{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# In-Depth: Decision Trees and Random Forests" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "< [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) | [Contents](Index.ipynb) | [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) >" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Previously\n", "\n", "- simple generative classifier (naive Bayes; see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) \n", "- powerful discriminative classifier (support vector machines; see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "\n", "## *Random Forests*\n", "- Another powerful & non-parametric algorithm \n", "- Random forests are an example of an **ensemble method**, \n", " - meaning that it relies on aggregating the results of an ensemble of simpler estimators.\n", "\n", "The sum can be greater than the parts: \n", "- a majority vote among a number of estimators can end up being better than any of the individual estimators doing the voting!\n", "\n", "We will see examples of this in the following sections." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Motivating Random Forests: Decision Trees" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T06:58:23.100831Z", "start_time": "2018-12-26T06:58:21.786163Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Random forests are an example of an *ensemble learner* built on decision trees.\n", "- For this reason we'll start by discussing decision trees.\n", "\n", "Decision trees are extremely intuitive ways to classify or label objects: \n", "- you simply ask a series of questions designed to zero-in on the classification.\n", "\n", "For example, if you wanted to build a decision tree to classify an animal you come across while on a hike, you might construct the one shown here:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Guess what is the animal I am thinking?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "![](figures/05.08-decision-tree.png)\n", "\n", "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Example)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The binary splitting makes this extremely efficient: in a well-constructed tree, \n", "- each question will cut the number of options by approximately half, \n", "- very quickly narrowing the options even among a large number of classes.\n", "\n", "The trick comes in deciding which questions to ask at each step.\n", "\n", "Using axis-aligned splits in the data: \n", "- each node in the tree splits the data into two groups using a cutoff value within one of the features.\n", "\n", "Let's now look at an example of this." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Creating a decision tree\n", "\n", "Consider the following two-dimensional data, which has one of four class labels:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T06:58:23.571323Z", "start_time": "2018-12-26T06:58:23.103258Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "\n", "X, y = make_blobs(n_samples=300, centers=4,\n", " random_state=0, cluster_std=1.0)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "A simple decision tree built on this data will iteratively split the data along one or the other axis \n", "- according to some quantitative criterion, and \n", "- at each level assign the label of the new region according to a majority vote of points within it.\n", "\n", "This figure presents a visualization of **the first four levels** of a decision tree classifier for this data:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![](figures/05.08-decision-tree-levels.png)\n", "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Levels)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Notice\n", "\n", "after the each split\n", "\n", "- Nodes that contain all of one color will not be splitted again. \n", "- At each level *every* region is again split along one of the two features." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "This process of fitting a decision tree to our data can be done in Scikit-Learn with the ``DecisionTreeClassifier`` estimator:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T06:58:23.626281Z", "start_time": "2018-12-26T06:58:23.573622Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "from sklearn.tree import DecisionTreeClassifier\n", "tree = DecisionTreeClassifier().fit(X, y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's write a quick utility function to help us visualize the output of the classifier:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T07:00:13.511603Z", "start_time": "2018-12-26T07:00:13.476742Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "def visualize_classifier(model, X, y, ax=None, cmap='rainbow'):\n", " ax = ax or plt.gca()\n", " \n", " # Plot the training points\n", " ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=cmap,\n", " clim=(y.min(), y.max()), zorder=3)\n", " ax.axis('tight')\n", " ax.axis('off')\n", " xlim = ax.get_xlim()\n", " ylim = ax.get_ylim()\n", " \n", " # fit the estimator\n", " model.fit(X, y)\n", " xx, yy = np.meshgrid(np.linspace(*xlim, num=200),\n", " np.linspace(*ylim, num=200))\n", " Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n", "\n", " # Create a color plot with the results\n", " n_classes = len(np.unique(y))\n", " contours = ax.contourf(xx, yy, Z, alpha=0.3,\n", " levels=np.arange(n_classes + 1) - 0.5,\n", " cmap=cmap, vmin = y.min(), vmax = y.max(),\n", " zorder=1)\n", "\n", " ax.set(xlim=xlim, ylim=ylim)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now we can examine what the decision tree classification looks like:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T07:16:21.081356Z", "start_time": "2018-12-26T07:16:20.926405Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "visualize_classifier(DecisionTreeClassifier(), X, y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If you're running this notebook live, you can use the helpers script included in [The Online Appendix](06.00-Figure-Code.ipynb#Helper-Code) to bring up an interactive visualization of the decision tree building process:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T07:16:48.072333Z", "start_time": "2018-12-26T07:16:47.884276Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'clim'\n", " s)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# helpers_05_08 is found in the online appendix\n", "import helpers_05_08\n", "helpers_05_08.plot_tree_interactive(X, y);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Notice that as the depth increases, we tend to get very strangely shaped classification regions; \n", "- for example, at a depth of five, there is a tall and skinny purple region between the yellow and blue regions.\n", "- It's clear that this is less a result of the true, intrinsic data distribution\n", "- It's more a result of the particular sampling or noise properties of the data.\n", "\n", "That is, this decision tree, even at only five levels deep, is clearly **over-fitting** our data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Decision trees and over-fitting\n", "\n", "Such over-fitting turns out to be a general property of decision trees: \n", "- it is very easy to go too deep in the tree\n", " - to fit details of the particular data rather than the overall properties of the distributions they are drawn from.\n", "\n", "Another way to see this over-fitting is \n", "- to look at models trained on different subsets of the data\n", "\n", "for example, in this figure we train two different trees, each on half of the original data:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![](figures/05.08-decision-tree-overfitting.png)\n", "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Overfitting)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "It is clear that \n", "- in some places, the two trees produce consistent results \n", " - e.g., in the four corners\n", "- while in other places, the two trees give very different classifications \n", " - e.g., in the regions between any two clusters\n", " \n", "The key observation is that the inconsistencies tend to happen where the classification is less certain, \n", "> ### by using information from *both* of these trees, we might come up with a better result!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If you are running this notebook live, the following function will allow you to interactively display the fits of trees trained on a random subset of the data:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2018-12-26T06:58:27.275825Z", "start_time": "2018-12-26T06:58:27.101954Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'clim'\n", " s)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# helpers_05_08 is found in the online appendix\n", "import helpers_05_08\n", "helpers_05_08.randomized_tree_interactive(X, y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Just as using information from two trees improves our results, we might expect that using information from many trees would improve our results even further." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Ensembles of Estimators: Random Forests\n", "\n", "Multiple overfitting estimators can be combined to reduce the effect of this overfitting.\n", "This notion is called **bagging**.\n", "- an ensemble method (集成学习)\n", "\n", "- Bagging makes use of an ensemble (a grab bag, perhaps) of parallel estimators, \n", " - each of which over-fits the data, and \n", " - averages the results to find a better classification.\n", "\n", "An ensemble of randomized decision trees is known as a **random forest**.\n", "\n", "This type of bagging classification can be done manually using Scikit-Learn's ``BaggingClassifier`` meta-estimator, as shown here:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:22:51.279359Z", "start_time": "2018-05-21T09:22:50.701772Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/matplotlib/contour.py:960: UserWarning: The following kwargs were not used by contour: 'clim'\n", " s)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.tree import DecisionTreeClassifier\n", "from sklearn.ensemble import BaggingClassifier\n", "\n", "tree = DecisionTreeClassifier()\n", "bag = BaggingClassifier(tree, n_estimators=100, max_samples=0.8,\n", " random_state=1)\n", "\n", "bag.fit(X, y)\n", "visualize_classifier(bag, X, y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In this example, we have randomized the data by fitting each estimator with a random subset of 80% of the training points.\n", "\n", "In practice, decision trees are more effectively randomized by **injecting some stochasticity in how the splits are chosen**: \n", "- this way **all the data contributes to the fit each time**\n", "- but the results of the fit still have the desired randomness.\n", "- when determining which feature to split on, the randomized tree might select from among the **top several features**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "You can read more technical details about these randomization strategies in the [Scikit-Learn documentation](http://scikit-learn.org/stable/modules/ensemble.html#forest) and references within.\n", "\n", "In Scikit-Learn, such an optimized ensemble of randomized decision trees is implemented in the ``RandomForestClassifier`` estimator, which takes care of all the randomization automatically.\n", "\n", "All you need to do is select a number of estimators, and it will very quickly (in parallel, if desired) fit the ensemble of trees:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:28:30.271183Z", "start_time": "2018-05-21T09:28:29.792594Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/matplotlib/contour.py:960: UserWarning: The following kwargs were not used by contour: 'clim'\n", " s)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.ensemble import RandomForestClassifier\n", "\n", "model = RandomForestClassifier(n_estimators=100, random_state=0)\n", "visualize_classifier(model, X, y);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We see that by averaging over 100 randomly perturbed models, we end up with an overall model that is much closer to our intuition about how the parameter space should be split." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Random Forest Regression\n", "\n", "In the previous section we considered random forests within the context of classification.\n", "\n", "Random forests can also be made to work in the case of regression (that is, continuous rather than categorical variables). \n", "- The estimator to use for this is the ``RandomForestRegressor``, and \n", "- the syntax is very similar to what we saw earlier.\n", "\n", "Consider the following data, drawn from the combination of a fast and slow oscillation:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:31:40.938055Z", "start_time": "2018-05-21T09:31:40.742169Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.RandomState(42)\n", "x = 10 * rng.rand(200)\n", "\n", "def model(x, sigma=0.3):\n", " fast_oscillation = np.sin(5 * x)\n", " slow_oscillation = np.sin(0.5 * x)\n", " noise = sigma * rng.randn(len(x))\n", "\n", " return slow_oscillation + fast_oscillation + noise\n", "\n", "y = model(x)\n", "plt.errorbar(x, y, 0.3, fmt='o');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Using the random forest regressor, we can find the best fit curve as follows:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:31:50.952109Z", "start_time": "2018-05-21T09:31:50.598789Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "forest = RandomForestRegressor(200)\n", "forest.fit(x[:, None], y)\n", "\n", "xfit = np.linspace(0, 10, 1000)\n", "yfit = forest.predict(xfit[:, None])\n", "ytrue = model(xfit, sigma=0)\n", "\n", "plt.errorbar(x, y, 0.3, fmt='o', alpha=0.5)\n", "plt.plot(xfit, yfit, '-r');\n", "plt.plot(xfit, ytrue, '-k', alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Here the true model is shown in the smooth gray curve, while the random forest model is shown by the jagged red curve.\n", "\n", "As you can see, the non-parametric random forest model is flexible enough to fit the multi-period data, without us needing to specifying a multi-period model!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Example: Random Forest for Classifying Digits\n", "\n", "Earlier we took a quick look at the hand-written digits data (see [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb)).\n", "\n", "Let's use that again here to see how the random forest classifier can be used in this context." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:33:28.977941Z", "start_time": "2018-05-21T09:33:28.852002Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "dict_keys(['images', 'data', 'DESCR', 'target_names', 'target'])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()\n", "digits.keys()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To remind us what we're looking at, we'll visualize the first few data points:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:33:38.130046Z", "start_time": "2018-05-21T09:33:36.539685Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# set up the figure\n", "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", "\n", "# plot the digits: each image is 8x8 pixels\n", "for i in range(64):\n", " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", " ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n", " \n", " # label the image with the target value\n", " ax.text(0, 7, str(digits.target[i]))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can quickly classify the digits using a random forest as follows:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:33:55.884986Z", "start_time": "2018-05-21T09:33:53.297093Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "from sklearn.cross_validation import train_test_split\n", "\n", "Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target,\n", " random_state=0)\n", "model = RandomForestClassifier(n_estimators=1000)\n", "model.fit(Xtrain, ytrain)\n", "ypred = model.predict(Xtest)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can take a look at the classification report for this classifier:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:34:14.349847Z", "start_time": "2018-05-21T09:34:14.344599Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " precision recall f1-score support\n", "\n", " 0 1.00 0.97 0.99 38\n", " 1 0.98 0.95 0.97 44\n", " 2 0.95 1.00 0.98 42\n", " 3 0.98 0.98 0.98 45\n", " 4 0.97 1.00 0.99 37\n", " 5 0.98 0.96 0.97 49\n", " 6 1.00 1.00 1.00 52\n", " 7 1.00 0.96 0.98 50\n", " 8 0.94 0.98 0.96 46\n", " 9 0.98 0.98 0.98 47\n", "\n", "avg / total 0.98 0.98 0.98 450\n", "\n" ] } ], "source": [ "from sklearn import metrics\n", "print(metrics.classification_report(ypred, ytest))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "And for good measure, plot the confusion matrix:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2018-05-21T09:34:33.359550Z", "start_time": "2018-05-21T09:34:33.001144Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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uv2/T+YfaQFUnlj1Q1SlAg8peICJ5qd87AvOBsUQ3lTksg1pjKhpWmalx4yZSVOR2aYevWrM9d/yMOTRtVJ8jD9g79vzK1WuZ/fEiTj/6oKypNfRcl9+36VynsEJE+hJd2gxwJrC8itfskfr9NuAkVV2QurPUU8Ax1ar0Z3wN1vQhpCGgLnPHTf8PiQTM/mQR+sXXDHhwLPdcexavv/cpvzm8Hbk5me88Zvs22Fq5LqXzt3IhcArRmocviNY8XJxmfrGqLgBQ1WVpvl9afA3W9CGkIaAuc0cP6E1+/97k3XQRsttO3HZJN5o3acSsjxdyVLu9qw7YirWGnutSOhcvfUHUFLZEExF5D2ggIr2BJ4B/AEu2vMTN8zVY04eQhoD6zC2z+Ktvad3CzULb0LZBCN+3lQ1ufUlVTxGRz9nMAFdV3bOyYBFJAgcS3RhmPtGl0XmqWlhVUT4Gt9oqSX9slaQ/PldJbtjwxRYPbu2T+r1zdd5QVQuAd8o9dX91cowxW1dlTaFLFZcjPOq4FmNMFqisKZTdS7ItsBfwCtGI9xOBj7GmYMw2qbIR7xfCppvCtFPVb1OPmwLjtk55xpitLZ1ThK2AVeUerwN29lOOMaampXPx0svAFBEZS3Rr+Z6Au9VCxpisUuEpyfJEpDvRWYhS4DVV9bp02u4laQDWL5vhJbdeq6O95IamontJpnuF4ddEBxevB753VZQxJvukc9+Ha4Bbie4U1QB4QET+6LswY0zNSGdP4QKgK7BOVVcBHbDBrcZss9JpCsWqurHc4w1EI9mMMdugdJrCNBG5k2hx02+J5jO+7rcsY0xNSacpXA8sIJrgfB7RlY12TMGYbVQ61ylMVNWuwAO+izHG1Lx0mkJ9EdlVVZd6r2YLJBIJRgwfzIHt9qegoIBL+l7PwoWLsy7Tcv1knnHBFTRsGE0F3GXnnTil67EMf/BRatWqRbOmjfn7zX+kXt26WVOvz1zXmek0hebAYhFZAawnuqqxtKp5Cr6Vn4rb8dCDGTpkIN26Z3ZSxEem5brPLCiIjns/PGLIpudOOfNiHr5vKM2bNeWukaN5fsIkzulxelbU6zvXdWY6TeHEaqeniEhzYKWqOrtS0cdU3NAm+IaU6zJTP1vEhg0F9Lm2P8XFJVxz6fmMHjGE5s2iaU7FxcUk69TOmnp957rOTKcpLAOuAI4jWjr9ClWMeBeRC4FdgZeAJ4lOY9YXkctV9bWMKk6paCpuJkMwfWRarvvMunWTXHBWd7qfeiJLln5J3z/czEtPPQTAa9Pe4p3/fMhVfc6rdq2u6/Wd6zoznabwEFCP6P4POURnIH4JXFvJay4nWivxInCaqs5PTXMeDzhpCj6m4oY2wTekXJeZbXZtzW67tCKRSNBmt11o0ngHvlm5iilTZzL5zZk8MGwQyWSdrKnXd67rzHROSXZU1Z6qOkFVxwM9gBOqeE2hqq4D1gCLYNM0Z2cfH3xMxQ1tgm9IuS4zx748maHDRwGw4puVrFv3Iy+8PJn3PpjLQ3f/naZNGmdVvb5zXWdWuUpSRCYCV6nqZ6nHOwOPqmqXSl5zI3A4MBf4FTCJ6NjEHFW9saqi0lklWXbEtd0B+22aiqu6sKqXbfVMy61+ZkWrJAsLCxlw2zC+Wr6CBAmuuuQ8+lw7gP33aUud1B7Cib/uxJm/2/wQ8nRWSW7r2xYqXiWZTlN4jegf+HSiYwpHEd0D4muIbkRbweuOIVoz0RxYCcxU1ZerrBRbOm0itnTar4qaQjrHFAb97PGd6byhqk4DpqXzZ40x2SOdm8HYP2xjtiNO7wRtjAmfNQVjTIw1BWNMjDUFY0xMWtOctzY7JemPjxuWhnaT3bXv+JkC0OSwy51n+ty2mU5zNsZsJ6wpGGNirCkYY2KsKRhjYqwpGGNirCkYY2KsKRhjYoJtColEgntH3M7M6S/y+pRnadu2TVZmhpgL0KFDeyZPftpZXkjbYOUPazjh8r/x+ZfLmbf4S84ZcDfnDxzOwJFjKCkpyTg/27etl6YgIjv4yC2v/ATb/gMGM3TIwKzMDDG3X7++jBw5hGQy6SQPwtkGhUXFDBr13KbBr/c/N5lLzziBR/52FYWFRUyfk9lUoxC2ra89ha9FpLenbCCMqbih5i5atIRevS5xklUmlG0w7PEJ9Dj+cFo2jUa67dumNT+s/ZHS0lLWbSigdm5mV4SGsG19NYUPgINE5I3UBCbnKppgm22ZIeaOGzeRoqKijHPKC2EbjH/zHZo2asCR7ffd9NzuOzfnjtEv8Nt+d7Dyh7Ucsn/bjOoNYdumM3mpOtar6pUicghwk4jcSzTFeZGq3uPiDUKYihtqrg8hbINxU/9NIgGz5y5AF3/JgHufQhcv4+k7+rHXrjsxZtJM/vHYi/Tv3T3jul2qiWnO1ZEAUNV3VbU7cCTRnaozm7tdTghTcUPN9SGEbTD6r1eQf8sV5P3lcqRNa2674vfssmMzGtaLPv+3aNqY1evWO6nbJdfb1teewsPlH6jqD8CE1C8nxo2byPG/7sSMaeM3TbDNxswQc30IdRv85dKe/Onux8nNzaF2rVwGXtLTab4LrreBLZ3eztjSaVs6vSnblk4bY9JhTcEYE2NNwRgTY03BGBNjTcEYE2NNwRgTY6cks5SPU4cQ3unDkKyZcJPzzEanDnaeWcZOSRpj0mJNwRgTY03BGBNjTcEYE2NNwRgTY03BGBNjTcEYExNsU7Bpzj/J9unAvjJDy1215ke6DhzN58tX8enSFXS5OZ/e94yl9z1jmfSf+VlTq68hKzEiUgfIVVVnY2vKT7DteOjBDB0ykG7dL8q6TJ+5EE0HPuusbqxb96OTPLBt6yO3sLiYQU9PJVk7+if36dJvOPfY9px33MFZV6uvEe/7iMhzIvKkiBwGzAU+FpFert7DpjlHQpgO7CszpNxh496ix5G/pEXjBgB8unQFMz5ewkV3P88tT77Oug0bs6ZWXx8fRgH3A88DLwHHAgcA17p6A5vmHAlhOrCvzFByx8/+lGYN63HEfrtveu4Xu+/IdacfSf413Wn9fzvwwKvvZEWt4K8p1FLV14CxwEpV/VJV1wGFrt7Apjn7Y9vWbe74WZ8wa94X9L5nLPrlN/z5sSkctf/u7L9bSwCOa9eWef/9JitqBX9NYbGIjAGeBdaKyG0icgPwlas3sGnO/ti2dZubf0138q7pTt7V3ZDWLbj13C5cO+plPlryNQDvzF/Kfru2zIpawd+BxvOB3wDzgbXAdcCPgJuja9g0Z59s2/r/OxvQszODn51G7Vq5NN+hPjf3Oq7aWTbNeTthS6fDY0unjTHbJGsKxpgYawrGmBhrCsaYGGsKxpgYawrGmBg7JWkyZqdP/VkzeZC37HqdL7JTksaYqllTMMbEWFMwxsRYUzDGxFhTMMbEWFMwxsQE2xRsuGh4uRDGkNmQcletXkfXG+/j869Xsmr1Oq6973kuGvoE5w95nKXffFetzGCbQvlhlf0HDGbokIFZmWm5P+nXry8jRw4hmUw6yYPwtoHL3MLiYgY9MWnTMNi7xr7JSYfuT/71Z3Pl6Ufz+derqpXrvSmIyGYvkMiUDRcNLzeUIbOh5A57bio9OrWnRZNoFNv7C79kxXdruPSuMbwy+xM67LNrtXJ9TXNuKyKvisgSYKOIzEpNdt7J1XvYcNHwckMZMhtC7vi3P6JZw/oc8Ys9Nz331bc/0Kh+XR647kx2arYDoyfNrlaNvvYU7gWuVtXdgaOBKcA/gDxXb2DDRcPL9SG0beAqd/xbHzLr08X0/seT6NIV/Hn0y+TkJOh84N4AHNNuLz5OzYDcUr6aQmNVnQ+gqrOAI1X1PaCpqzew4aLh5foQ2jZwlZt//dnk/fEs8v5wFrJrS2698GQ6tWvLzLkLAXhvwVLa7ty8Wtm+BrcuEpH7gYnAKcD7ItINWOfqDWy4aHi5PoS2DXxu235nHMdfH5vIM9Pm0KheksG9T6tWjpdVkqnbxPUB9gfeB/KBDsACVV1Z1ettlWRYbJWkPzWxStLLnoKqbiQ6rlDeLB/vZYxxK9jrFIwxflhTMMbEWFMwxsRYUzDGxFhTMMbEWFMwxsRk5TRnY0zNsT0FY0yMNQVjTIw1BWNMjDUFY0yMNQVjTIw1BWNMjDUFY0yMryEr3olIDnAfcCBQAFysqp85yu4I3KGqnR3l1SaaKdEGSAK3quqLDnJzgVGAAMXAhaq6MNPcVHZL4D2gi6rOc5GZyp0D/JB6+LmqXugg8ybgNKAOcJ+qZjz2T0QuAC5IPawLtAd2UtXvM8ytDTxC9L1QDPTJdPuKSBIYDewJrAauUNUF1c0LeU/ht0BdVT0cuJFoBmTGROQG4CGibwRXzgFWqurRwEnACEe5pwKo6pHAQGCYi9DUN+4DwHoXeeVy6wKoaufULxcNoTNwBHAkcAxQvRHGP6OqD5fVSdQcr860IaT8BqilqkcAfwNuc5DZB1irqocBV5Hh91fITeEo4FXYNAfyEEe5C4FujrLKPAvcXO6xk5HGqjoOKJuZvjuw3EUucCdwP7DMUV6ZA4H6IjJZRN4QkcMcZHYFPgJeACYALznI3EREDgF+oaoPOoqcD9RK7enuABQ6yNyfaPQhqqrAfpmEhdwUduCn3VCAYhHJ+OOQqj6Pm7+o8plrVXWNiDQCngP+7DC7SEQeAYansjOS2m3+RlUnZZq1GT8SNZyuQF/gCQd/Z82JfiD0KJfp8l4j/YG/OsxbS/TRYR7RR797HGS+D5wiIolUo22d+mhZLSE3hdVAo3KPc1TV7U0FHBKRXYGpwGOq+qTLbFU9H9gHGCUiDTKMuwjoIiJvEn2OftTh/TrmA4+ramlq2vdKYOcMM1cCk1R1Y+qn5AagRYaZAIhIE2BfVZ3qIi/lOqJ69yHac3qk7GNVBvKJ/j1MJfpI+Z6qVnvAZchN4S2iz2ekuuNHNVtOxURkR2Ay8CdVzXeYe27qIBtEP4VLiA5eVZuqdlLVY1K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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "mat = confusion_matrix(ytest, ypred)\n", "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False)\n", "plt.xlabel('true label')\n", "plt.ylabel('predicted label');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We find that a simple, untuned random forest results in a very accurate classification of the digits data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Summary of Random Forests\n", "\n", "This section contained a brief introduction to the concept of *ensemble estimators*, and in particular the random forest – an ensemble of randomized decision trees.\n", "Random forests are a powerful method with several advantages:\n", "\n", "- Both training and prediction are very fast, because of the simplicity of the underlying decision trees. \n", " - In addition, both tasks can be straightforwardly parallelized, because the individual trees are entirely independent entities.\n", "- The multiple trees allow for a probabilistic classification: \n", " - a majority vote among estimators gives an estimate of the probability (accessed in Scikit-Learn with the ``predict_proba()`` method).\n", "- The nonparametric model is extremely flexible, and can thus perform well on tasks that are under-fit by other estimators.\n", "\n", "A primary disadvantage of random forests is that the results are not easily interpretable: \n", "- if you would like to draw conclusions about the *meaning* of the classification model, random forests may not be the best choice." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "< [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) | [Contents](Index.ipynb) | [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) >" ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.4" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }