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@cjauvin
Last active December 29, 2015 14:28
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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Unit Loss Modeling with Probabilistic Binary Classification"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The idea is to replace the regression component of our unit loss ranking model by a binary classification mechanism (a logistic regression trained with SGD), on the basis that it should be easier to solve, given the extreme features (i.e. very long and thin tail) of the target distribution. Defined as the unit loss being *over* a certain (user-defined) threshold, the positive class can be thus interpreted simply as \"is an outstanding risk\". And since in the end we are only interested in the *ranking* of the risks, we can use the probabilities returned by the model as the ranking criterion. The use of a classification model also allows to explore the results in terms of precision, recall, AUC, etc, which can yield additional insights. **TLDR: with this method, at 0.5%, the test mean loss is maximized a bit below 2500\\$, using a threshold of 1000.**\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pandas as pd\n",
"from sklearn.preprocessing import *\n",
"from sklearn.metrics import *\n",
"from sklearn.linear_model import *\n",
"\n",
"df = pd.io.parsers.read_csv('/Users/cjauvin/Desktop/rsp/data/rsp_trainsub_ON_201310.csv')\n",
"df.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 56,
"text": [
"(4633152, 60)"
]
}
],
"prompt_number": 56
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"target = 'rsk_gldf_unit_losses'\n",
"\n",
"# remove NAs (i.e. missing)\n",
"df = df[pd.notnull(df[target])]\n",
"df.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 57,
"text": [
"(4572466, 60)"
]
}
],
"prompt_number": 57
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# train/test split\n",
"train = df[df['policy_group'] < 80]\n",
"test = df[df['policy_group'] >= 80]\n",
"\n",
"# retain these because we need to remove them of the training set,\n",
"# but will need them in the final error computation\n",
"train_rsk_act_ee_tot = train['rsk_act_ee_tot'].values\n",
"test_rsk_act_ee_tot = test['rsk_act_ee_tot'].values\n",
"train_target = train[target].values\n",
"test_target = test[target].values\n",
"\n",
"# remove certain columns\n",
"excluded = ['rsk_gpay_tot', 'rsk_ginc_tot', 'rsk_gldf_tot', 'rsk_act_ep_tot',\n",
" 'policy_nbr', 'risk_nbr', 'effective_date_of_policy',\n",
" 'policy_expiry_date', 'policy_relation', 'rsk_gcap_tot',\n",
" 'exp_rate', 'policy_group',\n",
" 'rsk_act_ee_tot', # <- used in top_ranked_loss\n",
" target] # <- target\n",
"\n",
"for c in excluded:\n",
" del df[c]\n",
" del train[c]\n",
" del test[c]\n",
" \n",
"# map string categorical features to integer\n",
"for c in ['ON_Region', 'gender', 'company_name', 'naf3yrs']:\n",
" le = LabelEncoder()\n",
" le.fit(df[c])\n",
" train[c] = le.transform(train[c])\n",
" test[c] = le.transform(test[c])\n",
"\n",
"# impute missing values\n",
"imp = Imputer(missing_values='NaN', strategy='mean', axis=0, copy=False)\n",
"imp.fit(train)\n",
"\n",
"# center to the mean and scale to unit variance\n",
"scaler = StandardScaler()\n",
"scaler.fit(imp.transform(train))\n",
"\n",
"X_train = pd.DataFrame(scaler.transform(imp.transform(train)),\n",
" columns=df.columns.tolist())\n",
"X_test = pd.DataFrame(scaler.transform(imp.transform(test)),\n",
" columns=df.columns.tolist())\n",
"\n",
"# make sure that we're not cheating!\n",
"assert target not in X_train.columns.tolist() and 'rsk_act_ee_tot' not in X_train.columns.tolist()\n",
"assert target not in X_test.columns.tolist() and 'rsk_act_ee_tot' not in X_test.columns.tolist()\n",
"\n",
"print 'train:', X_train.shape\n",
"print 'test:', X_test.shape"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 58
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now collect the AUC results obtained by classifiers trained with datasets for which the negative/positive class composition is given by different *target thresholds*, i.e. different \"definitions\" for the positive class. Note that no matter what threshold we use, the training set is always heavily skewed in favor of the negative class of course (hence the use of the AUC instead of a metric like accuracy, which would be meaningless in this context). For each threshold, we train a logistic regression model, which is done very efficiently (~3 minutes per classifier on 24-core machine) with stochastic gradient descent (SGD)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"rcParams['figure.figsize'] = 12, 8\n",
"\n",
"target_thresholds = range(0, 5001, 250)\n",
"train_aucs = []\n",
"test_aucs = []\n",
"train_preds = []\n",
"test_preds = []\n",
"for target_threshold in target_thresholds:\n",
" #print 'target_treshold =', target_threshold\n",
" #print '-------------------------'\n",
" y_train = (train_target > target_threshold).astype(int)\n",
" y_test = (test_target > target_threshold).astype(int)\n",
" #print 'train pos/neg: %d/%d' % ((y_train == 0).sum(), (y_train == 1).sum())\n",
" #print 'test pos/neg: %d/%d' % ((y_test == 0).sum(), (y_test == 1).sum())\n",
" clf = SGDClassifier(loss='log', class_weight='auto', n_iter=100)\n",
" clf.fit(X_train, y_train)\n",
" y_train_pred = clf.predict_proba(X_train)[:, 1] # get the predictions for \n",
" y_test_pred = clf.predict_proba(X_test)[:, 1] # the positive class\n",
" train_preds.append(y_train_pred)\n",
" test_preds.append(y_test_pred)\n",
" train_aucs.append(roc_auc_score(y_train, y_train_pred))\n",
" test_aucs.append(roc_auc_score(y_test, y_test_pred))\n",
" #print 'train AUC:', roc_auc_score(y_train, y_train_pred)\n",
" #print 'test AUC:', roc_auc_score(y_test, y_test_pred)\n",
"plot(target_thresholds, train_aucs, 'r-', label='train')\n",
"plot(target_thresholds, test_aucs, 'b-', label='test')\n",
"xlabel('target thresholds')\n",
"ylabel('AUC')\n",
"legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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J+XvvAdWrA9OnA7dvKxQ8ERERkSlFRwPffSdtBStXBs6fB95/H8iXT+3ITI4JeC7orsbD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\naPr3d/9Y/VBMjG0MM2yYdPCgt0eDurBokXTffXaly2bNvD0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VVkpNmtTp2wEAAADqhNsC\neEhIyK9uU1lZqXXr1mnx4sVaunSp7rnnHhUWFmrLli167LHHVFRUpJKSEh06dEizZ8/+9YM6HCpt\nmKTWraVaHB4AAADwuHB37TgmJkbFxcWu+8XFxa5Sk2Pi4uIUFRWlyMhIRUZGqnfv3lq/fr2qq6t1\n7rnnqnnz5pKkgQMHatWqVRo2bNjPjjN16lTX17nr1yv07Gup/wYAAMBvUlBQoIKCArfsO8QYY9yx\n46qqKqWkpGj58uVq06aNunbtqrlz5yotLc21zZdffqnx48dr6dKlOnr0qLp166b58+ersrJSw4YN\n09q1a1W/fn2NHDlSXbt21bhx42oOPiRENYbfqZPmX/2yXvkkUS+/7I53BQAAgGD0s9z5G7htBjw8\nPFzTp09XXl6enE6nRo8erbS0NM2YMUOSNHbsWKWmpqpfv37KzMxUaGioxowZo/bt20uSrrvuOuXk\n5Cg0NFSdOnXSjTfe+OsHdThUWhXFBZgAAADwWW6bAfeEGp9EKiqkM8/U5IlH1Kx5qG67zbtjAwAA\nQOCoyxnwwFkJs7RUio5WyfZQZsABAADgswIngNMDHAAAAH6AAA4AAAB4UEAGcNoQAgAAwFcFVAA/\n3LKtysqks87y9mAAAACAEwuoAL69wTlq1YpVMAEAAOC7AiqAl0acTf03AAAAfFpgBXC1pv4bAAAA\nPi0wArgxksOhkqPNmQEHAACATwuMAL53r1Svnkr31COAAwAAwKcFRgCnBzgAAAD8RMAFcGrAAQAA\n4MsCKoCXlDADDgAAAN8WUAGcEhQAAAD4uoAJ4BXRcdq/X2rRwtuDAQAAAE4uYAL4jgYJatlSCg2M\ndwQAAIAAFRhx1eFQSXgc5ScAAADweYERwLdtU2l1KwI4AAAAfJ7/B/CjR6X9+1Va3oQADgAAAJ/n\n/wG8pERq1UqlO0LpAQ4AAACf5/8BnB7gAAAA8CMBE8DpAQ4AAAB/QAAHAAAAPCigAjg14AAAAPB1\nARHAq1rFatcuqWVLbw8GAAAA+GUBEcB3NohX8+ZSeLi3BwMAAAD8soAI4KVhsdR/AwAAwC/4fwAv\nKVFpdUvqvwEAAOAX/D+AR0aqZHd9ZsABAADgF/w/gNOCEAAAAH6EAA4AAAB4UEAE8JISeoADAADA\nPwREAGcGHAAAAP6CAA4AAAB4kN8H8OrWMdq5U2rVytsjAQAAAH6d3wfw7xu0VZMm0hlneHskAAAA\nwK/z+wBeGhpD+QkAAAD8hv8H8CPNCOAAAADwG/4fwHeEEsABAADgN/w+gNMDHAAAAP7E7wM4LQgB\nAADgT9wawJcsWaLU1FQlJydr2rRpJ9ymoKBA2dnZSk9PV25uriTpq6++UnZ2tuvWpEkTPfHEEyd8\nPQEcAAAA/iTEGGPcsWOn06mUlBQtW7ZMMTEx6tKli+bOnau0tDTXNvv27VPPnj21dOlSxcbGateu\nXYqKiqqxn+rqasXExGjNmjWKi4urOfiQEHXvbvTQQ1LPnu54FwAAAIDNnXUVm902A75mzRolJSUp\nPj5eERERGjx4sBYsWFBjmzlz5mjQoEGKjY2VpJ+Fb0latmyZEhMTfxa+j6EGHAAAAP7EbQHc4XDU\nCM2xsbFyOBw1tiksLNSePXvUp08f5eTkKD8//2f7mTdvnoYOHXrS42zfTgkKAAAA/Ee4u3YcEhLy\nq9tUVlZq3bp1Wr58ucrLy9WjRw91795dycnJkqSKigotXLjwpPXj9jhTdf/99uvc3FxXHTkAAABw\nugoKClRQUOCWfbstgMfExKi4uNh1v7i42FVqckxcXJyioqIUGRmpyMhI9e7dW+vXr3cF8Lffflud\nO3dWixYtTnqcc86ZqqlT3fIWAAAAEKR+OrF711131dm+3VaCkpOTo8LCQhUVFamiokLz58/XgAED\namxzxRVXaOXKlXI6nSovL9fq1avVvn171/Nz587VkCFDfvE41H8DAADAn7htBjw8PFzTp09XXl6e\nnE6nRo8erbS0NM2YMUOSNHbsWKWmpqpfv37KzMxUaGioxowZ4wrgZWVlWrZsmWbOnPmLx6H+GwAA\nAP7EbW0IPSEkJESTJhk98IC3RwIAAIBA5hdtCD2FGXAAAAD4E78P4NSAAwAAwJ/4fQBnBhwAAAD+\nhAAOAAAAeBABHAAAAPAgv++C4sfDBwAAgJ+gCwoAAADgpwjgAAAAgAcRwAEAAAAPIoADAAAAHkQA\nBwAAADyIAA4AAAB4EAEcAAAA8CACOAAAAOBBBHAAAADAgwjgAAAAgAcRwAEAAAAPIoADAAAAHkQA\nBwAAADyIAA4AAAB4EAEcAAAA8CACOAAAAOBBBHAAAADAgwjgAAAAgAcRwAEAAAAPIoADAAAAHkQA\nBwAAADyIAA4AAAB4EAEcAAAA8CACOAAAAOBBBHAAAADAgwjgAAAAgAcRwAEAAAAPIoADAAAAHkQA\nBwAAADyIAA4AAAB4EAEcAAAA8CACOAAAAOBBBHAAAADAgwjgAAAAgAcRwAEAAAAPcmsAX7JkiVJT\nU5WcnKxp06adcJuCggJlZ2crPT1dubm5rsf37dunq6++WmlpaWrfvr0+/PBDdw4VAaSgoMDbQ4AP\n4rzAiXBe4EQ4L+BubgvgTqdT48eP15IlS7Rx40bNnTtXmzZtqrHNvn37NG7cOC1cuFCff/65Xnnl\nFddzEydO1KWXXqpNmzZpw4YNSktLc9dQEWD4xokT4bzAiXBe4EQ4L+Bubgvga9asUVJSkuLj4xUR\nEaHBgwdrwYIFNbaZM2eOBg0apNjYWElSVFSUJGn//v1asWKFRo0aJUkKDw9XkyZN3DVUAAAAwGPc\nFsAdDofi4uJc92NjY+VwOGpsU1hYqD179qhPnz7KyclRfn6+JGnr1q1q0aKFrr/+enXq1EljxoxR\neXm5u4YKAAAAeI5xk1deecXccMMNrvv5+flm/PjxNbYZN26c6dGjhykvLze7du0yycnJZvPmzWbt\n2rUmPDzcrFmzxhhjzMSJE80dd9zxs2MkJiYaSdy4cePGjRs3bty4ufWWmJhYZzk5XG4SExOj4uJi\n1/3i4mJXqckxcXFxioqKUmRkpCIjI9W7d29t2LBB5513nmJjY9WlSxdJ0tVXX63777//Z8f4+uuv\n3TV8AAAAwC3cVoKSk5OjwsJCFRUVqaKiQvPnz9eAAQNqbHPFFVdo5cqVcjqdKi8v1+rVq5WWlqbo\n6GjFxcVp8+bNkqRly5apQ4cO7hoqAAAA4DFumwEPDw/X9OnTlZeXJ6fTqdGjRystLU0zZsyQJI0d\nO1apqanq16+fMjMzFRoaqjFjxqh9+/aSpCeffFLDhg1TRUWFEhMT9fzzz7trqAAAAIDHhBhjjLcH\nAQAAAAQLv10JszaL/CAwjBo1StHR0crIyHA9tmfPHvXt21ft2rXTxRdfrH379rme+8c//qHk5GSl\npqbqnXfecT3+8ccfKyMjQ8nJyZo4caJH3wPqXnFxsfr06aMOHTooPT1dTzzxhCTOjWB35MgRdevW\nTR07dlT79u01ZcoUSZwXsJxOp7Kzs9W/f39JnBeQ4uPjlZmZqezsbHXt2lWSh86LOruc04OqqqpM\nYmKi2bp1q6moqDBZWVlm48aN3h4W3OT9998369atM+np6a7HJk2aZKZNm2aMMeb+++83kydPNsYY\n88UXX5isrCxTUVFhtm7dahITE011dbUxxpguXbqY1atXG2OMueSSS8zbb7/t4XeCulRaWmo++eQT\nY4wxBw8eNO3atTMbN27k3IApKyszxhhTWVlpunXrZlasWMF5AWOMMQ8//LAZOnSo6d+/vzGGnyUw\nJj4+3uzevbvGY544L/xyBrw2i/wgcPTq1UvNmjWr8dibb76pESNGSJJGjBihN954Q5K0YMECDRky\nRBEREYqPj1dSUpJWr16t0tJSHTx40PXp9rrrrnO9Bv6pVatW6tixoyTpzDPPVFpamhwOB+cG1KBB\nA0lSRUWFnE6nmjVrxnkBbdu2TYsXL9YNN9wg80P1LecFJLnOh2M8cV74ZQCvzSI/CGw7duxQdHS0\nJCk6Olo7duyQJJWUlNRod3ns3Pjp4zExMZwzAaSoqEiffPKJunXrxrkBVVdXq2PHjoqOjnaVKXFe\n4Oabb9aDDz6o0NAfow/nBUJCQnTRRRcpJydHM2fOlOSZ88JtXVDcKSQkxNtDgA8JCQnhnAhihw4d\n0qBBg/T444+rUaNGNZ7j3AhOoaGh+vTTT7V//37l5eXp3XffrfE850XwWbRokVq2bKns7GwVFBSc\ncBvOi+D0wQcfqHXr1vr+++/Vt29fpaam1njeXeeFX86A12aRHwS26Ohobd++XZJUWlqqli1bSvr5\nubFt2zbFxsYqJiZG27Ztq/F4TEyMZweNOldZWalBgwZp+PDhuvLKKyVxbuBHTZo00WWXXaaPP/6Y\n8yLIrVq1Sm+++aYSEhI0ZMgQ/ec//9Hw4cM5L6DWrVtLklq0aKGrrrpKa9as8ch54ZcBvDaL/CCw\nDRgwQLNmzZIkzZo1yxW+BgwYoHnz5qmiokJbt25VYWGhunbtqlatWqlx48ZavXq1jDHKz893vQb+\nyRij0aNHq3379rrppptcj3NuBLddu3a5OhYcPnxY//73v5Wdnc15EeTuu+8+FRcXa+vWrZo3b54u\nuOAC5efnc14EufLych08eFCSVFZWpnfeeUcZGRmeOS/q6ipST1u8eLFp166dSUxMNPfdd5+3hwM3\nGjx4sGndurWJiIgwsbGx5l//+pfZvXu3ufDCC01ycrLp27ev2bt3r2v7e++91yQmJpqUlBSzZMkS\n1+MfffSRSU9PN4mJiWbChAneeCuoQytWrDAhISEmKyvLdOzY0XTs2NG8/fbbnBtBbsOGDSY7O9tk\nZWWZjIwM88ADDxhjDOcFXAoKClxdUDgvgts333xjsrKyTFZWlunQoYMrT3rivGAhHgAAAMCD/LIE\nBQAAAPBXBHAAAADAgwjgAAAAgAcRwAEAAAAPIoADAAAAHkQABwAAADyIAA4AdWD//v365z//6ZFj\nLViwQJs2barVc7m5ufr444/r9PhFRUXKyMg4pdeMHDlSr7766s8eLygoUP/+/etqaADgFwjgAFAH\n9u7dq6effvqUXmOM0eksxfD6669r48aNtXouJCTkV/dXVVV1ymM4VSEhIbUaCwAEAwI4ANSB2267\nTVu2bFF2drYmT56ssrIyXXTRRercubMyMzP15ptvSrKzxykpKRoxYoQyMjJUXFyse+65R6mpqerV\nq5eGDh2qhx9+WJK0ZcsWXXLJJcrJyVHv3r311VdfadWqVVq4cKEmTZqk7OxsffPNN64xHP9cp06d\nXM+9/PLL6tatm1JSUrRy5UpJ0gsvvKABAwbowgsvVN++fVVeXq5Ro0apW7du6tSpk2u8X3zxhbp1\n66bs7GxlZWVpy5YtkiSn06kbb7xR6enpysvL05EjRyRJn376qbp3766srCwNHDjQtSy8JNeHjSVL\nligtLU2dO3fW66+/7nr+vffeU3Z2trKzs9WpUycdOnTILf9WAOB1dbqmJwAEqaKiIpOenu66X1VV\nZQ4cOGCMMeb77783SUlJxhhjtm7dakJDQ83q1auNMcasWbPGdOzY0Rw9etQcPHjQJCcnm4cfftgY\nY8wFF1xgCgsLjTHGfPjhh+aCCy4wxhgzcuRI8+qrr55wHD99Ljc319x6663GGGMWL15sLrroImOM\nMc8//7yJjY11LbE8ZcoU8+KLLxpjjNm7d69p166dKSsrMxMmTDCzZ882xhhTWVlpDh8+bLZu3WrC\nw8PN+vXrjTHG/O53v3O9NiMjw7z//vvGGGPuvPNOc9NNN9UY1+HDh01cXJz5+uuvXa89tix4//79\nzapVq4wxxpSVlZmqqqpT+BcAAP8R7u0PAAAQCMxPSkmqq6s1ZcoUrVixQqGhoSopKdHOnTslSW3b\ntlXXrl0lSR988IGuvPJKnXHGGTrjjDNc9dBlZWVatWqVrrnmGtc+KyoqTnq8XxrLwIEDJUmdOnVS\nUVGR6/G+ffuqadOmkqR33nlHCxcu1EMPPSRJOnr0qL777jv16NFD9957r7Zt26aBAwcqKSlJkpSQ\nkKDMzExJUufOnVVUVKQDBw5o//796tWrlyRpxIgRNcZvjNGXX36phIQEJSYmSpKuvfZaPfvss5Kk\nnj176uabb9awYcM0cOBAxcTEnPQ9AoA/I4ADgBvMnj1bu3bt0rp16xQWFqaEhARXmUbDhg1d24WE\nhNQIzMe+rq6uVrNmzfTJJ5+ccP+/VE/90+fq1asnSQoLC6tR7338OCTptddeU3Jyco3HUlNT1b17\ndy1atEiXXnqpZsyYoYSEBNc+j+332Hs73ok+JPx0bMdvM3nyZF1++eV666231LNnTy1dulQpKSkn\nfZ8A4K+oAQeAOtCoUSMdPHjQdf/AgQNq2bKlwsLC9O677+rbb7894et69uyphQsX6ujRozp06JDe\neust1/4SEhL0yiuvSLJBdcOGDa7nDhw4cNJxnOy5X5KXl6cnnnjCdf9Y8N+6dasSEhI0YcIEXXHF\nFfrss89OGP6NMWrcuLGaNWvmqjPPz89Xbm6ua5uQkBClpqaqqKjIVZ8+d+5c1/NbtmxRhw4d9Oc/\n/1ldunTRV199dcrvAwD8AQEcAOpA8+bN1bNnT2VkZGjy5MkaNmyYPvroI2VmZio/P19paWmubY8P\nsDk5ORowYIAyMzN16aWXKiMjQ02aNJFkZ9Gfe+45dezYUenp6a4LIwcPHqwHH3xQnTt3rnER5q89\nd/yxf9qV5I477lBlZaUyMzOVnp6uv/3tb5Kkl156Senp6crOztYXX3yh6667TsaYn4XwY/dnzZql\nSZMmKSsrSxs2bNCdd95ZY7t69erp2Wef1WWXXabOnTsrOjra9drHH39cGRkZysrK0hlnnKFLLrnk\nFP4FAMB/hJhfKiQEALhdWVmZGjZsqPLycp1//vmaOXOmOnbs6O1hAQDchBpwAPCyG2+8URs3btSR\nI0c0cuRIwjcABDhmwAEAAAAPogYcAAAA8CACOAAAAOBBBHAAAADAgwjgAAAAgAcRwAEAAAAP+v9I\nAf5FZuEZJwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x86c4dd8>"
]
}
],
"prompt_number": 62
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can finally use the ranking function to report the results at the multiple thresholds. Note that instead of sorting by the actual loss, we sort by the \"probability of being an outstanding risk\" (i.e. having a unit loss over a certain threshold), which seems to be a reasonable proxy in this context. **At 0.5%, the test mean loss is maximized a bit below 2500\\$, at a threshold of 1000.**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from collections import defaultdict\n",
"\n",
"def top_ranked_loss(data, thresholds, target='rsk_gldf_unit_losses',\n",
" score='rsk_gldf_unit_losses_pred'):\n",
" # 0 - totw = sum(rsk_act_ee_tot) over all test set\n",
" # 1 - sort test set risks in decreasing order of score (model output).\n",
" # 2 - take top x% of risks as measured by sum(rsk_act_ee_tot),\n",
" # i.e. [sum(rsk_act_ee_tot) over top x% ]/totw = x%\n",
" # 3 - compute\n",
" # - 365.25 * 0.85 * sum(rsk_gldf_unit_losses * rsk_act_ee_tot) /\n",
" # sum(rsk_act_ee_tot)\n",
" # - sum(rsk_act_ee_tot) for top x%\n",
" # Repeat for x = 0.5%, 0.6%, ... 1.5%\n",
" thresholds = thresholds[:]\n",
" rsk_act_ee_tot_sum = data['rsk_act_ee_tot'].sum()\n",
" data.sort(score, ascending=False, inplace=True) # sort by probabilistic outcome\n",
" data.reset_index(inplace=True)\n",
" #print data.loc[:10, [score, target]]\n",
" rsk_act_ee_tot_cumul = 0\n",
" loss_cumul = 0 # rsk_gldf_unit_losses * rsk_act_ee_tot\n",
" results = []\n",
" n = 0\n",
" for _, row in data.iterrows():\n",
" n += 1\n",
" rsk_act_ee_tot_cumul += row['rsk_act_ee_tot']\n",
" loss_cumul += row[target] * row['rsk_act_ee_tot']\n",
" if rsk_act_ee_tot_cumul / rsk_act_ee_tot_sum >= thresholds[0]:\n",
" results.append((365.25 * 0.85 * loss_cumul / rsk_act_ee_tot_cumul,\n",
" rsk_act_ee_tot_cumul, row[score], n))\n",
" thresholds.pop(0)\n",
" if not thresholds:\n",
" break\n",
" return results\n",
"\n",
"# 0.5% to 1.5%, in 0.1% increments\n",
"thresholds = (np.arange(0.5, 1.6, 0.1) / 100).tolist()\n",
"\n",
"train_losses = defaultdict(list) # threshold -> []\n",
"test_losses = defaultdict(list)\n",
"\n",
"for i, tt in enumerate(target_thresholds):\n",
"\n",
" train_results = pd.DataFrame({\n",
" 'rsk_act_ee_tot': train_rsk_act_ee_tot,\n",
" target: train_target,\n",
" '%s_pred' % target: train_preds[i]\n",
" })\n",
" \n",
" test_results = pd.DataFrame({\n",
" 'rsk_act_ee_tot': test_rsk_act_ee_tot,\n",
" target: test_target,\n",
" '%s_pred' % target: test_preds[i]\n",
" })\n",
"\n",
" train_trl = top_ranked_loss(train_results, thresholds)\n",
" test_trl = top_ranked_loss(test_results, thresholds)\n",
" \n",
" train_losses['0.5%'].append(train_trl[0][0])\n",
" train_losses['1.5%'].append(train_trl[10][0])\n",
" test_losses['0.5%'].append(test_trl[0][0])\n",
" test_losses['1.5%'].append(test_trl[10][0])\n",
"\n",
"plot(target_thresholds, train_losses['0.5%'], 'r-', label='train 0.5%')\n",
"plot(target_thresholds, test_losses['0.5%'], 'b-', label='test 0.5%')\n",
"plot(target_thresholds, train_losses['1.5%'], 'r--', label='train 1.5%')\n",
"plot(target_thresholds, test_losses['1.5%'], 'b--', label='test 1.5%')\n",
"xlabel('target thresholds')\n",
"ylabel('mean loss')\n",
"legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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MlSpVaNWqFTt27HDMga8QEBBA2J91ftWrV89Ksi964okniIuLY+HChWzatInS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\nRyLieErEpah6/HH49VfTBaQ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HDRgAL70EwcGFE5e4l8aN4X//g7Q0uyPJPacl4gkJCTRt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\nTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x86d3be0>"
]
}
],
"prompt_number": 65
}
],
"metadata": {}
}
]
}
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