loandefault.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Art of Data Science\n",
    "## RIHAD VARIAWA, Data Scientist\n",
    "\n",
    "> “Jack of all trades, master of none, though oft times better than master of one.\"\n",
    "\n",
    "**Motivation for this task**\n",
    "\n",
    "- Solve a business problem\n",
    "- Understand the end-to-end approach\n",
    "- Build a data-driven Machine Learning application on the cloud\n",
    "\n",
    "\n",
    "** Approach ** to take a case-driven task to showcase this. We will aim to go-wide VS. go-deep. The approach will be both practical and scalable. Let's start by understanding the overall steps involved in building a data-driven application."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "![The Art of DataScience Process](static/datascience.svg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FRAME \n",
    "\n",
    "> \"Doing data science requires more time thinking than doing.\"\n",
    "\n",
    "A financial institution provides loans to consumers and has been doing so for a number of years. It now plans to adopt a data-driven lens to its loan portfolio. What are the **type of questions** it can ask?\n",
    "- What is the trend in loan defaults?\n",
    "- Do older customers have more loan defaults?\n",
    "- Which customers are likely to have a loan default?\n",
    "- Why do customers default on their loans?\n",
    "\n",
    "\n",
    "### Type of data-driven analytics\n",
    "- **Descriptive**: Understand historic patterns, trends, deviations, relationships and outlier\n",
    "- **Inquisitive**: Conduct hypothesis testing\n",
    "- **Predictive**: Make a prediction\n",
    "\n",
    "**Case Question: What is the probability of a loan default?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ACQUIRE\n",
    "\n",
    "> \"Data is the new oil\"\n",
    "\n",
    "**Ways to acquire data** (typical data source)\n",
    "\n",
    "- Download from an internal system\n",
    "- Obtained from client, or other 3rd party\n",
    "- Extracted from a web-based API\n",
    "- Scraped from a website\n",
    "- Extracted from a PDF file\n",
    "- Gathered manually and recorded\n",
    "\n",
    "**Data Formats**: flat files (e.g. csv, tsv, xls), databases (e.g. MySQL), streaming (e.g. json), storage (e.g. HDFS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "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>default</th>\n",
       "      <th>amount</th>\n",
       "      <th>grade</th>\n",
       "      <th>years</th>\n",
       "      <th>ownership</th>\n",
       "      <th>income</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1000</td>\n",
       "      <td>B</td>\n",
       "      <td>2.0</td>\n",
       "      <td>RENT</td>\n",
       "      <td>19200.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6500</td>\n",
       "      <td>A</td>\n",
       "      <td>2.0</td>\n",
       "      <td>MORTGAGE</td>\n",
       "      <td>66000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2400</td>\n",
       "      <td>A</td>\n",
       "      <td>2.0</td>\n",
       "      <td>RENT</td>\n",
       "      <td>60000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>10000</td>\n",
       "      <td>C</td>\n",
       "      <td>3.0</td>\n",
       "      <td>RENT</td>\n",
       "      <td>62000.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>4000</td>\n",
       "      <td>C</td>\n",
       "      <td>2.0</td>\n",
       "      <td>RENT</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   default  amount grade  years ownership   income  age\n",
       "0        0    1000     B    2.0      RENT  19200.0   24\n",
       "1        1    6500     A    2.0  MORTGAGE  66000.0   28\n",
       "2        0    2400     A    2.0      RENT  60000.0   36\n",
       "3        0   10000     C    3.0      RENT  62000.0   24\n",
       "4        1    4000     C    2.0      RENT  20000.0   28"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the libraries and configuration\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# Load the data and see head\n",
    "data = pd.read_csv(\"loan.csv\") \n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Target*\n",
    "- **default**: whether the applicant defaulted (1) or not (0)?\n",
    "\n",
    "*Features*\n",
    "- **age**: age of the applicant\n",
    "- **income**: annual income of the applicant\n",
    "- **year**: no. of years of employment\n",
    "- **ownership**: type of house owned\n",
    "- **amount** : amount of loan requested by the applicant\n",
    "- **grade**: credit grade of the applicant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## REFINE\n",
    "\n",
    "> \"Data is messy\"\n",
    "\n",
    "- **Remove** e.g. remove redundant data from the dataframe\n",
    "- **Derive** e.g. state and city from the location field\n",
    "- **Parse** e.g. extract date from year and month column\n",
    "\n",
    "Also, you need to check for consistency and quality of the data\n",
    "- **Missing** e.g. Check for missing or incomplete data\n",
    "- **Quality** e.g. Check for duplicates, accuracy, unusual data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "default        0\n",
       "amount         0\n",
       "grade          0\n",
       "years        279\n",
       "ownership      0\n",
       "income         0\n",
       "age            0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's check for missing values in our data\n",
    "data.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Handling missing values\n",
    "\n",
    "- **REMOVE** - NaN rows or columns\n",
    "- **IMPUTATE** - Replace them with something? mean, median, fixed number (based on domain) or high number (e..g 999, though could have issues later)\n",
    "- **BIN** - Convert to categorical variable and \"missing becomes a category\"\n",
    "- **DOMAIN SPECIFIC** - Entry error, pipeline, etc.\n",
    "\n",
    "In our case, let's replace missing values for years with mean\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.086331901181525"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us replace the NaNs with mean for years\n",
    "np.mean(data.years)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# There is a fillna function for missing data\n",
    "data.years = data.years.fillna(np.mean(data.years))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXPLORE\n",
    "\n",
    "> \"I don't know, what I don't know\"\n",
    "\n",
    "### Data Types\n",
    "\n",
    "- **Categorical**\n",
    "   - *Nominal*: home owner [rent, own, mortgage] \n",
    "   - *Ordinal*: credit grade [A > B > C > D > E]\n",
    "- **Continuous**\n",
    "    - *Interval*: approval date  [20/04/16, 19/11/15]\n",
    "    - *Ratio*: loan amount [3000, 10000]\n",
    "\n",
    "### Visual Exploration\n",
    "- Explore **One dimension visualisation**\n",
    "- Explore **Two dimensions visualiation**\n",
    "- Explore **Multi dimensionsal visualisation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the plotting libraries \n",
    "from plotnine import *\n",
    "%matplotlib inline\n",
    "from plotnine.themes import theme_538\n",
    "\n",
    "# Convert `default` to categorical variable\n",
    "data_plot = data.copy()\n",
    "data_plot['default'] = data_plot['default'].astype('category')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two Dimension Exploration \n",
    "\n",
    "We expect the default rate to go up as the credit score of the customer go down."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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+/OMfN/qgAAAAaLnqHZ1xcXG+NzN1OBy6++671bFjR2ODAQAAoPVo0M90PvDAA409BwAA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\nIzoBAABgHNEJAAAA4/4P7HM3+lE7JLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad686d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (296569159)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the relationship between `grade` and `default`\n",
    "(ggplot(data_plot) + aes('grade', fill =\"default\") + \n",
    "   geom_bar(position = 'fill') + theme_538())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Three Dimension Exploration \n",
    "\n",
    "We would like to understand what impact does age and income have on the default rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7HTU1NSguLoa9l7AN048TwbWKSmSfMqH5DYVCuvdrXzMT25u6x3v6nm/p3qdk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\n8euimfkZb5y46IfMukp+bHH8q0EM5F9FEr6O75l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zJzRi43tetHYJxnR3Y/7kVuH+Y/s2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\nG18iIiIisoX/DyW1KYHYaNWyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cfb5b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223372036556016545)>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us see the relationship between `age`, `income` and `default`\n",
    "( ggplot(data_plot) + aes('age', 'income', color='default') + \n",
    "    geom_bin2d() + scale_y_log10() +\n",
    "    facet_wrap(\"default\") + theme_538()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TRANSFORM\n",
    "\n",
    "> \"What is measured may not help answer what is needed \"\n",
    "\n",
    "**Scale Transformation** e.g.\n",
    "- Log Transform\n",
    "- Sqrt Transform\n",
    "\n",
    "**Mutate & Summarize** e.g.\n",
    "- **Convert** e.g. free text to coded value\n",
    "- **Calculate** e.g. percentages, proportion\n",
    "- **Merge** e.g. first and surname for full name\n",
    "- **Aggregate** e.g. rollup by year, cluster by area\n",
    "- **Filter** e.g. exclude based on location\n",
    "- **Sample** e.g. extract a representative data\n",
    "- **Summary** e.g. show summary stats like mean\n",
    "\n",
    "**Categorical Encodings** e.g.\n",
    "- Label Encoding\n",
    "- One Hot Encoding "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two of the columns are categorical in nature - `grade` and `ownership`. To build models, we need all of the features to be numeric. There exists a number of ways to transform categorical variables to numeric values.\n",
    "\n",
    "We will use one of the popular options: `LabelEncoding`\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the library for preprocessing \n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "\n",
    "# Let's not modify the original dataset. Let's copy it in another dataset\n",
    "data_encoded = data.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "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>default</th>\n",
       "      <th>amount</th>\n",
       "      <th>grade</th>\n",
       "      <th>years</th>\n",
       "      <th>ownership</th>\n",
       "      <th>income</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1000</td>\n",
       "      <td>1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>19200.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6500</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>66000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2400</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>60000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>10000</td>\n",
       "      <td>2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3</td>\n",
       "      <td>62000.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>4000</td>\n",
       "      <td>2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   default  amount  grade  years  ownership   income  age\n",
       "0        0    1000      1    2.0          3  19200.0   24\n",
       "1        1    6500      0    2.0          0  66000.0   28\n",
       "2        0    2400      0    2.0          3  60000.0   36\n",
       "3        0   10000      2    3.0          3  62000.0   24\n",
       "4        1    4000      2    2.0          3  20000.0   28"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instantiate label encoder\n",
    "le_grade = LabelEncoder()\n",
    "le_ownership = LabelEncoder()\n",
    "\n",
    "# fit label encoder\n",
    "le_grade = le_grade.fit(data_encoded[\"grade\"])\n",
    "le_ownership = le_ownership.fit(data[\"ownership\"])\n",
    "\n",
    "# Transform the label\n",
    "data_encoded.grade = le_grade.transform(data_encoded.grade)\n",
    "data_encoded.ownership = le_ownership.transform(data_encoded.ownership)\n",
    "\n",
    "# Lets see the encoded data now\n",
    "data_encoded.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MODEL\n",
    "\n",
    "\n",
    "> \"All models are wrong, Some of them are useful\"\n",
    "\n",
    "\n",
    "### Supervised Learning\n",
    "\n",
    "Given a set of **feature** `X`, to predict the value of **target** `y`\n",
    "- If `y` is *continuous* - **Regression**\n",
    "- If `y` is *categorical* - **Classification**\n",
    "\n",
    "**Model Family**\n",
    "- Linear\n",
    "- Tree-Based\n",
    "- Kernel-Baed\n",
    "- Neural Network\n",
    "\n",
    "**Choosing a Model**\n",
    "\n",
    "1. Interpretability\n",
    "2. Run-time\n",
    "3. Model complexity\n",
    "4. Scalability\n",
    "\n",
    "Let's build two tree-based classifier - Decision Tree & Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the library\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "# Setup the features and target\n",
    "X = data_encoded.iloc[:,1:]\n",
    "y = data_encoded.iloc[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Save the prediction class and probabilities\n",
    "def prediction(clf, X, y):\n",
    "    clf = clf.fit(X,y)\n",
    "    y_pred = clf.predict(X)\n",
    "    y_proba = clf.predict_proba(X)[:,1]\n",
    "    prediction = pd.DataFrame({\"actual\": np.array(y), \"predicted\": y_pred, \"probability\": y_proba})\n",
    "    prediction['predicted'] = prediction['predicted'].astype('category')\n",
    "    prediction['actual'] = prediction['actual'].astype('category')\n",
    "    return prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Build a Decision Tree Classifier\n",
    "clf_tree = DecisionTreeClassifier(max_depth=10)\n",
    "prediction_tree = prediction(clf_tree, X, y)\n",
    "\n",
    "# Build a Random Forest Classifier\n",
    "clf_forest = RandomForestClassifier(n_estimators=40)\n",
    "prediction_forest = prediction(clf_forest, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see how well the classifiers are performing in separating the two classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H0tLS0N3eHkoqKqyjtJiZiytu/fknHj58yDoKkRC3b99GxOTJGDRjJkbO+QLKqqrQ0NLC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124586080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223372036555365660)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting predicted probability VS. actuals for Decision Tree Classifier\n",
    "(ggplot(prediction_tree) + aes('probability', fill='actual') + \n",
    "    geom_density(alpha = 0.5) + theme_538()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IiPRuw6ZNiDayRaRvJ3TwEBzYvx9NTU2io5DEsAjq0OmTJxHgYbxF0EKhwDsP/xHfLV3K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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12488e6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223372036555835574)>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting predicted probability VS. actuals for Random Forest Classifier\n",
    "(ggplot(prediction_forest) + aes('probability', fill='actual') + \n",
    "    geom_density(alpha = 0.5) + theme_538()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## INSIGHT\n",
    "\n",
    "> \"The purpose of data science is to create insight\"\n",
    "\n",
    "While we have created many model, we still don't have a *measure* of how good each of the model is and which one should we pick. We need to measure some accuracy metric of the model and have confidence that it will generalize well. We should be confident that when we put the model in production (real-life), the accuracy we get from the model results should mirror the metrics we obtained when we built the model.\n",
    "\n",
    "- Choosing an Error Metric: `Area Under Curve`\n",
    "- Cross Validation: How well will the model generalize on unseen data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Validation using AUC\n",
    "\n",
    "We will use `StratifiedKFold`. This ensures that in each fold, the proportion of positive class and negative class remain similar to the original dataset. This is the process we will follow to get the mean cv-score\n",
    "\n",
    "1. Generate k-fold\n",
    "2. Train the model using k-1 fold\n",
    "3. Predict for the kth fold \n",
    "4. Find the accuracy.\n",
    "5. Append it to the array\n",
    "6. Repeat 2-5 for different validation folds\n",
    "7. Report the mean cross validation score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the libraries\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.model_selection import StratifiedKFold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Setup a function to conduct cross-validation\n",
    "def cross_validation(clf, X, y, k):\n",
    "    \n",
    "    # Instantiate stratified k fold.\n",
    "    kf = StratifiedKFold(n_splits=k)\n",
    "    \n",
    "    # Let's use an array to store the results of cross-validation\n",
    "    kfold_auc_score = []\n",
    "\n",
    "    # Run kfold CV\n",
    "    for train_index, test_index in kf.split(X,y):\n",
    "        clf = clf.fit(X.iloc[train_index], y.iloc[train_index])\n",
    "        proba = clf.predict_proba(X.iloc[test_index])[:,1]\n",
    "        auc_score = roc_auc_score(y.iloc[test_index],proba)\n",
    "        print(auc_score)\n",
    "        kfold_auc_score.append(auc_score)\n",
    "    \n",
    "    print(\"Mean K Fold CV:\", np.mean(kfold_auc_score))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.616927939105\n",
      "0.628056468379\n",
      "0.645746381167\n",
      "0.703180980266\n",
      "0.689194203152\n",
      "Mean K Fold CV: 0.656621194414\n"
     ]
    }
   ],
   "source": [
    "# Lets get the cross-validation score for Decision Tree Classifier\n",
    "cross_validation(clf_tree, X, y, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.693877003554\n",
      "0.682467641339\n",
      "0.715824650708\n",
      "0.767269833488\n",
      "0.800936481128\n",
      "Mean K Fold CV: 0.732075122043\n"
     ]
    }
   ],
   "source": [
    "# Lets get the cross-validation score for Random Forest Classifier\n",
    "cross_validation(clf_forest, X, y, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DEPLOY \n",
    "\n",
    "> \"What you build - you test, you ship and you maintain\"\n",
    "\n",
    "Once the final model has been selected, we need to ensure that other data application can access the model and use it in their process. This requires us to do two important tasks.\n",
    "\n",
    "- Serialising the Model (e.g. `pickle`)\n",
    "- Serving the ML Model as a Service \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Build the selected model\n",
    "loan_default_model = RandomForestClassifier(n_estimators=40).fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Serialization\n",
    "\n",
    "We will need to serialize both the model and the encoders used to create them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Use joblib to serialize the model\n",
    "from sklearn.externals import joblib\n",
    "\n",
    "joblib.dump(loan_default_model, \"loan_default_model.pkl\")\n",
    "joblib.dump(le_grade, \"le_grade.pkl\")\n",
    "joblib.dump(le_ownership, \"le_ownership.pkl\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ML as a service \n",
    "\n",
    "While we can package the model with the application and use it, it created tight coupling between the two. Everytime the model changes, the application will have to change. What if there are more than one application using the same model? \n",
    "\n",
    "It is lot simpler to deploy the ML model as a service exposing it's functionality through an HTTP API.\n",
    "\n",
    "In this task we are going to use a tool called firefly for running the model as a service."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting loan_default_api.py\n"
     ]
    }
   ],
   "source": [
    "%%file loan_default_api.py\n",
    "\n",
    "\"\"\"Service to expose the credit risk model as an API.\n",
    "\"\"\"\n",
    "from sklearn.externals import joblib\n",
    "\n",
    "# read the encoders and the model\n",
    "grade_encoder = joblib.load(\"le_grade.pkl\")\n",
    "ownership_encoder = joblib.load(\"le_ownership.pkl\")\n",
    "model = joblib.load(\"loan_default_model.pkl\")\n",
    "\n",
    "def predict(amount, years, age, ownership, income, grade):\n",
    "    \"\"\"Returns the probablity of default for given features.\n",
    "    \"\"\"\n",
    "    # encoders work on a vector. Wrapping in a list as we only have a single value\n",
    "    ownership_code = ownership_encoder.transform([ownership])[0]\n",
    "    grade_code = grade_encoder.transform([grade])[0]\n",
    "    \n",
    "    # important to pass the features in the same order as we built the model\n",
    "    features = [amount, grade_code, years, ownership_code, income, age]\n",
    "    \n",
    "    # probablity for not-defaulting and defaulting\n",
    "    # Again, wrapping in a list as a list of features is expected\n",
    "    p0, p1 = model.predict_proba([features])[0]\n",
    "    return p1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Start the ML Service \n",
    "Run the following command in your terminal \n",
    "\n",
    "     firefly loan_default_api.predict\n",
    "     \n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BUILD \n",
    "\n",
    "> \"The role of data scientist is to build a data-driven product solution\n",
    "\n",
    "Now that we have a prediction API, this can be consumed as part of many applications to provide insight and help in decision making.\n",
    "\n",
    "- Dashboards \n",
    "- Web / Mobile Application \n",
    "- IoT Applications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the libaries\n",
    "from firefly.client import Client\n",
    "\n",
    "# Access the predict function from the jupyter notebook\n",
    "loan_default_api = Client(\"http://127.0.0.1:8000\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.425"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 1\n",
    "loan_default_api.predict(amount=100000, years=2, age=35, ownership='RENT', income=12345, grade='A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 2\n",
    "loan_default_api.predict(amount=100000, years=2, age=35, ownership='RENT', income=12345, grade='G')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.65"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 3\n",
    "loan_default_api.predict(amount=100, years=2, age=35, ownership='RENT', income=12345, grade='G')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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