, 3.4, 4.7],\n",
    "                   [0, 2.6, 5.7, 8.9],\n",
    "                   [0, 2.2, 4.1, 9.8] ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Use data as float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph_f = chmm_r.baum_welch( time, data, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate(time, data) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "or use the **trick** so the intervals were integral.\n",
    "Here it is enough to **multiply** it times 10.   \n",
    "**Notice**: Here we are working with randomly generated jump rates matrix, otherwise you would need to reevaluate its values, when multiplying times. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph = chmm_r.baum_welch( time*10, data, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate( time*10, data ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Example 2: Approximate the time values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sometimes, depending upon the data, the exact observation time may not be important, so the small approximation can be helpful to get better computational time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data = np.array(  [[0, 0, 0, 1],\n",
    "                   [0, 2, 0, 0],\n",
    "                   [2, 0, 1, 0] ] )\n",
    "time = np.array(  [[0, 1.54587435, 3.4435434, 4.74535345],\n",
    "                   [0, 2.64353245, 5.7435435, 8.94353454],\n",
    "                   [0, 2.24353455, 4.1345435, 9.83454354] ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Use data as float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph_f = chmm_r.baum_welch( time, data, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate(time, data) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "or perform the **trick**. Here multiply by 100 and round to the integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "time = np.round( time * 100 )\n",
    "\n",
    "chmm_r = hmms.CtHMM.random( 2,3 )\n",
    "graph = chmm_r.baum_welch( time, data, 10, est=True ) \n",
    "np.exp( chmm_r.data_estimate(time, data) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='dsest'></a>\n",
    "### Datasets Probability Estimations "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We have showed previously how to compute sequence probability estimations in [The discrete](#dtest) and [continuous](#ctest) model.  \n",
    "Here it is showed, how to make it for whole dataset by using just one command.  \n",
    "(We will show it at continuous time model, the discrete one is analogous, just omit the time sequences.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "seq_num= 10   #number of data sequences\n",
    "seq_len= 10   #length of each sequence\n",
    "\n",
    "# Create data and generate model\n",
    "\n",
    "chmm = hmms.CtHMM.random(3,3)\n",
    "t,s,e = chmm.generate_data( (seq_num,seq_len), states=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### The Probability of the Time and Emission Sequences\n",
    "We can compute the probability, of the emissions sequence given model and its time sequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm.data_estimate( t, e ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### The Probability of the State, Time and Emission Sequences\n",
    "Similary we can compute the probabilty of the state, time and emission sequences given the model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm.full_data_estimate( s, t, e ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Multi Training"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "\n",
    "For more convenient train from various random begnings, you can use *multi_train* function.  \n",
    "It has parameters   \n",
    "method: \n",
    "- 'exp' - [default] Use exponential distribution for random initialization\n",
    "- 'unif' - Use uniform distribution for random initialization  \n",
    "\n",
    "and ret: \n",
    "- 'all' - Return all trained models, sorted by their probability estimation\n",
    "- 'best' - [default] Return only the model with the best probability estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t,e = chmm.generate_data( (5,10) )\n",
    "hidden_states = 3\n",
    "runs = 10\n",
    "iterations = 50\n",
    "out = hmms.multi_train_ct( hidden_states , t, e, runs, iterations, ret='all', method='exp')\n",
    "out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "<hr/>\n",
    "You can play with the models as you like and feel free to share your result with me, if you have made some interesting experiment!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "Contact: (lopatovsky@gmail.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Experimental features\n",
    "#### Fast Convergence "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "#The experiment is frozen\n",
    "\n",
    "\n",
    "seq_num= 1   #number of data sequences\n",
    "seq_len= 4  #length of each sequence\n",
    "\n",
    "t,e = chmm.generate_data( (seq_num,seq_len) )\n",
    "t,e\n",
    "\n",
    "\n",
    "t = np.array([[ 0,1,3,5,6,7,9,11,12]])\n",
    "e = np.array([[ 0,0,0,1,2,1,0,0,1]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ct1 = hmms.CtHMM.random(3,3)\n",
    "ct2 = hmms.CtHMM( *ct1.params )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "iter_num = 50\n",
    "out1 = ct1.baum_welch( t,e, iter_num, est=True )\n",
    "#out2 = ct2.baum_welch( t,e, iter_num )\n",
    "out1,out2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "plt.plot( out1[1:] / dreal , color = \"red\" )\n",
    "plt.plot( out2[1:] / dreal  )\n",
    "#plt.savefig('graph.svg')  #Optional save the figure\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hmms.print_parameters(ct1)\n",
    "hmms.print_parameters(ct2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Exponential random generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Q is the matrix of transition rates from state [row] to state [column].\n",
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "# B is the matrix of probabilities that the state [row] will emmit output variable [column].\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "# Pi is the vector of initial state probabilities.   \n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "# Create CtHMM by given parameters.\n",
    "chmm = hmms.CtHMM(Q,B,Pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "seq_num= 5   #number of data sequences\n",
    "seq_len= 30  #length of each sequence\n",
    "\n",
    "t,e = chmm.generate_data( (seq_num,seq_len) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 3,3, method='unif' )\n",
    "chmm_re = hmms.CtHMM.random( 3,3, method='exp' )\n",
    "\n",
    "out  =  chmm_r.baum_welch( t,e, 10 )\n",
    "oute = chmm_re.baum_welch( t,e, 10 )\n",
    "\n",
    "\n",
    "#aout =  np.average(out,  axis=0)\n",
    "#aoute = np.average(oute, axis=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "out = hmms.multi_train(3, t, e, 10, 200, ret='all', method='exp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "aout =  np.average(out,  axis=0)\n",
    "aoute = np.average(oute, axis=0)\n",
    "\n",
    "mout =  np.min(out,  axis=0)\n",
    "moute = np.min(oute, axis=0)\n",
    "\n",
    "\n",
    "real = chmm.data_estimate( t, e )\n",
    "#For better visibility of the graph, we cut first two values.\n",
    "\n",
    "offset = 3\n",
    "\n",
    "#plt.plot(  aout[offset:] / real , color = \"red\" )\n",
    "#plt.plot( aoute[offset:] / real , color = \"blue\" )\n",
    "\n",
    "#plt.plot(  mout[offset:] / real , color = \"orange\" )\n",
    "#plt.plot( moute[offset:] / real , color = \"green\")\n",
    "\n",
    "for line in out:\n",
    "    print( line/real )\n",
    "    plt.plot(  line[offset:] / real )\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t, e )\n",
    "\n",
    "offset = 3\n",
    "\n",
    "print(out)\n",
    "\n",
    "for line in out:\n",
    "    #graph= line[1]\n",
    "    #print( type(line) )\n",
    "    #print( line[1]/real )\n",
    "    plt.plot(  line[1][offset:] / real )\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "oute"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Test different length of vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_l = [ np.array( [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1] ) ,\n",
    "         np.array( [0, 1, 0, 0, 1, 0, 1 ] ),\n",
    "         np.array( [2, 0, 1, 0, 0, 0, 0, 0, 0, 0] ) ]\n",
    "\n",
    "data_n = np.array(  [[0, 0, 0, 1, 1, 1, 1, 1, 1, 1],\n",
    "        [0, 0, 0, 2, 2, 2, 1, 0, 1, 0],\n",
    "        [2, 0, 1, 0, 0, 0, 0, 0, 0, 0]] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Test Numpy matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm_r = hmms.DtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_n = dhmm_r.baum_welch( data_n, 10, est=True ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm_r.maximum_likelihood_estimation(data_n, data_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( dhmm_r.data_estimate(data_n) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Test List of numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dhmm_r = hmms.DtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_l = dhmm_r.baum_welch( data_l, 10, est=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( dhmm_r.data_estimate(data_l) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "plt.plot( graph_n, color='red' )\n",
    "plt.plot( graph_l )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Make the similar for the continuous model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data_l = [ np.array( [0, 0, 2, 0 ] ) ,\n",
    "         np.array( [0, 1, 0, 0, 1 ] ),\n",
    "         np.array( [2, 0, 1 ] ) ]\n",
    "\n",
    "data_n = np.array(  [[0, 0, 0, 1],\n",
    "        [0, 2, 0, 0],\n",
    "        [2, 0, 1, 0] ] )\n",
    "\n",
    "time_l = [ np.array( [0, 1, 2, 4 ] ) ,\n",
    "         np.array( [0, 1, 3, 5, 6 ] ),\n",
    "         np.array( [0, 2, 3 ] ) ]\n",
    "\n",
    "time_n = np.array(  [[0, 1, 3, 4],\n",
    "        [0, 2, 3, 5],\n",
    "        [0, 2, 4, 6] ] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_n = chmm_r.baum_welch( time_n, data_n, 10, est=True ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm_r.data_estimate(time_n, data_n) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_n = chmm_r.baum_welch( time_l, data_l, 10, est=True ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm_r.data_estimate(time_l, data_l) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Test double times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data = [ np.array( [0, 0, 2, 0 ] ) ,\n",
    "         np.array( [0, 1, 0, 0, 1 ] ),\n",
    "         np.array( [2, 0, 1 ] ) ]\n",
    "\n",
    "time_i = [ np.array( [0, 1, 2, 4 ] ) ,\n",
    "         np.array( [0, 1, 3, 5, 6 ] ),\n",
    "         np.array( [0, 2, 3 ] ) ]\n",
    "\n",
    "time_f = [ np.array( [0, 1.1, 2.1, 4.1 ] ) ,\n",
    "         np.array( [0, 1.1, 3.1, 5.1, 6.1 ] ),\n",
    "         np.array( [0, 2.1, 3.1 ] ) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_i = chmm_r.baum_welch( time_i, data, 10, est=True ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm_r.data_estimate(time_i, data) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "double"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_r = hmms.CtHMM.random( 2,3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_f = chmm_r.baum_welch( time_f, data, 10, est=True ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.exp( chmm_r.data_estimate(time_f, data) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "plt.plot( graph_i, color='red' )\n",
    "plt.plot( graph_f )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Soft & Hard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "chmm = hmms.CtHMM( Q,B,Pi )\n",
    "#chmm = hmms.CtHMM.random(15,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t,e = chmm.generate_data( (50,10) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "chmm_s = hmms.CtHMM.random( 3,3 )\n",
    "chmm_h = hmms.CtHMM( * chmm_s.params )\n",
    "chmm_c = hmms.CtHMM( * chmm_s.params )\n",
    "\n",
    "print(\"comb\")\n",
    "#graph_comb = chmm_c.baum_welch( t, e, 5, est=True, method=\"hard\" ) \n",
    "#graph_comb = np.append( graph_comb,  chmm_c.baum_welch( t, e, 95, est=True, method=\"soft\" ) )\n",
    "print(\"hard\")\n",
    "graph_hard = chmm_h.baum_welch( t, e, 100, est=True, method=\"hard\" )\n",
    "print(\"soft\")\n",
    "graph_soft = chmm_s.baum_welch( t, e, 100, est=True, method=\"soft\" ) \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "#real = 0\n",
    "#for tt,ee in zip(t,e): \n",
    "#   x,_ = chmm.viterbi( tt, ee )\n",
    "#    real += x\n",
    "\n",
    "#For better visibility of the graph, we cut first two values.\n",
    "plt.plot( graph_soft[1:] / real, color=\"red\"  )\n",
    "plt.plot( graph_hard[1:] / real, color=\"blue\"  )\n",
    "##plt.plot( graph_comb[1:-1] / real, color=\"purple\")\n",
    "plt.rcParams['figure.figsize'] = [20,20]\n",
    "plt.savefig('graph.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "print( chmm_h.data_estimate( t,e ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hmms.print_parameters( chmm )\n",
    "hmms.print_parameters( chmm_s )\n",
    "hmms.print_parameters( chmm_h )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_h.check_params() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Int-intervals vs Double-intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "chmm = hmms.CtHMM( Q,B,Pi )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t,e = chmm.generate_data( (50,50) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_i = hmms.CtHMM.random( 3,3 )\n",
    "chmm_d = hmms.CtHMM( * chmm_i.params )\n",
    "\n",
    "import time\n",
    "\n",
    "time0 = time.time()\n",
    "graph_i = chmm_i.baum_welch( t, e, 100, est=True, method=\"soft\", fast=True )\n",
    "time1 = time.time()\n",
    "graph_d = chmm_d.baum_welch( t, e, 100, est=True, method=\"soft\", fast=False ) \n",
    "time2 = time.time()\n",
    "print(time2-time1)\n",
    "print(time1-time0)\n",
    "chmm_i.print_ts()\n",
    "chmm_d.print_ts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "plt.plot( graph_i[1:] / real, color=\"red\"  )\n",
    "plt.plot( graph_d[1:] / real, color=\"blue\"  )\n",
    "\n",
    "hmms.print_parameters( chmm_i )\n",
    "hmms.print_parameters( chmm_d )\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [25,25]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_i.q[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_d.q[0,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# Q is the matrix of transition rates from state [row] to state [column].\n",
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "# B is the matrix of probabilities that the state [row] will emmit output variable [column].\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "# Pi is the vector of initial state probabilities.   \n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "# Create CtHMM by given parameters.\n",
    "chmm = hmms.CtHMM(Q,B,Pi)\n",
    "\n",
    "\n",
    "t,e = chmm.generate_data( (10,50) )\n",
    "\n",
    "\n",
    "\n",
    "# Q is the matrix of transition rates from state [row] to state [column].\n",
    "Q = np.array( [[-0.125,0.125,0.0],[0.45,-0.45,0.0],[0.25,0.125,-0.375]] )\n",
    "# B is the matrix of probabilities that the state [row] will emmit output variable [column].\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "# Pi is the vector of initial state probabilities.   \n",
    "Pi = np.array( [0.6,0.4,0.0] )\n",
    "\n",
    "# Create CtHMM by given parameters.\n",
    "chmm_i = hmms.CtHMM(Q,B,Pi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "graph_i = chmm_i.baum_welch( t, e, 100, est=True, method=\"soft\", fast=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hmms.print_parameters( chmm_i )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### random tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Q = np.array( [[-0.375,0.125,0.25],[0.25,-0.5,0.25],[0.25,0.125,-0.375]] )\n",
    "B = np.array( [[0.8,0.05,0.15],[0.05,0.9,0.05],[0.2,0.05,0.75]] )\n",
    "Pi = np.array( [0.6,0,0.4] )\n",
    "\n",
    "chmm = hmms.CtHMM( Q,B,Pi )\n",
    "t,e = chmm.generate_data( (50,50) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "chmm_i = hmms.CtHMM.random( 3,3 )\n",
    "chmm_d = hmms.CtHMM( * chmm_i.params )\n",
    "\n",
    "graph_i = chmm_i.baum_welch( t, e, 100, est=True, method=\"soft\", fast=True )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "plt.plot( graph_i[1:]/real , color=\"red\"  )\n",
    "\n",
    "#hmms.print_parameters( chmm_i )\n",
    "\n",
    "#plt.rcParams['figure.figsize'] = [25,25]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "plt.plot(  real-graph_i[1:]  , color=\"red\"  )\n",
    "\n",
    "#hmms.print_parameters( chmm_i )\n",
    "\n",
    "#plt.rcParams['figure.figsize'] = [25,25]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "plt.plot(  np.exp(graph_i[1:] - real) , color=\"red\"  )\n",
    "print(np.exp(graph_i[1:] - real))\n",
    "#hmms.print_parameters( chmm_i )\n",
    "\n",
    "#plt.rcParams['figure.figsize'] = [25,25]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "real = chmm.data_estimate( t,e )\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_yscale(\"log\", nonposx='clip')\n",
    "\n",
    "plt.plot(  np.exp(graph_i[1:] - real) , color=\"red\"  )\n",
    "\n",
    "#plt.rcParams['figure.figsize'] = [25,25]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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