{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

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" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# code for loading the format for the notebook\n", "import os\n", "\n", "# path : store the current path to convert back to it later\n", "path = os.getcwd()\n", "os.chdir(os.path.join('..', '..', 'notebook_format'))\n", "\n", "from formats import load_style\n", "load_style(plot_style=False)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ethen 2017-09-22 16:18:29 \n", "\n", "CPython 3.5.2\n", "IPython 6.1.0\n", "\n", "numpy 1.13.1\n", "pandas 0.20.3\n", "matplotlib 2.0.0\n", "sklearn 0.18.1\n" ] } ], "source": [ "os.chdir(path)\n", "\n", "# 1. magic for inline plot\n", "# 2. magic to print version\n", "# 3. magic so that the notebook will reload external python modules\n", "# 4. magic to enable retina (high resolution) plots\n", "# https://gist.github.com/minrk/3301035\n", "%matplotlib inline\n", "%load_ext watermark\n", "%load_ext autoreload\n", "%autoreload 2\n", "%config InlineBackend.figure_format='retina'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from sklearn.ensemble import RandomForestClassifier\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.metrics import roc_auc_score, roc_curve, auc\n", "from sklearn.metrics import precision_recall_curve, average_precision_score\n", "\n", "%watermark -a 'Ethen' -d -t -v -p numpy,pandas,matplotlib,sklearn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# ROC/AUC for Binary Classification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this documentation, we'll be working with a human resource dataset. Our goal is to find out the employees that are likely to leave in the future and act upon our findings, i.e. retain them before they choose to leave. This dataset contains 12000 observations and 7 variables, each representing :\n", "\n", "- `S` The satisfaction level on a scale of 0 to 1\n", "- `LPE` Last project evaluation by a client on a scale of 0 to 1\n", "- `NP` Represents the number of projects worked on by employee in the last 12 month\n", "- `ANH` Average number of hours worked in the last 12 month for that employee\n", "- `TIC` Amount of time the employee spent in the company, measured in years\n", "- `Newborn` This variable will take the value 1 if the employee had a newborn within the last 12 month and 0 otherwise\n", "- `left` 1 if the employee left the company, 0 if they're still working here. This is our response variable" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dimensions: (12000, 7)\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " S LPE NP ANH TIC Newborn left\n", "0 0.38 0.53 2 157 3 0 1\n", "1 0.80 0.86 5 262 6 0 1\n", "2 0.11 0.88 7 272 4 0 1\n", "3 0.72 0.87 5 223 5 0 1\n", "4 0.37 0.52 2 159 3 0 1" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "filename = 'HR.csv'\n", "data = pd.read_csv(filename)\n", "print('dimensions: ', data.shape)\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To train and evaluate the model, we’ll perform a simple train/test split. 80 percent of the dataset will be used to actually train the model, while the rest will be used to evaluate the accuracy of this model, i.e. out of sample error. Note that the best practice is to split it in three ways train/validation/test split." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "labels distribution: [ 0.83333333 0.16666667]\n" ] } ], "source": [ "label_col = 'left'\n", "label = data[label_col].values\n", "data = data.drop(label_col, axis = 1)\n", "print('labels distribution:', np.bincount(label) / label.size)\n", "\n", "test_size = 0.2\n", "random_state = 1234\n", "data_train, data_test, y_train, y_test = train_test_split(\n", " data, label, test_size = test_size, random_state = random_state, stratify = label)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This probability table tells you that around 16 percent of the employees who became a staff member of yours have left! If those employees are all the ones that are performing well in the company, then this is probably not a good sign. We'll leave the exploratory analysis part to you ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sklearn Transformer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then convert perform some generic data preprocessing including standardizing the numeric columns and one-hot-encode the categorical columns (the \"Newborn\" variable is treated as a categorical variable) and convert everything into a numpy array that sklearn expects. This generic preprocessing step is written as a custom sklearn Transformer. You don't have to follow this structure if you prefer your way of doing it.\n", "\n", "To roll out our own Transformer a adheres to the sklearn API, we need to \n", "\n", "- Ensure that all arguments to the `__init__` method should be explicit: i.e. `*args` or `**kwargs` should be avoided, as they will not be correctly handled within cross-validation routines\n", "- Subclass/Inherit [`BaseEstimator`](http://scikit-learn.org/stable/modules/generated/sklearn.base.BaseEstimator.html) to get some free stuff. It will give us class representations that are more informative when printing the class object. And provides us a `get_params` and `set_params` functions. These functionalities are used in sklearn's methods such as GridSearch and RandomSearch.\n", "- Subclass/Inherit an appropriate class for your task (one of ClassifierMixin, RegressorMixin, ClusterMixin, TransformerMixin). In our case, we will be implementing a Transformer, thus we'll be subclassing [`TransformerMixin`](http://scikit-learn.org/stable/modules/generated/sklearn.base.TransformerMixin.html). For transformer, we need to implement a `.fit` method which fits some stuff on the training data and a `.transform` method that can perform transformation on both the training and test data. Note that we don't need to subclass [`TransformerMixin`](http://scikit-learn.org/stable/modules/generated/sklearn.base.TransformerMixin.html) this to work, but it does give the end-user the idea that this is a Transformer and we get the `.fit_transform` method that does the fitting and transformer on the training data in one shot for free\n", "- In the fit implementation, you'll notice results that were learned during the `.fit` method is stored with a trailing underscore (e.g., self.colnames_). This is a convention used in sklearn so that we can quickly scan the members of an estimator and distinguish which members are fitting during training time\n", "\n", "If you would like to read more on this topic. The following two link might be of interest to you.\n", "\n", "- [Blog: Creating your own estimator in scikit-learn](http://danielhnyk.cz/creating-your-own-estimator-scikit-learn/)\n", "- [scikit-learn Documentation: Rolling your own estimator](http://scikit-learn.org/dev/developers/contributing.html#rolling-your-own-estimator)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "from collections import defaultdict\n", "from sklearn.base import BaseEstimator, TransformerMixin\n", "from sklearn.preprocessing import LabelEncoder, OneHotEncoder, StandardScaler\n", "\n", "\n", "class Preprocess(BaseEstimator, TransformerMixin):\n", " \"\"\"\n", " Generic data preprocessing including:\n", " - standardize numeric columns\n", " - one-hot encode categorical columns\n", "\n", " Parameters\n", " ----------\n", " num_cols : list\n", " Numeric column's name\n", "\n", " cat_cols : list\n", " Categorical column's name\n", "\n", " Attributes\n", " ----------\n", " colnames_ : list\n", " Column name of the transformed numpy array\n", "\n", " label_encode_dict_ : dict of sklearn's LabelEncoder\n", " LabelEncoder that was used to encode the value\n", " of the categorical columns into with value between\n", " 0 and n_classes-1. Categorical columns will go through\n", " this encoding process before being one-hot encoded\n", "\n", " cat_encode_ : sklearn's OneHotEncoder\n", " OneHotEncoder that was used to one-hot encode the\n", " categorical columns\n", "\n", " scaler_ : sklearn's StandardScaler\n", " Scaler that was used to standardize the numeric columns\n", " \"\"\"\n", "\n", " def __init__(self, num_cols = None, cat_cols = None):\n", " self.num_cols = num_cols\n", " self.cat_cols = cat_cols\n", "\n", " def fit(self, data):\n", " \"\"\"\n", " Fit the Preprocess Transformer\n", "\n", " Parameters\n", " ----------\n", " data : DataFrame\n", " \"\"\"\n", " data = data.copy()\n", "\n", " # Label encoding across multiple columns in scikit-learn\n", " # https://stackoverflow.com/questions/24458645/label-encoding-across-multiple-columns-in-scikit-learn\n", " if self.cat_cols is not None:\n", " self.label_encode_dict_ = defaultdict(LabelEncoder)\n", " label_encoded = (data[self.cat_cols].\n", " apply(lambda x: self.label_encode_dict_[x.name].fit_transform(x)))\n", "\n", " self.cat_encode_ = OneHotEncoder(sparse = False)\n", " self.cat_encode_.fit(label_encoded)\n", "\n", " if self.num_cols is not None:\n", " self.scaler_ = StandardScaler().fit(data[self.num_cols])\n", "\n", " # store the column names (numeric columns comes before the\n", " # categorical columns) so we can refer to them later\n", " if self.num_cols is not None:\n", " colnames = self.num_cols.copy()\n", " else:\n", " colnames = []\n", "\n", " if self.cat_cols is not None:\n", " for col in self.cat_cols:\n", " cat_colnames = [col + '_' + str(classes)\n", " for classes in self.label_encode_dict_[col].classes_]\n", " colnames += cat_colnames\n", "\n", " self.colnames_ = colnames\n", " return self\n", "\n", " def transform(self, data):\n", " \"\"\"\n", " Trasform the data using the fitted Preprocess Transformer\n", "\n", " Parameters\n", " ----------\n", " data : DataFrame\n", " \"\"\"\n", " if self.cat_cols is not None:\n", " label_encoded = (data[self.cat_cols].\n", " apply(lambda x: self.label_encode_dict_[x.name].transform(x)))\n", " cat_encoded = self.cat_encode_.transform(label_encoded)\n", "\n", " if self.num_cols is not None:\n", " scaled = self.scaler_.transform(data[self.num_cols])\n", "\n", " # combine encoded categorical columns and scaled numerical\n", " # columns, it's the same as concatenate it along axis 1\n", " if self.cat_cols is not None and self.num_cols is not None:\n", " X = np.hstack((scaled, cat_encoded))\n", " elif self.num_cols is None:\n", " X = cat_encoded\n", " else:\n", " X = scaled\n", "\n", " return X" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "colnames ['S', 'LPE', 'NP', 'ANH', 'TIC', 'Newborn_0', 'Newborn_1']\n" ] }, { "data": { "text/plain": [ "array([[ 0.24997745, 0.61402599, 0.16885833, ..., 0.72182646,\n", " 1. , 0. ],\n", " [ 0.12545568, -0.27568766, 1.02655144, ..., -0.22007024,\n", " 1. , 0. ],\n", " [ 0.58203549, -1.34334405, 0.16885833, ..., -0.22007024,\n", " 1. , 0. ],\n", " ..., \n", " [-1.32729826, -0.75020161, -0.68883478, ..., -0.22007024,\n", " 1. , 0. ],\n", " [ 0.58203549, -0.21637342, -0.68883478, ..., -1.16196694,\n", " 0. , 1. ],\n", " [ 0.45751372, 0.25814053, -0.68883478, ..., -0.22007024,\n", " 1. , 0. ]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "num_cols = ['S', 'LPE', 'NP', 'ANH', 'TIC']\n", "cat_cols = ['Newborn']\n", "\n", "preprocess = Preprocess(num_cols, cat_cols)\n", "X_train = preprocess.fit_transform(data_train)\n", "X_test = preprocess.transform(data_test)\n", "\n", "print('colnames', preprocess.colnames_)\n", "X_train" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n", " max_depth=4, max_features='auto', max_leaf_nodes=None,\n", " min_impurity_split=1e-07, min_samples_leaf=1,\n", " min_samples_split=2, min_weight_fraction_leaf=0.0,\n", " n_estimators=10, n_jobs=1, oob_score=False, random_state=None,\n", " verbose=0, warm_start=False)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# pick your favorite classfication model\n", "tree = RandomForestClassifier(max_depth = 4)\n", "tree.fit(X_train, y_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After training our model, we need to evaluate whether its any good or not and the most straightforward and intuitive metric for a supervised classifier's performance is accuracy. Unfortunately, there are circumstances where simple accuracy does not work well. For example, with a disease that only affects 1 in a million people, a completely bogus screening test that always reports \"negative\" will be 99.9999% accurate. Unlike accuracy, ROC curves are less sensitive to class imbalance; the bogus screening test would have an AUC of 0.5, which is like not having a test at all." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ROC curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**ROC curve (Receiver Operating Characteristic)** is a commonly used way to visualize the performance of a binary classifier and AUC (Area Under the ROC Curve) is used to summarize its performance in a single number. Most machine learning algorithms have the ability to produce probability scores that tells us the strength in which it thinks a given observation is positive. Turning these probability scores into yes or no predictions requires setting a threshold; cases with scores above the threshold are classified as positive, and vice versa. Different threshold values can lead to different result:\n", "\n", "- A higher threshold is more conservative about labeling a case as positive; this makes it less likely to produce false positive (an observation that has a negative label but gets classified as positive by the model) results but more likely to miss cases that are in fact positive (lower true positive rate)\n", "- A lower threshold produces positive labels more liberally, so it creates more false positives but also generate more true positives\n", "\n", "A quick refresher on terminology:\n", "\n", "\\begin{align}\n", "[\\text{true positive rate}]\n", "&= \\frac{[\\text{# positive data points with positive predictions}]}{\\text{[# all positive data points]}} \\\\\n", "&= \\frac{[\\text{# true positives}]}{[\\text{# true positives}] + [\\text{# false negatives}]}\n", "\\end{align}\n", "\n", "true positive rate is also known as **recall** or **sensitivity**\n", "\n", "\\begin{align}\n", "[\\text{false positive rate}]\n", "&= \\frac{[\\text{# positive data points with positive predictions}]}{\\text{[# all negative data points]}} \\\\\n", "&= \\frac{[\\text{# false positives}]}{[\\text{# false positives}] + [\\text{# true negatives}]}\n", "\\end{align}\n", "\n", "The ROC curve is created by plotting the true positive rate (when it's actually a yes, how often does it predict yes?) on the y axis against the false positive rate (when it's actually a no, how often does it predict yes?) on the x axis at various cutoff settings, giving us a picture of the whole spectrum of the trade-off we're making between the two measures.\n", "\n", "If all these true/false positive terminology is confusing to you, consider reading the material at the following link. [Blog: Simple guide to confusion matrix terminology](http://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are packages to plot ROC curves and to compute metrics from them, but it can still be worthwhile to work through how these curves are calculated from scratch to try and understand better what exactly are they showing us." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "def _binary_clf_curve(y_true, y_score):\n", " \"\"\"\n", " Calculate true and false positives per binary classification\n", " threshold (can be used for roc curve or precision/recall curve);\n", " the calcuation makes the assumption that the positive case\n", " will always be labeled as 1\n", "\n", " Parameters\n", " ----------\n", " y_true : 1d ndarray, shape = [n_samples]\n", " True targets/labels of binary classification\n", "\n", " y_score : 1d ndarray, shape = [n_samples]\n", " Estimated probabilities or scores\n", "\n", " Returns\n", " -------\n", " tps : 1d ndarray\n", " True positives counts, index i records the number\n", " of positive samples that got assigned a\n", " score >= thresholds[i].\n", " The total number of positive samples is equal to\n", " tps[-1] (thus false negatives are given by tps[-1] - tps)\n", "\n", " fps : 1d ndarray\n", " False positives counts, index i records the number\n", " of negative samples that got assigned a\n", " score >= thresholds[i].\n", " The total number of negative samples is equal to\n", " fps[-1] (thus true negatives are given by fps[-1] - fps)\n", "\n", " thresholds : 1d ndarray\n", " Predicted score sorted in decreasing order\n", "\n", " References\n", " ----------\n", " Github: scikit-learn _binary_clf_curve\n", " - https://github.com/scikit-learn/scikit-learn/blob/ab93d65/sklearn/metrics/ranking.py#L263\n", " \"\"\"\n", "\n", " # sort predicted scores in descending order\n", " # and also reorder corresponding truth values\n", " desc_score_indices = np.argsort(y_score)[::-1]\n", " y_score = y_score[desc_score_indices]\n", " y_true = y_true[desc_score_indices]\n", "\n", " # y_score typically consists of tied values. Here we extract\n", " # the indices associated with the distinct values. We also\n", " # concatenate a value for the end of the curve\n", " distinct_indices = np.where(np.diff(y_score))[0]\n", " end = np.array([y_true.size - 1])\n", " threshold_indices = np.hstack((distinct_indices, end))\n", "\n", " thresholds = y_score[threshold_indices]\n", " tps = np.cumsum(y_true)[threshold_indices]\n", "\n", " # (1 + threshold_indices) = the number of positives\n", " # at each index, thus number of data points minus true\n", " # positives = false positives\n", " fps = (1 + threshold_indices) - tps\n", " return tps, fps, thresholds" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "thresholds: [ 0.8 0.45 0.4 0.35]\n", "true positive count: [1 2 2 3]\n", "false positive count: [0 0 1 2]\n" ] } ], "source": [ "# we'll work with some toy data so it's easier to\n", "# show and confirm the calculated result\n", "y_true = np.array([1, 0, 1, 0, 1])\n", "y_score = np.array([0.45, 0.4, 0.35, 0.35, 0.8])\n", "\n", "tps, fps, thresholds = _binary_clf_curve(y_true, y_score)\n", "print('thresholds:', thresholds)\n", "print('true positive count:', tps)\n", "print('false positive count:', fps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the result above, we can see that the function will compute the true/false positive count for all unique threshold in the predicted score `y_score`. We can validate the result by hand to confirm that the calculation this in fact correct.\n", "\n", "Recall that ROC curve plots that true positive rate on the y-axis and false positive rate on the x-axis. Thus all we need to do is to convert the count into rate and we have our ROC curve." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "true positive rate: [ 0. 0.33333333 0.66666667 0.66666667 1. ]\n", "false positive rate: [ 0. 0. 0. 0.5 1. ]\n" ] }, { "data": { "image/png": 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2qqjjdaWB7dramLzbGxppVzNvTCNt/iginmhgVqsvhSdJkiRJXdmRHhq/pGJr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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 392, "width": 504 } }, "output_type": "display_data" } ], "source": [ "# convert count to rate, append 0 to\n", "# both true positive and false positive\n", "# so the visualization will start from origin (0, 0)\n", "tpr = np.hstack((0, tps / tps[-1]))\n", "fpr = np.hstack((0, fps / fps[-1]))\n", "print('true positive rate:', tpr)\n", "print('false positive rate:', fpr)\n", "\n", "plt.rcParams['figure.figsize'] = 8, 6\n", "plt.rcParams['font.size'] = 12\n", "\n", "fig = plt.figure()\n", "plt.plot(fpr, tpr, marker = 'o', lw = 1)\n", "plt.xlabel('false positive rate')\n", "plt.ylabel('true positive rate')\n", "plt.title('Receiver Operator Characteristic')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now to calculate the AUC (Area Under the Curve) for the ROC curve, we need sum up the rectangular area and the triangular area under the curve. Depicted by the visualization below:\n", "\n", "- For the rectangular area (the plot on the left illustrates one of them), the height are the TPR (true positive rate) and widths are in the difference in the FPR (false positive rate), so the total area of all the rectangles is the dot product of TPR and FPR's differences\n", "- For the triangular area (the plot on the right illustrates one of them), the height are the difference in TPR (true positive rate) and widths are in the difference in the FPR (false positive rate), so the total area of all the rectangles is the dot product of both TPR's and FPR's difference. But only half the area of each rectangle is below its segment of the ROC curve, thus we divide the rectangle by 2 to obtain the triangular area" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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VAJPBkiRJkiRJklQATAZLkiRJkiRJUgEwGSxJkiRJkiRJBaBVJINDCF1CCB8M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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 440, "width": 705 } }, "output_type": "display_data" } ], "source": [ "import matplotlib.patches as patches\n", "\n", "\n", "fig, ax = plt.subplots(1, 2, figsize = (10, 6))\n", "fig.suptitle('Receiver Operator Characteristic', y = 1.02)\n", "\n", "# this part is hard-coded for illustration purpose\n", "fpr_diff = fpr[3] - fpr[0]\n", "tpr_diff = tpr[3] - tpr[0]\n", "rect1 = patches.Rectangle(xy = (0, 0), width = fpr_diff,\n", " height = tpr_diff, alpha = 0.3)\n", "ax[0].add_patch(rect1)\n", "\n", "fpr_diff = fpr[-1] - fpr[-2]\n", "tpr_diff = tpr[-1] - tpr[-2]\n", "rect2 = patches.Rectangle(xy = (fpr[-2], tpr[-2]), width = fpr_diff,\n", " height = tpr_diff, alpha = 0.3)\n", "ax[1].add_patch(rect2)\n", "\n", "for i in range(len(ax)):\n", " ax[i].plot(fpr, tpr, marker = 'o', lw = 1)\n", " ax[i].set_xlabel('false positive rate')\n", " ax[i].set_ylabel('true positive rate')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "def _roc_auc_score(y_true, y_score):\n", " \"\"\"\n", " Compute Area Under the Curve (AUC) from prediction scores\n", "\n", " Parameters\n", " ----------\n", " y_true : 1d ndarray, shape = [n_samples]\n", " True targets/labels of binary classification\n", "\n", " y_score : 1d ndarray, shape = [n_samples]\n", " Estimated probabilities or scores\n", "\n", " Returns\n", " -------\n", " auc : float\n", " \"\"\"\n", "\n", " # ensure the target is binary\n", " if np.unique(y_true).size != 2:\n", " raise ValueError('Only two class should be present in y_true. ROC AUC score '\n", " 'is not defined in that case.')\n", " \n", " tps, fps, _ = _binary_clf_curve(y_true, y_score)\n", "\n", " # convert count to rate\n", " tpr = tps / tps[-1]\n", " fpr = fps / fps[-1]\n", "\n", " # compute AUC using the trapezoidal rule;\n", " # appending an extra 0 is just to ensure the length matches\n", " zero = np.array([0])\n", " tpr_diff = np.hstack((np.diff(tpr), zero))\n", " fpr_diff = np.hstack((np.diff(fpr), zero))\n", " auc = np.dot(tpr, fpr_diff) + np.dot(tpr_diff, fpr_diff) / 2\n", " return auc" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "auc score: 0.75\n", "package auc socre: 0.75\n" ] } ], "source": [ "auc_score = _roc_auc_score(y_true, y_score)\n", "print('auc score:', auc_score)\n", "\n", "# confirm with scikit-learn's result\n", "auc_score = roc_auc_score(y_true, y_score)\n", "print('package auc socre:', auc_score)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After working through the implementation of ROC curve and AUC score from sratch, we now pull back and visualize:\n", "\n", "- The ROC curve of our original model\n", "- Dotted line represents the ROC curve of a purely random classifier and a perfect classifier" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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jBjKKOgAAANDHRJqyurm5WUeOHNHSpUtTHB26E8kYQNIPnj2hHz13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\nERERERGRLFIyRkREREREREQki5SMERERERERERHJIiVjRERER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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 418, "width": 561 } }, "output_type": "display_data" } ], "source": [ "# calling the roc_curve, extract the probability of \n", "# the positive class from the predicted probability\n", "tree_test_pred = tree.predict_proba(X_test)[:, 1]\n", "fpr, tpr, thresholds = roc_curve(y_test, tree_test_pred, pos_label = 1)\n", "\n", "# AUC score that summarizes the ROC curve\n", "roc_auc = auc(fpr, tpr)\n", "\n", "plt.plot(fpr, tpr, lw = 2, label = 'ROC AUC: {:.2f}'.format(roc_auc))\n", "plt.plot([0, 1], [0, 1],\n", " linestyle = '--',\n", " color = (0.6, 0.6, 0.6),\n", " label = 'random guessing')\n", "plt.plot([0, 0, 1], [0, 1, 1],\n", " linestyle = ':',\n", " color = 'black', \n", " label = 'perfect performance')\n", "\n", "plt.xlim([-0.05, 1.05])\n", "plt.ylim([-0.05, 1.05])\n", "plt.xlabel('false positive rate')\n", "plt.ylabel('true positive rate')\n", "plt.title('Receiver Operator Characteristic')\n", "plt.legend(loc = \"lower right\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of visualizing the ROC curve is to let us know how well can our classifier be expected to perform in general, at a variety of different baseline probabilities (percentage of the majority class)?\n", "\n", "The diagonal line depicts a completely random classifier and ideally our model's ROC curve should be toward the top-left corner and stay as far away from the diagonal line as possible.\n", "\n", "Side note: Apart from comparing the model's ROC curve against the ROC curve of a classifier that does random guessing, it's also useful to plot the ROC curve of different classifiers to compare performance against each other." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### AUC probabilistic interpretation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The probabilistic interpretation of the AUC metric is that if we randomly choose a positive case and a negative case, the probability that the positive case outranks the negative case according to the classifier's prediction. Hopefully, this is evident from the ROC curve figure, where plot is enumerating all possible combinations of positive and negative cases, and the fraction under the curve comprises of the area where the positive case outranks the negative one. I personally find this interpretation extremely useful when conveying what AUC is measuring to a non-technical audience." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.97633000000000003" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def auc_probability(y_true, y_score, size = 100000):\n", " \"\"\"probabilistic interpretation of AUC\"\"\"\n", " labels = y_true.astype(np.bool)\n", " pos = np.random.choice(y_score[labels], size = size, replace = True)\n", " neg = np.random.choice(y_score[~labels], size = size, replace = True)\n", " auc = np.sum(pos > neg) + np.sum(pos == neg) / 2\n", " auc /= size\n", " return auc\n", "\n", "\n", "# we want this be close the score returned\n", "# by roc_auc_score\n", "auc_probability(y_true = y_test, y_score = tree_test_pred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Precision Recall Curve" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apart from ROC curve, there is also the **precision recall curve**. Instead of plotting true positive rate (a.k.a recall) versus false positive rate. We now plot precision versus recall.\n", "\n", "\\begin{align}\n", "[\\text{precision}]\n", "&= \\frac{[\\text{# positive data points with positive predicitions}]}{\\text{[# all data points with positive predictions]}} \\\\\n", "&= \\frac{[\\text{# true positives}]}{[\\text{# true positives}] + [\\text{# false positives}]}\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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JyhnGSJIkSU1m1tR2jtlvwbbtlhag7Mmk7127nJOesSuLZncW3zhJko8pSZIk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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 418, "width": 561 } }, "output_type": "display_data" } ], "source": [ "tree_test_pred = tree.predict_proba(X_test)[:, 1]\n", "precision, recall, thresholds = precision_recall_curve(\n", " y_test, tree_test_pred, pos_label = 1)\n", "\n", "# AUC score that summarizes the precision recall curve\n", "avg_precision = average_precision_score(y_test, tree_test_pred)\n", "\n", "label = 'Precision Recall AUC: {:.2f}'.format(avg_precision)\n", "plt.plot(recall, precision, lw = 2, label = label)\n", "plt.xlabel('Recall') \n", "plt.ylabel('Precision') \n", "plt.title('Precision Recall Curve')\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A classifier with high recall but low precision flags many positive results, but most of its predicted labels are incorrect when compared to its corresponding labels. On the other hand, a classifier with high precision but low recall is just the opposite, returning very few results, but most of its predicted labels are correct when compared to the training labels. An ideal system with high precision and high recall will return many results, with all results labeled correctly.\n", "\n", "Precision recall curve answers a fundamentally different question compared to ROC curve. By definition, precision directly answers the question, \"What is the probability that this is a real hit given my classifier says it is? Thus it is useful in practice for needle-in-haystack type problems or problems where the \"positive\" class is more interesting than the negative class.\n", "\n", "You can also think about it in the following way. ROC AUC looks at TPR and FPR, the entire confusion matrix for all thresholds. On the other hand, Precision-Recall AUC looks at Precision and Recall (TPR), it doesn't look at True Negative Rate (TNR). Because of that PR AUC can be a better choice when you care only about the \"positive\" while ROC AUC cares about both \"positive\" and \"negative\". Since PR AUC doesn't use TNR directly it can also be better for highly imbalanced problems. You may want to take a look at this [Blog: F1 Score vs ROC AUC vs Accuracy vs PR AUC: Which Evaluation Metric Should You Choose?](https://neptune.ml/blog/f1-score-accuracy-roc-auc-pr-auc). \n", "\n", "Although ROC curve is presumably the more popular choice when evaluating binary classifiers, it is highly recommended to use precision recall curve as a supplement to ROC curves to get a full picture when evaluating and comparing classifiers. For more discussion on this topic, consider taking a look at another documentation. [Notebook: Evaluating Imbalanced Datasets](http://nbviewer.jupyter.org/github/ethen8181/machine-learning/blob/master/model_selection/imbalanced/imbalanced_metrics.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Thresholding via Cost" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lots of real world binary classification needs a threshold to convert the model into a business decision. i.e. All cases with a model score above the threshold get some sort of special treatment. For example:\n", "\n", "- **Fraud Prevention**: We're a social network company and we'd like to delete fake accounts. We build a classifier that assigns a \"fraud score\" between 0 and 1 to each account and, after some research, decide that all accounts whose score is above 0.9 should be sent to our fraud team, which will review each case and delete the accounts that are actually fake\n", "- **Response/Propensity Modeling**: We're at an enterprise software company and we'd like to improve our outbound sales program. We buy a large database of potential customers and build a classifier to predict which ones are likely buy our product if contacted by our sales team. We decide that all customers with a \"response score\" of above threshold 0.7 should get a call\n", "- **Shopping Cart Abandonment**: We're at an e-commerce company, and we'd like to email a 10% off coupon to users who abandoned their shopping carts and won't return organically. (We don't want to give a 10% off coupon to users who are going to return anyway, since then you'd be losing 10% of the sale price.) We build a classifier to predict which users will never return to their carts, and decide that all users with a \"abandonment score\" above 0.85 should get the 10% off coupon\n", "- Etc.\n", "\n", "Thresholding is popular because of its simplicity and ease of implementation: We translate a continuous score to a binary yes/no decision, and act on it in a predetermined way. The biggest question for the thresholding pattern is: Where should I set the threshold point?\n", "\n", "Up until this point, we've been using AUC to give us a single-number summary of classifier performance. This might be suitable in some circumstances, but for binary classifiers, evaluation metrics that take into account the actual costs of false positive and false negative errors may be much more appropriate than AUC. If we know these costs, we can use them not only to tie the evaluation metric more directly to the business value but also choose an appropriate final cutoff threshold for the classifier.\n", "\n", "In real world application, the cost that comes along with making these two mistakes (false positive and false negative) are usually a whole lot different. Take our case for example, a false negative (FN) means an employee left our company but our model failed to detect that, while a false positive (FP) means an employee is still currently working at our company and our model told us that they will be leaving. The former mistake would be a tragedy, since, well, the employee left and we didn't do anything about it! As for conducting the latter mistake, we might be wasting like 20 minutes of a HR manager's time when we arrange a face to face interview with a employee, questioning about how the company can do better to retain him/her, while he/she is perfectly fine with the current situation.\n", "\n", "In the code cell below, we assign a cost for a false negative (FN) and false positive (FP) to be 100 and 1000 respectively, given the cost associated with the two mistakes we will multiply them with the false negative and false positive rate at each threshold to figure out where's the best cutoff value. Note that the cost associated with the mistake can just be a back of the envelope number as long as we're sure about which one is more \"expensive\" than the other." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "fpr, tpr, thresholds = roc_curve(y_test, tree_test_pred, pos_label = 1)\n", "fnr = tpr[-1] - tpr\n", "\n", "# fn = false negative, meaning the employee left and we\n", "# didn't do anything about it, in our case this will be\n", "# substantially more expensive than a false positive\n", "fp_cost = 100\n", "fn_cost = 1000\n", "\n", "costs = (fpr * fp_cost + fnr * fn_cost) * y_test.size" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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av2O/JGnGhNF63fGzEo4I+ZCMARpEe3t7vzID+gIAAAAjz7J0tlXM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\nv/+TrVu3WqW39Jjp2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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 418, "width": 561 } }, "output_type": "display_data" } ], "source": [ "best = np.argmin(costs)\n", "best_cost = np.round(costs[best])\n", "best_threshold = np.round(thresholds[best], 2)\n", "\n", "plt.plot(thresholds, costs, label = 'cost ($)')\n", "label = 'best cost: {} at threshold {}'.format(best_cost, best_threshold)\n", "plt.axvline(best_threshold, linestyle = '--', lw = 2, color = 'black', label = label)\n", "plt.xlabel('threshold') \n", "plt.ylabel('$') \n", "plt.title('Cost as a Function of Threshold')\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just to hit the notion home, when executing on a project, if we are able to compute expected cost for each mistake, consider maximizing that directly instead of AUC or another general-purpose metrics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reference" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Scikit-learn Documentation: Precision Recall](http://scikit-learn.org/stable/auto_examples/model_selection/plot_precision_recall.html)\n", "- [StackExchange: ROC vs precision-and-recall curves](https://stats.stackexchange.com/questions/7207/roc-vs-precision-and-recall-curves)\n", "- [Blog: Calculating AUC: the area under a ROC Curve](http://blog.revolutionanalytics.com/2016/11/calculating-auc.html)\n", "- [Blog: F1 Score vs ROC AUC vs Accuracy vs PR AUC: Which Evaluation Metric Should You Choose?](https://neptune.ml/blog/f1-score-accuracy-roc-auc-pr-auc)\n", "- [Blog: Machine Learning Meets Economics](http://blog.mldb.ai/blog/posts/2016/01/ml-meets-economics/)\n", "- [Blog: Visualizing Machine Learning Thresholds to Make Better Business Decisions](http://blog.insightdatalabs.com/visualizing-classifier-thresholds/)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { 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