microsoftml/quickstarts/binary-classification/Binary+Classification+Quickstart.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# microsoftml Quickstart: Breast Cancer Prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "This quickstart is a simple example to show the use of the rx_fast_linear function to build a binary classifier model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Load the breast cancer data \n",
    "We'll be using the breast cancer dataset that is built into scikit-learn. We will then use pandas and numpy to convert the data to a dataframe so that we can take a look at the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0        17.99         10.38          122.80     1001.0          0.11840   \n",
       "1        20.57         17.77          132.90     1326.0          0.08474   \n",
       "2        19.69         21.25          130.00     1203.0          0.10960   \n",
       "3        11.42         20.38           77.58      386.1          0.14250   \n",
       "4        20.29         14.34          135.10     1297.0          0.10030   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0           0.27760          0.3001              0.14710         0.2419   \n",
       "1           0.07864          0.0869              0.07017         0.1812   \n",
       "2           0.15990          0.1974              0.12790         0.2069   \n",
       "3           0.28390          0.2414              0.10520         0.2597   \n",
       "4           0.13280          0.1980              0.10430         0.1809   \n",
       "\n",
       "   mean fractal dimension   ...    worst texture  worst perimeter  worst area  \\\n",
       "0                 0.07871   ...            17.33           184.60      2019.0   \n",
       "1                 0.05667   ...            23.41           158.80      1956.0   \n",
       "2                 0.05999   ...            25.53           152.50      1709.0   \n",
       "3                 0.09744   ...            26.50            98.87       567.7   \n",
       "4                 0.05883   ...            16.67           152.20      1575.0   \n",
       "\n",
       "   worst smoothness  worst compactness  worst concavity  worst concave points  \\\n",
       "0            0.1622             0.6656           0.7119                0.2654   \n",
       "1            0.1238             0.1866           0.2416                0.1860   \n",
       "2            0.1444             0.4245           0.4504                0.2430   \n",
       "3            0.2098             0.8663           0.6869                0.2575   \n",
       "4            0.1374             0.2050           0.4000                0.1625   \n",
       "\n",
       "   worst symmetry  worst fractal dimension  target  \n",
       "0          0.4601                  0.11890     0.0  \n",
       "1          0.2750                  0.08902     0.0  \n",
       "2          0.3613                  0.08758     0.0  \n",
       "3          0.6638                  0.17300     0.0  \n",
       "4          0.2364                  0.07678     0.0  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "bc = load_breast_cancer()\n",
    "\n",
    "bc_df = pd.DataFrame(data = np.c_[bc['data'], bc['target']],\n",
    "                     columns = bc['feature_names'].tolist() + ['target'])\n",
    "\n",
    "bc_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Split the data into a train and test dataset\n",
    "We will now split the data into 2 datasets. A train dataset to train the model, and a test dataset to gauge how good is  the model. We'll use 80% of the data for the train dataset and 20% for the test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of rows in training set =  14105\n",
      "# of rows in test set =  3534\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "bc_train, bc_test = train_test_split(bc_df, test_size=0.2)\n",
    "\n",
    "print(\"# of rows in training set = \",bc_train.size)\n",
    "print(\"# of rows in test set = \",bc_test.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 3. Train a binary classifier model\n",
    "Now that we have the dataset to train with, we'll train a model using that data. We will be using the [rx_fast_linear](https://docs.microsoft.com/en-us/r-server/python-reference/microsoftml/rx-fast-linear) function from the [microsoftml](https://docs.microsoft.com/en-us/r-server/python-reference/microsoftml/microsoftml-package) package to train the model. \n",
    "\n",
    "The first parameter to the rx_fast_linear function specifies the target label followed by the features to train the model. This is known as the *formula* and has the format of \"a ~ [b]\" where \"a\" is the column name of the target and \"[b]\" is the list of feature columns to train with.\n",
    "\n",
    "In this example, we create list of columns from the training dataset by taking all columns but dropping the target column (called \"target\" in this case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Express Edition will continue to be enforced.\n",
      "Automatically adding a MinMax normalization transform, use 'norm=Warn' or 'norm=No' to turn this behavior off.\n",
      "Beginning processing data.\n",
      "Rows Read: 455, Read Time: 0, Transform Time: 0\n",
      "Beginning processing data.\n",
      "Beginning processing data.\n",
      "Rows Read: 455, Read Time: 0.001, Transform Time: 0\n",
      "Beginning processing data.\n",
      "Beginning processing data.\n",
      "Rows Read: 455, Read Time: 0.001, Transform Time: 0\n",
      "Beginning processing data.\n",
      "Using 2 threads to train.\n",
      "Automatically choosing a check frequency of 2.\n",
      "Auto-tuning parameters: maxIterations = 3294.\n",
      "Auto-tuning parameters: L2 = 2.670477E-05.\n",
      "Auto-tuning parameters: L1Threshold (L1/L2) = 0.\n",
      "Using best model from iteration 368.\n",
      "Not training a calibrator because it is not needed.\n",
      "Elapsed time: 00:00:06.1734881\n",
      "Elapsed time: 00:00:00.4967690\n"
     ]
    }
   ],
   "source": [
    "from microsoftml import rx_fast_linear\n",
    "\n",
    "features = bc_df.columns.drop([\"target\"])\n",
    "model = rx_fast_linear(\"target ~ \" + \"+\".join(features), data=bc_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Predict using the trained model\n",
    "At this point we have a model that we have trained on the training data, using the rx_fast_linear binary classification algorithm. Let's now use that model to predict using the [rx_predict](https://docs.microsoft.com/en-us/r-server/python-reference/microsoftml/rx-predict), based on the test dataset. \n",
    "\n",
    "We will also take a look at the return result of rx_predict function. The *PredictedLabel* column indicates whether the data represents a cancerous sample or not. The *Probability* column indicates the confidence of the prediction for that particular row of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beginning processing data.\n",
      "Rows Read: 114, Read Time: 0.001, Transform Time: 0\n",
      "Beginning processing data.\n",
      "Elapsed time: 00:00:00.6729840\n",
      "Finished writing 114 rows.\n",
      "Writing completed.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PredictedLabel</th>\n",
       "      <th>Score</th>\n",
       "      <th>Probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>True</td>\n",
       "      <td>6.273149</td>\n",
       "      <td>9.981173e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>-17.446648</td>\n",
       "      <td>2.648605e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>True</td>\n",
       "      <td>5.057464</td>\n",
       "      <td>9.936786e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>True</td>\n",
       "      <td>1.958880</td>\n",
       "      <td>8.764117e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>False</td>\n",
       "      <td>-2.303647</td>\n",
       "      <td>9.082136e-02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  PredictedLabel      Score   Probability\n",
       "0           True   6.273149  9.981173e-01\n",
       "1          False -17.446648  2.648605e-08\n",
       "2           True   5.057464  9.936786e-01\n",
       "3           True   1.958880  8.764117e-01\n",
       "4          False  -2.303647  9.082136e-02"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from microsoftml import rx_predict\n",
    "\n",
    "prediction = rx_predict(model, data=bc_test)\n",
    "\n",
    "prediction.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Evaluating the model\n",
    "Let's now gauge the quality of the model we have. A standard metric to use is the AUC (Area Under the Curve) metric. Assuming no overfiiting of the model has taken place, the closer the value of the AUC is to 1, the better the quality of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.960526315789\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "fpr, tpr, thresholds = roc_curve(bc_test[\"target\"], prediction[\"PredictedLabel\"])\n",
    "\n",
    "roc_auc = auc(fpr, tpr)\n",
    "print(roc_auc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also look at the ROC (Receiver Operating Characteristics) curve to visually see the performance of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fPlMQEVavfoSYmGLMn/+AJQgTdHJszFbVRe7Tuqo60/MBBO/dPUkHnWQRVQbC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\nsCIMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x221882d4588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         lw=lw, label='ROC curve (area = %0.2f)' % roc_auc)\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('ROC of Breast Cancer Prediction')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}