1.2-TFRLinearExercicio.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "T81o_AzEOp9C"
   },
   "source": [
    "<h1 align=center> <font size = 5> Exercicio</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "58MRQMqUOp9E"
   },
   "source": [
    "## Regressão linear "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aQ2rj42zOp9G"
   },
   "source": [
    "Neste exercício, vamos modelar a relação linear entre o canto do grilo e a temperatura no solo. Para isso, serão usados os dados fornecidos por G. W. Pierce no livro \"Songs of Insects\" (1948). O objetivo é obter a função linear que melhor corresponda à tendência do número número de \"cri-cris\" que o grilo irá cantar a cada 15 segundos (Chirps) e a temperatura do solo (Temp), usando TensorFlow. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1c6UcbDhOp9I"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda\\lib\\site-packages\\h5py\\__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "03EfKZl1Op9O"
   },
   "source": [
    "### Obtendo os dados "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bDAGqTq2Op9Q"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chirps</th>\n",
       "      <th>Temp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20.0</td>\n",
       "      <td>88.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>16.0</td>\n",
       "      <td>71.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.8</td>\n",
       "      <td>93.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18.4</td>\n",
       "      <td>84.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.1</td>\n",
       "      <td>80.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Chirps  Temp\n",
       "0    20.0  88.6\n",
       "1    16.0  71.6\n",
       "2    19.8  93.3\n",
       "3    18.4  84.3\n",
       "4    17.1  80.6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/PierceCricketData.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UqfIJ4yDOp9X"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Temp (F)')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2a5333b6828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_data, y_data = (df[\"Chirps\"].values, df[\"Temp\"].values)\n",
    "\n",
    "# grafico com os dados\n",
    "plt.plot(x_data, y_data, 'ro')\n",
    "plt.xlabel(\"# Chirear/15 seg\")\n",
    "plt.ylabel(\"Temp (F)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LUYDyta6Op9d"
   },
   "source": [
    "Observamos uma clara a relação linear entre o canto e a temperatura. Uma função linear que descreva essa relação é definida como: \n",
    "\n",
    "$Y_{pred} = m X + c$ \n",
    "\n",
    "Dado que temos os valores de X (o canto observado), precisamos estimar _m_ e _c_ para determinar a temperatura $Y_{pred}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jVNqhtItOp9e"
   },
   "source": [
    "### Modelagem em Tensorflow\n",
    "\n",
    "Vamos inicialmente observar algumas estimativas para valores arbitrários para _m_ e _c_, por exemplo, _m_ = 3 e _c_ = 2, usando Tensorflow. Para tanto, crie as constantes _m_ e _c_ e os _placeholders_ para a entrada _X_ (um vetor de dimensão x_data.size) e a temperatura _Y_ (um vetor de dimensão y_data.size). Finalmente, descreva a equação $Y_{pred}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fu-9ZKUVOp9g"
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=(x_data.size))\n",
    "Y = tf.placeholder(tf.float32, shape=(x_data.size))\n",
    "m = tf.constant(3.0)\n",
    "c = tf.constant(2.0)\n",
    "\n",
    "Yhat = m*X+c\n",
    "# seu código aqui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SUTJCF9ZOp9k"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#createvar\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"createvar\" class=\"collapse\">\n",
    "```\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(x_data.size))\n",
    "Y = tf.placeholder(tf.float32, shape=(y_data.size))\n",
    "\n",
    "m = tf.Variable(3.0)\n",
    "c = tf.Variable(2.0)\n",
    "\n",
    "Ypred = X * m + c\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZW3y9lu4Op9l"
   },
   "source": [
    "###  Agora crie uma sessão do TF para obter Ypred\n",
    "\n",
    "<h6>Obs:</h6> Fique à vontade para usar diferentes valores inicais para _m_ e _c_ e ver como eles mudam a estimativa.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "3XoWqMqEOp9m"
   },
   "outputs": [],
   "source": [
    "session = tf.Session()\n",
    "session.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zIFoRkhuOp9p"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 8.036384    0.8644427   7.677787    5.1676073   2.8367264  -0.03204989\n",
      " -1.4664378   2.8367264  -0.21134853  1.2230397  -0.9285426   3.016025\n",
      "  0.8644427   2.6574278  -2.5422292 ]\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "t5_hLMHDOp9v"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#matmul1\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"matmul1\" class=\"collapse\">\n",
    "```\n",
    "\n",
    "pred = session.run(Ypred, feed_dict={X:x_data})\n",
    "\n",
    "#plot initial prediction against datapoints\n",
    "plt.plot(x_data, pred)\n",
    "plt.plot(x_data, y_data, 'ro')\n",
    "# label the axis\n",
    "plt.xlabel(\"# Cantos/15 seg\")\n",
    "plt.ylabel(\"Temp (F)\")\n",
    "\n",
    "\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AGo6LONFOp9v"
   },
   "source": [
    "### Estimando valores ótimos para _m_ e _c_\n",
    "\n",
    "Para estimar _m_ e _c_ temos que minimizar a diferença entre a temperatura prevista $Y_{pred}$ e a real $Y$. Esta diferença pode ser calculada através da média do quadrado do erro (disponibilizada no TF como __tf.squared_difference__). \n",
    "      \n",
    "$$ loss = \\frac{1}{n}\\sum_{i=1}^n{[\\eta Ypred_i - \\eta {Y}_i]^2} $$\n",
    "\n",
    "onde $\\eta = 0.1$ é um fator de normalização (usado neste caso porque os dados originalmente não foram normalizados)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "yUhBxlHZOp9w"
   },
   "outputs": [],
   "source": [
    "# seu código aqui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tqRCKY7bOp91"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#matmul12\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"matmul12\" class=\"collapse\">\n",
    "```\n",
    "# normalization factor\n",
    "nf = 1e-1\n",
    "# seting up the loss function\n",
    "loss = tf.reduce_mean(tf.squared_difference(Ypred*nf,Y*nf))\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tPm2Dn-8Op92"
   },
   "source": [
    "### Use como algoritmo de otimização o gradiente descendente com taxa de aprendizado de 0.01 para minizar a sua função de perda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "a_nNiLukOp93"
   },
   "outputs": [],
   "source": [
    "# Seu codigo aqui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "olWLNVgaOp9_"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#matmul13\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"matmul13\" class=\"collapse\">\n",
    "```\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.01)\n",
    "#optimizer = tf.train.AdagradOptimizer(0.01 )\n",
    "\n",
    "# pass the loss function that optimizer should optimize on.\n",
    "train = optimizer.minimize(loss)\n",
    "\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GCby6uIFOp9_"
   },
   "source": [
    "### Inicialize as variáveis novamente\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "gJu58oOqOp-A"
   },
   "outputs": [],
   "source": [
    "session.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7d0PqDx3Op-D"
   },
   "source": [
    "###  Rode a sessão para treinar e prever os valores de _m_ e _c_ para diferentes passos de treino ao mesmo tempo que armazenando as perdas observadas em cada passo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wNmCA_NTOp-E"
   },
   "source": [
    "Obtenha os valores previstos para _m_ e _c_ rodando a sessão para treinar o modelo linear. Também registre as perdas em diferentes passos para impressão e ploting.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "iHGRflAdOp-F"
   },
   "outputs": [],
   "source": [
    "convergenceTolerance = 0.0001\n",
    "previous_m = np.inf\n",
    "previous_c = np.inf\n",
    "losses = []\n",
    "\n",
    "for k in range(100000):\n",
    "    ########## Seu código aqui ###########\n",
    "    losses = losses + [_l]\n",
    "    \n",
    "    if (np.abs(previous_m - _m) or np.abs(previous_c - _c) ) <= convergenceTolerance:\n",
    "        print \"Terminado pelo critério de convergência: %d passos com perda %f\"%(k, _l)\n",
    "        break\n",
    "    previous_m = _m, \n",
    "    previous_c = _c, \n",
    "    \n",
    "session.close() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lsP0N0lcOp-I"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#matmul18\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"matmul18\" class=\"collapse\">\n",
    "```\n",
    "# run a session to train , get m and c values with loss function \n",
    "_, _m , _c,_l = session.run([train, m, c,loss],feed_dict={X:x_data,Y:y_data}) \n",
    "\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5yOdsKr9Op-L"
   },
   "source": [
    "### Exibindo função de perda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "LbtziepGOp-N"
   },
   "outputs": [],
   "source": [
    "plt.plot(losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "gD7J7j1hOp-Q"
   },
   "outputs": [],
   "source": [
    "plt.plot(x_data, y_data, 'o')\n",
    "plt.plot(x_data, _m*x_data + _c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "v4xiqO4FOp-T"
   },
   "source": [
    "### Quais os valores de $m$ e $c$ encontrados?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "vnbXbYfxOp-U"
   },
   "outputs": [],
   "source": [
    "# solucao aqui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LmF4u4vROp-a"
   },
   "source": [
    "<div align=\"right\">\n",
    "<a href=\"#mc\" class=\"btn btn-default\" data-toggle=\"collapse\">Solução</a>\n",
    "</div>\n",
    "<div id=\"mc\" class=\"collapse\">\n",
    "```\n",
    "print previous_m, previous_c \n",
    "\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nKB8KkBFOp-b"
   },
   "source": [
    "# Referência"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5kg8WcHLOp-c"
   },
   "source": [
    "http://mathbits.com/MathBits/TISection/Statistics2/linearREAL.htm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yiqNyT2bOp-d"
   },
   "source": [
    "Primeira parte do exercício proposta por <a href = \"https://ca.linkedin.com/in/shashibushan-yenkanchi\"> Shashibushan Yenkanchi </a> </h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "qAh3ZU4cOp-e"
   },
   "outputs": [],
   "source": []
  }
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