2-05_logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook you will use GPU-accelerated logistic regression to predict infection risk based on features of our population members."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By the time you complete this notebook you will be able to:\n",
    "\n",
    "- Use GPU-accelerated logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cudf\n",
    "import cuml\n",
    "\n",
    "import cupy as cp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "gdf = cudf.read_csv('./data/pop_2-05.csv', usecols=['age', 'sex', 'infected'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age         float64\n",
       "sex         float64\n",
       "infected    float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdf.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(58479894, 3)"
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "gdf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>infected</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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      "text/plain": [
       "   age  sex  infected\n",
       "0  0.0  0.0       0.0\n",
       "1  0.0  0.0       0.0\n",
       "2  0.0  0.0       0.0\n",
       "3  0.0  0.0       0.0\n",
       "4  0.0  0.0       0.0"
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdf.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression can be used to estimate the probability of an outcome as a function of some (assumed independent) inputs. In our case, we would like to estimate infection risk based on population members' age and sex.\n",
    "\n",
    "Here we create a cuML logistic regression instance `logreg`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "logreg = cuml.LogisticRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Regress Infected Status"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `logreg.fit` method takes 2 arguments: the model's independent variables *X*, and the dependent variable *y*. Fit the `logreg` model using the `gdf` columns `age` and `sex` as *X* and the `infected` column as *y*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(penalty='l2', tol=0.0001, C=1.0, fit_intercept=True, max_iter=1000, linesearch_max_iter=50, verbose=4, l1_ratio=None, solver='qn', handle=<cuml.common.handle.Handle object at 0x7f0afda13d90>, output_type='cudf')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg.fit(gdf[['age','sex']],gdf['infected'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/regress_infected\n",
    "logreg.fit(gdf[['age', 'sex']], gdf['infected'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Viewing the Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting the model, we could use `logreg.predict` to estimate whether someone has more than a 50% chance to be infected, but since the virus has low prevalence in the population (around 1-2%, in this dataset), individual probabilities of infection are well below 50% and the model should correctly predict that no one is individually likely to have the infection.\n",
    "\n",
    "However, we also have access to the model coefficients at `logreg.coef_` as well as the intercept at `logreg.intercept_`. Both of these values are cuDF Series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cudf.core.series.Series"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(logreg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cudf.core.series.Series"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(logreg.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we view these values. Notice that changing sex from 0 to 1 has the same effect via the coefficients as changing the age by ~48 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [age, sex]\n",
      "[0.014701467289187226, 0.7002792190571455]\n",
      "Intercept:\n",
      "-5.215624611703686\n"
     ]
    }
   ],
   "source": [
    "logreg_coef = logreg.coef_\n",
    "logreg_int = logreg.intercept_\n",
    "\n",
    "print(\"Coefficients: [age, sex]\")\n",
    "print([logreg_coef[0], logreg_coef[1]])\n",
    "\n",
    "print(\"Intercept:\")\n",
    "print(logreg_int[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimate Probability of Infection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with all logistic regressions, the coefficients allow us to calculate the logit for each; from that, we can calculate the estimated percentage risk of infection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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       "<p>58479894 rows × 2 columns</p>\n",
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       "                 0         1\n",
       "0         0.994598  0.005402\n",
       "1         0.994598  0.005402\n",
       "2         0.994598  0.005402\n",
       "3         0.994598  0.005402\n",
       "4         0.994598  0.005402\n",
       "...            ...       ...\n",
       "58479889  0.960540  0.039460\n",
       "58479890  0.960540  0.039460\n",
       "58479891  0.960540  0.039460\n",
       "58479892  0.960540  0.039460\n",
       "58479893  0.960540  0.039460\n",
       "\n",
       "[58479894 rows x 2 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class_probs = logreg.predict_proba(gdf[['age', 'sex']])\n",
    "class_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remembering that a 1 indicates 'infected', we assign that class' probability to a new column in the original dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "gdf['risk'] = class_probs[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the original records with their new estimated risks, we can see how estimated risk varies across individuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>infected</th>\n",
       "      <th>risk</th>\n",
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      "text/plain": [
       "           age  sex  infected      risk\n",
       "15897951  42.0  0.0       0.0  0.009970\n",
       "15150513  40.0  0.0       0.0  0.009684\n",
       "17600721  47.0  0.0       0.0  0.010722\n",
       "42247662  37.0  1.0       0.0  0.018499\n",
       "38487468  27.0  1.0       0.0  0.016010"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdf.take(cp.random.choice(gdf.shape[0], size=5, replace=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Show Infection Prevalence is Related to Age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The positive coefficient on age suggests that the virus is more prevalent in older people, even when controlling for sex.\n",
    "\n",
    "For this exercise, show that infection prevalence has some relationship to age by printing the mean `infected` values for the oldest and youngest members of the population when grouped by age:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age\n",
       "0.0     0.000000\n",
       "1.0     0.000889\n",
       "2.0     0.001960\n",
       "3.0     0.002715\n",
       "4.0     0.003586\n",
       "          ...   \n",
       "86.0    0.023417\n",
       "87.0    0.023256\n",
       "88.0    0.024569\n",
       "89.0    0.024412\n",
       "90.0    0.025017\n",
       "Name: infected, Length: 91, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdf.groupby('age')['infected'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     infected\n",
      "age          \n",
      "0.0  0.000000\n",
      "1.0  0.000889\n",
      "2.0  0.001960\n",
      "3.0  0.002715\n",
      "4.0  0.003586\n",
      "      infected\n",
      "age           \n",
      "86.0  0.023417\n",
      "87.0  0.023256\n",
      "88.0  0.024569\n",
      "89.0  0.024412\n",
      "90.0  0.025017\n"
     ]
    }
   ],
   "source": [
    "# %load solutions/risk_by_age\n",
    "age_groups = gdf[['age', 'infected']].groupby(['age'])\n",
    "print(age_groups.mean().head())\n",
    "print(age_groups.mean().tail())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Show Infection Prevalence is Related to Sex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the positive coefficient on sex suggests that the virus is more prevalent in people with sex = 1 (females), even when controlling for age.\n",
    "\n",
    "For this exercise, show that infection prevalence has some relationship to sex by printing the mean `infected` values for the population when grouped by sex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sex\n",
       "0.0    0.010140\n",
       "1.0    0.020713\n",
       "Name: infected, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdf.groupby('sex')['infected'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/risk_by_sex\n",
    "sex_groups = gdf[['sex', 'infected']].groupby(['sex'])\n",
    "sex_groups.mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making Predictions with Separate Training and Test Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cuML gives us a simple method for producing paired training/testing data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test  = cuml.train_test_split(gdf[['age', 'sex']], gdf['infected'], train_size=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Fit Logistic Regression Model Using Training Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this exercise, create a new logistic regression model `logreg`, and fit it with the *X* and *y* training data just created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(penalty='l2', tol=0.0001, C=1.0, fit_intercept=True, max_iter=1000, linesearch_max_iter=50, verbose=4, l1_ratio=None, solver='qn', handle=<cuml.common.handle.Handle object at 0x7f0afda13d90>, output_type='cudf')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/fit_training\n",
    "logreg = cuml.LogisticRegression()\n",
    "logreg.fit(X_train, y_train)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use Test Data to Validate Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now use the same procedure as above to predict infection risk using the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0          0.008375\n",
       "1          0.006156\n",
       "2          0.019814\n",
       "3          0.007128\n",
       "4          0.016894\n",
       "             ...   \n",
       "5847985    0.014822\n",
       "5847986    0.022567\n",
       "5847987    0.019222\n",
       "5847988    0.006156\n",
       "5847989    0.037805\n",
       "Name: 1, Length: 5847990, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test_pred = logreg.predict_proba(X_test, convert_dtype=True)[1]\n",
    "y_test_pred.index = X_test.index\n",
    "y_test_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw before, very few people are actually infected in the population, even among the highest-risk groups. As a simple way to check our model, we split the test set into above-average predicted risk and below-average predicted risk, then observe that the prevalence of infections correlates closely to those predicted risks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>infected</th>\n",
       "      <th>predicted_risk</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>high_risk</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>41.472844</td>\n",
       "      <td>0.526807</td>\n",
       "      <td>0.015991</td>\n",
       "      <td>0.010347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>7.583074</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.003964</td>\n",
       "      <td>0.023301</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "                 age       sex  infected  predicted_risk\n",
       "high_risk                                               \n",
       "False      41.472844  0.526807  0.015991        0.010347\n",
       "True        7.583074  0.000000  0.003964        0.023301"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_results = cudf.DataFrame()\n",
    "test_results['age'] = X_test['age']\n",
    "test_results['sex'] = X_test['sex']\n",
    "test_results['infected'] = y_test\n",
    "test_results['predicted_risk'] = y_test_pred\n",
    "\n",
    "test_results['high_risk'] = test_results['predicted_risk'] > test_results['predicted_risk'].mean()\n",
    "\n",
    "risk_groups = test_results.groupby('high_risk')\n",
    "risk_groups.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, in a few milliseconds, we can do a two-tier analysis by sex and age:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 32 ms, sys: 44 ms, total: 76 ms\n",
      "Wall time: 76.4 ms\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>infected</th>\n",
       "      <th>predicted_risk</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <th>age</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">0.0</th>\n",
       "      <th>0.0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.015395393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.000656</td>\n",
       "      <td>0.015450358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.001346</td>\n",
       "      <td>0.015517516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.001856</td>\n",
       "      <td>0.015568505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.002615</td>\n",
       "      <td>0.015522402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">1.0</th>\n",
       "      <th>86.0</th>\n",
       "      <td>0.030582</td>\n",
       "      <td>&lt;NA&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87.0</th>\n",
       "      <td>0.029942</td>\n",
       "      <td>&lt;NA&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88.0</th>\n",
       "      <td>0.031099</td>\n",
       "      <td>&lt;NA&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89.0</th>\n",
       "      <td>0.030081</td>\n",
       "      <td>&lt;NA&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90.0</th>\n",
       "      <td>0.028144</td>\n",
       "      <td>&lt;NA&gt;</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>182 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          infected predicted_risk\n",
       "sex age                          \n",
       "0.0 0.0   0.000000    0.015395393\n",
       "    1.0   0.000656    0.015450358\n",
       "    2.0   0.001346    0.015517516\n",
       "    3.0   0.001856    0.015568505\n",
       "    4.0   0.002615    0.015522402\n",
       "...            ...            ...\n",
       "1.0 86.0  0.030582           <NA>\n",
       "    87.0  0.029942           <NA>\n",
       "    88.0  0.031099           <NA>\n",
       "    89.0  0.030081           <NA>\n",
       "    90.0  0.028144           <NA>\n",
       "\n",
       "[182 rows x 2 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "s_groups = test_results[['sex', 'age', 'infected', 'predicted_risk']].groupby(['sex', 'age'])\n",
    "s_groups.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<div align=\"center\"><h2>Please Restart the Kernel</h2></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import IPython\n",
    "app = IPython.Application.instance()\n",
    "app.kernel.do_shutdown(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next notebook, you will use GPU-accelerated k-nearest-neighbors algorithm to locate the nearest road nodes to each hospital."
   ]
  }
 ],
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