07_sparkml_and_bqml/logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1> Logistic Regression using Spark ML </h1>\n",
    "\n",
    "Set up bucket"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "BUCKET='cloud-training-demos-ml'  # CHANGE ME\n",
    "\n",
    "os.environ['BUCKET'] = BUCKET"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<pyspark.sql.session.SparkSession object at 0x7f36a5e228d0>\n",
      "<SparkContext master=yarn appName=pyspark-shell>\n"
     ]
    }
   ],
   "source": [
    "# Create spark session\n",
    "\n",
    "from __future__ import print_function\n",
    "from pyspark.sql import SparkSession\n",
    "from pyspark import SparkContext\n",
    "\n",
    "sc = SparkContext('local', 'logistic')\n",
    "spark = SparkSession \\\n",
    "    .builder \\\n",
    "    .appName(\"Logistic regression w/ Spark ML\") \\\n",
    "    .getOrCreate()\n",
    "\n",
    "print(spark)\n",
    "print(sc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pyspark.mllib.classification import LogisticRegressionWithLBFGS\n",
    "from pyspark.mllib.regression import LabeledPoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Read dataset </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "traindays = spark.read \\\n",
    "    .option(\"header\", \"true\") \\\n",
    "    .csv('gs://{}/flights/trainday.csv'.format(BUCKET))\n",
    "traindays.createOrReplaceTempView('traindays')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+------------+\n",
      "|   FL_DATE|is_train_day|\n",
      "+----------+------------+\n",
      "|2015-01-01|        True|\n",
      "|2015-01-04|        True|\n",
      "|2015-01-05|        True|\n",
      "|2015-01-07|        True|\n",
      "|2015-01-08|        True|\n",
      "+----------+------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "spark.sql(\"SELECT * from traindays LIMIT 5\").show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pyspark.sql.types import StringType, FloatType, StructType, StructField\n",
    "\n",
    "header = 'FL_DATE,UNIQUE_CARRIER,AIRLINE_ID,CARRIER,FL_NUM,ORIGIN_AIRPORT_ID,ORIGIN_AIRPORT_SEQ_ID,ORIGIN_CITY_MARKET_ID,ORIGIN,DEST_AIRPORT_ID,DEST_AIRPORT_SEQ_ID,DEST_CITY_MARKET_ID,DEST,CRS_DEP_TIME,DEP_TIME,DEP_DELAY,TAXI_OUT,WHEELS_OFF,WHEELS_ON,TAXI_IN,CRS_ARR_TIME,ARR_TIME,ARR_DELAY,CANCELLED,CANCELLATION_CODE,DIVERTED,DISTANCE,DEP_AIRPORT_LAT,DEP_AIRPORT_LON,DEP_AIRPORT_TZOFFSET,ARR_AIRPORT_LAT,ARR_AIRPORT_LON,ARR_AIRPORT_TZOFFSET,EVENT,NOTIFY_TIME'\n",
    "\n",
    "def get_structfield(colname):\n",
    "   if colname in ['ARR_DELAY', 'DEP_DELAY', 'DISTANCE', 'TAXI_OUT']:\n",
    "      return StructField(colname, FloatType(), True)\n",
    "   else:\n",
    "      return StructField(colname, StringType(), True)\n",
    "\n",
    "schema = StructType([get_structfield(colname) for colname in header.split(',')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "inputs = 'gs://{}/flights/tzcorr/all_flights-00000-*'.format(BUCKET) # 1/30th;  you may have to change this to find a shard that has training data\n",
    "#inputs = 'gs://{}/flights/tzcorr/all_flights-*'.format(BUCKET)  # FULL\n",
    "flights = spark.read\\\n",
    "            .schema(schema)\\\n",
    "            .csv(inputs)\n",
    "\n",
    "# this view can now be queried ...\n",
    "flights.createOrReplaceTempView('flights')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Clean up </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trainquery = \"\"\"\n",
    "SELECT\n",
    "  f.*\n",
    "FROM flights f\n",
    "JOIN traindays t\n",
    "ON f.FL_DATE == t.FL_DATE\n",
    "WHERE\n",
    "  t.is_train_day == 'True'\n",
    "\"\"\"\n",
    "traindata = spark.sql(trainquery)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Row(FL_DATE=u'2015-11-26', UNIQUE_CARRIER=u'B6', AIRLINE_ID=u'20409', CARRIER=u'B6', FL_NUM=u'1447', ORIGIN_AIRPORT_ID=u'12197', ORIGIN_AIRPORT_SEQ_ID=u'1219702', ORIGIN_CITY_MARKET_ID=u'31703', ORIGIN=u'HPN', DEST_AIRPORT_ID=u'15304', DEST_AIRPORT_SEQ_ID=u'1530402', DEST_CITY_MARKET_ID=u'33195', DEST=u'TPA', CRS_DEP_TIME=u'2015-11-26T19:10:00', DEP_TIME=u'2015-11-26T19:14:00', DEP_DELAY=4.0, TAXI_OUT=13.0, WHEELS_OFF=u'2015-11-26T19:27:00', WHEELS_ON=u'2015-11-26T21:37:00', TAXI_IN=u'5.00', CRS_ARR_TIME=u'2015-11-26T22:03:00', ARR_TIME=u'2015-11-26T21:42:00', ARR_DELAY=-21.0, CANCELLED=u'0.00', CANCELLATION_CODE=None, DIVERTED=u'0.00', DISTANCE=1032.0, DEP_AIRPORT_LAT=u'41.06694444', DEP_AIRPORT_LON=u'-73.70750000', DEP_AIRPORT_TZOFFSET=u'-18000.0', ARR_AIRPORT_LAT=u'27.97555556', ARR_AIRPORT_LON=u'-82.53333333', ARR_AIRPORT_TZOFFSET=u'-18000.0', EVENT=None, NOTIFY_TIME=None), Row(FL_DATE=u'2015-11-26', UNIQUE_CARRIER=u'B6', AIRLINE_ID=u'20409', CARRIER=u'B6', FL_NUM=u'1454', ORIGIN_AIRPORT_ID=u'14843', ORIGIN_AIRPORT_SEQ_ID=u'1484304', ORIGIN_CITY_MARKET_ID=u'34819', ORIGIN=u'SJU', DEST_AIRPORT_ID=u'11697', DEST_AIRPORT_SEQ_ID=u'1169704', DEST_CITY_MARKET_ID=u'32467', DEST=u'FLL', CRS_DEP_TIME=u'2015-11-26T23:25:00', DEP_TIME=u'2015-11-26T23:36:00', DEP_DELAY=11.0, TAXI_OUT=11.0, WHEELS_OFF=u'2015-11-26T23:47:00', WHEELS_ON=u'2015-11-27T02:12:00', TAXI_IN=u'7.00', CRS_ARR_TIME=u'2015-11-27T02:11:00', ARR_TIME=u'2015-11-27T02:19:00', ARR_DELAY=8.0, CANCELLED=u'0.00', CANCELLATION_CODE=None, DIVERTED=u'0.00', DISTANCE=1046.0, DEP_AIRPORT_LAT=u'18.43944444', DEP_AIRPORT_LON=u'-66.00222222', DEP_AIRPORT_TZOFFSET=u'-14400.0', ARR_AIRPORT_LAT=u'26.07166667', ARR_AIRPORT_LON=u'-80.14972222', ARR_AIRPORT_TZOFFSET=u'-18000.0', EVENT=None, NOTIFY_TIME=None)]\n"
     ]
    }
   ],
   "source": [
    "print(traindata.head(2))  # if this is empty, try changing the shard you are using."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+----------+--------------+------------------+-------+------------------+------------------+---------------------+---------------------+------+------------------+-------------------+-------------------+----+-------------------+-------------------+------------------+------------------+-------------------+-------------------+-----------------+-------------------+-------------------+------------------+--------------------+-----------------+--------------------+-----------------+------------------+------------------+--------------------+------------------+------------------+--------------------+-----+-----------+\n",
      "|summary|   FL_DATE|UNIQUE_CARRIER|        AIRLINE_ID|CARRIER|            FL_NUM| ORIGIN_AIRPORT_ID|ORIGIN_AIRPORT_SEQ_ID|ORIGIN_CITY_MARKET_ID|ORIGIN|   DEST_AIRPORT_ID|DEST_AIRPORT_SEQ_ID|DEST_CITY_MARKET_ID|DEST|       CRS_DEP_TIME|           DEP_TIME|         DEP_DELAY|          TAXI_OUT|         WHEELS_OFF|          WHEELS_ON|          TAXI_IN|       CRS_ARR_TIME|           ARR_TIME|         ARR_DELAY|           CANCELLED|CANCELLATION_CODE|            DIVERTED|         DISTANCE|   DEP_AIRPORT_LAT|   DEP_AIRPORT_LON|DEP_AIRPORT_TZOFFSET|   ARR_AIRPORT_LAT|   ARR_AIRPORT_LON|ARR_AIRPORT_TZOFFSET|EVENT|NOTIFY_TIME|\n",
      "+-------+----------+--------------+------------------+-------+------------------+------------------+---------------------+---------------------+------+------------------+-------------------+-------------------+----+-------------------+-------------------+------------------+------------------+-------------------+-------------------+-----------------+-------------------+-------------------+------------------+--------------------+-----------------+--------------------+-----------------+------------------+------------------+--------------------+------------------+------------------+--------------------+-----+-----------+\n",
      "|  count|      9559|          9559|              9559|   9559|              9559|              9559|                 9559|                 9559|  9559|              9559|               9559|               9559|9559|               9559|               9533|              9533|              9531|               9531|               9527|             9527|               9559|               9527|              9514|                9559|               31|                9559|             9559|              9559|              9559|                9559|              9559|              9559|                9559|    0|          0|\n",
      "|   mean|      null|          null|19854.703630086828|   null| 2609.077937022701| 12652.85406423266|   1265288.2625797677|    31715.02761795167|  null|12585.991526310283| 1258602.0389162046| 31682.230986504863|null|               null|               null|2.6588691912304627|14.627845976287903|               null|               null|7.149889786921381|               null|               null|-4.238385537103216|0.003243017051992886|             null|0.001464588346061...| 869.220002092269|35.918674925542206|-94.73029416819357| -21903.546396066533| 35.94444581049187|-94.47358455185994|  -21806.75802908254| null|       null|\n",
      "| stddev|      null|          null|402.70507420771446|   null|2053.3431814617616|1522.4049784934023|   152240.17071675116|   1276.3603481399443|  null|1543.5954555365124| 154359.19877849414| 1280.0838349094581|null|               null|               null|29.729841487731417| 7.282754066063705|               null|               null|4.979740156733318|               null|               null|32.565523694571986| 0.05685805211885097|             null|0.038243905845130204|617.1870728197283| 6.320118789761992| 19.16114616034329|   4869.836503663976|6.2752435684194845|19.090188990683455|   4865.578774855603| null|       null|\n",
      "|    min|2015-11-26|            AA|             19393|     AA|                 1|             10135|              1013503|                30070|   ABE|             10135|            1013503|              30070| ABE|2015-11-26T05:55:00|2015-11-26T05:58:00|             -31.0|               2.0|2015-11-26T06:13:00|2015-11-26T09:41:00|             1.00|2015-11-26T10:02:00|2015-11-26T09:49:00|             -62.0|                0.00|                A|                0.00|             31.0|      -14.33000000|     -101.70583333|            -14400.0|      -14.33000000|     -100.74583333|            -14400.0| null|       null|\n",
      "|    max|2015-11-27|            WN|             21171|     WN|               999|             15991|              1599102|                35991|   YAK|             15991|            1599102|              35991| YAK|2015-11-28T10:25:00|2015-11-28T10:03:00|            1631.0|             133.0|2015-11-28T10:16:00|2015-11-28T15:45:00|            93.00|2015-11-29T06:54:00|2015-11-28T15:59:00|            1638.0|                1.00|                B|                1.00|           4983.0|       71.28472222|      -99.46166667|                   0|       71.28472222|      -99.68194444|                   0| null|       null|\n",
      "+-------+----------+--------------+------------------+-------+------------------+------------------+---------------------+---------------------+------+------------------+-------------------+-------------------+----+-------------------+-------------------+------------------+------------------+-------------------+-------------------+-----------------+-------------------+-------------------+------------------+--------------------+-----------------+--------------------+-----------------+------------------+------------------+--------------------+------------------+------------------+--------------------+-----+-----------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "traindata.describe().show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the counts for the various columns are all different; We have to remove NULLs in the delay variables (these correspond to canceled or diverted flights)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Logistic regression </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "|summary|         DEP_DELAY|         TAXI_OUT|         ARR_DELAY|         DISTANCE|\n",
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "|  count|              9514|             9514|              9514|             9514|\n",
      "|   mean|2.6394786630229135|14.62528904771915|-4.238385537103216|870.8421273912129|\n",
      "| stddev|29.693248310855065| 7.28500427136442|32.565523694571986| 617.509578518596|\n",
      "|    min|             -31.0|              2.0|             -62.0|             31.0|\n",
      "|    max|            1631.0|            133.0|            1638.0|           4983.0|\n",
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "trainquery = \"\"\"\n",
    "SELECT\n",
    "  DEP_DELAY, TAXI_OUT, ARR_DELAY, DISTANCE\n",
    "FROM flights f\n",
    "JOIN traindays t\n",
    "ON f.FL_DATE == t.FL_DATE\n",
    "WHERE\n",
    "  t.is_train_day == 'True' AND\n",
    "  f.dep_delay IS NOT NULL AND \n",
    "  f.arr_delay IS NOT NULL\n",
    "\"\"\"\n",
    "traindata = spark.sql(trainquery)\n",
    "traindata.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "|summary|         DEP_DELAY|         TAXI_OUT|         ARR_DELAY|         DISTANCE|\n",
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "|  count|              9514|             9514|              9514|             9514|\n",
      "|   mean|2.6394786630229135|14.62528904771915|-4.238385537103216|870.8421273912129|\n",
      "| stddev|29.693248310855065| 7.28500427136442|32.565523694571986| 617.509578518596|\n",
      "|    min|             -31.0|              2.0|             -62.0|             31.0|\n",
      "|    max|            1631.0|            133.0|            1638.0|           4983.0|\n",
      "+-------+------------------+-----------------+------------------+-----------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "trainquery = \"\"\"\n",
    "SELECT\n",
    "  DEP_DELAY, TAXI_OUT, ARR_DELAY, DISTANCE\n",
    "FROM flights f\n",
    "JOIN traindays t\n",
    "ON f.FL_DATE == t.FL_DATE\n",
    "WHERE\n",
    "  t.is_train_day == 'True' AND\n",
    "  f.CANCELLED == '0.00' AND \n",
    "  f.DIVERTED == '0.00'\n",
    "\"\"\"\n",
    "traindata = spark.sql(trainquery)\n",
    "traindata.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def to_example(fields):\n",
    "  return LabeledPoint(\\\n",
    "              float(fields['ARR_DELAY'] < 15), #ontime? \\\n",
    "              [ \\\n",
    "                  fields['DEP_DELAY'], \\\n",
    "                  fields['TAXI_OUT'],  \\\n",
    "                  fields['DISTANCE'],  \\\n",
    "              ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "examples = traindata.rdd.map(to_example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.162365742978,-0.160228517204,3.75487291939e-05] 5.95703978472\n"
     ]
    }
   ],
   "source": [
    "lrmodel = LogisticRegressionWithLBFGS.train(examples, intercept=True)\n",
    "print(lrmodel.weights,lrmodel.intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "print(lrmodel.predict([6.0,12.0,594.0]))\n",
    "print(lrmodel.predict([36.0,12.0,594.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.956161192349\n",
      "0.143248721331\n"
     ]
    }
   ],
   "source": [
    "lrmodel.clearThreshold()\n",
    "print(lrmodel.predict([6.0,12.0,594.0]))\n",
    "print(lrmodel.predict([36.0,12.0,594.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "lrmodel.setThreshold(0.7) # cancel if prob-of-ontime < 0.7\n",
    "print(lrmodel.predict([6.0,12.0,594.0]))\n",
    "print(lrmodel.predict([36.0,12.0,594.0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Predict with the model </h2>\n",
    "\n",
    "First save the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "!gsutil -m rm -r gs://$BUCKET/flights/sparkmloutput/model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "MODEL_FILE='gs://' + BUCKET + '/flights/sparkmloutput/model'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lrmodel.save(sc, MODEL_FILE)\n",
    "print('{} saved'.format(MODEL_FILE))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "lrmodel = 0\n",
    "print(lrmodel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now retrieve the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pyspark.mllib.classification import LogisticRegressionModel\n",
    "lrmodel = LogisticRegressionModel.load(sc, MODEL_FILE)\n",
    "lrmodel.setThreshold(0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print(lrmodel.predict([36.0,12.0,594.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(lrmodel.predict([8.0,4.0,594.0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Examine the model behavior </h2>\n",
    "\n",
    "For dep_delay=20 and taxiout=10, how does the distance affect prediction?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.755139551394\n"
     ]
    }
   ],
   "source": [
    "lrmodel.clearThreshold() # to make the model produce probabilities\n",
    "print(lrmodel.predict([20, 10, 500]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "dist = np.arange(10, 2000, 10)\n",
    "prob = [lrmodel.predict([20, 10, d]) for d in dist]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f36a5c2a3d0>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bzU7Kl7m8uzmbixU1dAttR1KCFWtUF3dHE/FYTsvCW2+9xUsvvUSHDh0cxy2Y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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36a5d56690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style(\"whitegrid\")\n",
    "ax = plt.plot(dist, prob)\n",
    "plt.xlabel('distance (miles)')\n",
    "plt.ylabel('probability of ontime arrival')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f36a4423290>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VnKueSNew4Inokbq0dUT/YHckpRcg8thNqeMQUSOx4ImoXn8d3QEWpgps2BOPnPxSqeMQ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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36a5cc6e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay = np.arange(-20, 60, 1)\n",
    "prob = [lrmodel.predict([d, 10, 500]) for d in delay]\n",
    "ax = plt.plot(delay, prob)\n",
    "plt.xlabel('departure delay (minutes)')\n",
    "plt.ylabel('probability of ontime arrival')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Evaluate model </h2>\n",
    "\n",
    "Evaluate on the test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SELECT\n",
      "  DEP_DELAY, TAXI_OUT, ARR_DELAY, DISTANCE\n",
      "FROM flights f\n",
      "JOIN traindays t\n",
      "ON f.FL_DATE == t.FL_DATE\n",
      "WHERE\n",
      "  t.is_train_day == 'False' AND\n",
      "  f.CANCELLED == '0.00' AND \n",
      "  f.DIVERTED == '0.00'\n",
      "\n"
     ]
    }
   ],
   "source": [
    "inputs = 'gs://{}/flights/tzcorr/all_flights-00001-*'.format(BUCKET) # you may have to change this to find a shard that has test data\n",
    "flights = spark.read\\\n",
    "            .schema(schema)\\\n",
    "            .csv(inputs)\n",
    "flights.createOrReplaceTempView('flights')\n",
    "testquery = trainquery.replace(\"t.is_train_day == 'True'\",\"t.is_train_day == 'False'\")\n",
    "print(testquery)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testdata = spark.sql(testquery)\n",
    "examples = testdata.rdd.map(to_example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+-----------------+------------------+------------------+-----------------+\n",
      "|summary|        DEP_DELAY|          TAXI_OUT|         ARR_DELAY|         DISTANCE|\n",
      "+-------+-----------------+------------------+------------------+-----------------+\n",
      "|  count|            31721|             31721|             31721|            31721|\n",
      "|   mean|22.06188329497809|17.100438195517164|18.437785694019734|861.5131301030863|\n",
      "| stddev|55.27263492541411|  9.92470074434109| 58.42307362543692| 623.824325676582|\n",
      "|    min|            -43.0|               1.0|             -65.0|             31.0|\n",
      "|    max|           1239.0|             140.0|            1214.0|           4983.0|\n",
      "+-------+-----------------+------------------+------------------+-----------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "testdata.describe().show()  # if this is empty, change the shard you are using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All flights:\n",
      "{'correct_cancel': 0.8220530174844896, 'total_noncancel': 21083, 'correct_noncancel': 0.938765830289807, 'total_cancel': 10638}\n",
      "Flights near decision threshold:\n",
      "{'correct_cancel': 0.30975143403441685, 'total_noncancel': 461, 'correct_noncancel': 0.7700650759219089, 'total_cancel': 523}\n"
     ]
    }
   ],
   "source": [
    "def eval(labelpred):\n",
    "    cancel = labelpred.filter(lambda (label, pred): pred < 0.7)\n",
    "    nocancel = labelpred.filter(lambda (label, pred): pred >= 0.7)\n",
    "    corr_cancel = cancel.filter(lambda (label, pred): label == int(pred >= 0.7)).count()\n",
    "    corr_nocancel = nocancel.filter(lambda (label, pred): label == int(pred >= 0.7)).count()\n",
    "    \n",
    "    cancel_denom = cancel.count()\n",
    "    nocancel_denom = nocancel.count()\n",
    "    if cancel_denom == 0:\n",
    "        cancel_denom = 1\n",
    "    if nocancel_denom == 0:\n",
    "        nocancel_denom = 1\n",
    "    return {'total_cancel': cancel.count(), \\\n",
    "            'correct_cancel': float(corr_cancel)/cancel_denom, \\\n",
    "            'total_noncancel': nocancel.count(), \\\n",
    "            'correct_noncancel': float(corr_nocancel)/nocancel_denom \\\n",
    "           }\n",
    "\n",
    "# Evaluate model\n",
    "lrmodel.clearThreshold() # so it returns probabilities\n",
    "labelpred = examples.map(lambda p: (p.label, lrmodel.predict(p.features)))\n",
    "print('All flights:')\n",
    "print(eval(labelpred))\n",
    "\n",
    "# keep only those examples near the decision threshold\n",
    "print('Flights near decision threshold:')\n",
    "labelpred = labelpred.filter(lambda (label, pred): pred > 0.65 and pred < 0.75)\n",
    "print(eval(labelpred))ß"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright 2019 Google Inc. Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License."
   ]
  }
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