{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Evaluation\n", "This material is adapted from the following,\n", "- [Scikit Learn](http://scikit-learn.org/stable/) \n", "- [Sebastian Raschka](https://github.com/rasbt/python-machine-learning-book) \n", "- [Jake Vanderplas](https://github.com/jakevdp/sklearn_tutorial)\n", "- [Andreas Mueller](http://amueller.github.io) \n", "- [Kyle Kastner](https://kastnerkyle.github.io/) \n", "- [Quantopian Research](https://github.com/quantopian/research_public)\n", "- [Python for Probability, Statistics, and Machine Learning](http://www.springer.com/fr/book/9783319307152), [github](https://github.com/unpingco/Python-for-Probability-Statistics-and-Machine-Learning)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.core.display import display, HTML\n", "display(HTML(\"\"))\n", "\n", "%load_ext line_profiler\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import seaborn as sns; sns.set()\n", "\n", "# Ignore Warnings\n", "def warn(*args, **kwargs):\n", " pass\n", "import warnings\n", "warnings.warn = warn\n", "\n", "from helper_functions import tic, toc\n", "\n", "\"\"\" Include Parent Directory in Python Path \"\"\"\n", "import os,sys,inspect\n", "currentdir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n", "parentdir = os.path.dirname(currentdir)\n", "sys.path.insert(0,parentdir)\n", "\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import Image\n", "from sklearn import __version__ as sklearn_version\n", "from distutils.version import LooseVersion as Version" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cross-Validation\n", "It is good practice to split a dataset into two parts, a training set and a test set. This helps avoid overfitting, while aiding in improved generalization performance (how well it performs on new, unseen data). Use the training set to fit a model and the test set to evaluate its generalization performance.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, often (labeled) data is precious, and this approach lets us only use ~ 3/4 of our data for training. On the other hand, we will only ever try to apply our model 1/4 of our data for testing.\n", "A common way to use more of the data to build a model, but also get a more robust estimate of the generalization performance, is cross-validation.\n", "In cross-validation, the data is split repeatedly into a training and non-overlapping test-sets, with a separate model built for every pair. The test-set scores are then aggregated for a more robust estimate.\n", "\n", "The most common way to do cross-validation is k-fold cross-validation, in which the data is first split into k (often 5 or 10) equal-sized folds, and then for each iteration, one of the k folds is used as test data, and the rest as training data. This way, each data point will be in the test-set exactly once, and we can use all but a k'th of the data for training.\n", "Let us apply this technique to evaluate the KNeighborsClassifier algorithm on the Iris dataset:\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Parameter selection, Validation, and Testing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most models have parameters that influence how complex a model they can learn. Recall that we demonstrated the impact of regularization as a means to avoid overfitting in the first class. We also noted that it's favourable to prefer simpler models.\n", "\n", "![](../images/plot_kneigbors_regularization.png)\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above figure, we see fits for three different values of ``n_neighbors``.\n", "For ``n_neighbors=2``, the data is overfit, the model is too flexible and can adjust too much to the noise in the training data. For ``n_neighbors=20``, the model is not flexible enough, and can not model the variation in the data appropriately.\n", "\n", "In the middle, for ``n_neighbors = 5``, we have found a good mid-point. It fits\n", "the data fairly well, and does not suffer from the overfit or underfit\n", "problems seen in the figures on either side. What we would like is a\n", "way to quantitatively identify overfit and underfit, and optimize the\n", "hyperparameters (in this case, the polynomial degree d) in order to\n", "determine the best algorithm.\n", "\n", "We trade off remembering too much about the particularities and noise of the training data vs. not modeling enough of the variability. This is a trade-off that needs to be made in basically every machine learning application and is a central concept, called bias-variance-tradeoff or \"overfitting vs underfitting\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](../images/overfitting_underfitting_cartoon.svg)\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperparameters, Over-fitting, and Under-fitting\n", "\n", "Unfortunately, there is no general rule how to find the sweet spot, and so machine learning practitioners have to find the best trade-off of model-complexity and generalization by trying several hyperparameter settings. Hyperparameters are the internal knobs or tuning parameters of a machine learning algorithm (in contrast to model parameters that the algorithm learns from the training data -- for example, the weight coefficients of a linear regression model); the number of *k* in K-nearest neighbors is such a hyperparameter.\n", "\n", "Most commonly this \"hyperparameter tuning\" is done using a brute force search, for example over multiple values of ``n_neighbors``:\n", "\n", "![](../images/grid_search_cross_validation.svg)\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some practitioners go for an easier scheme, splitting the data simply into three parts, training, validation and testing. This is a possible alternative if your training set is very large, or it is infeasible to train many models using cross-validation because training a model takes very long.\n", "You can do this with scikit-learn for example by splitting of a test-set and then applying GridSearchCV with ShuffleSplit cross-validation with a single iteration:\n", "\n", "![](../images/train_validation_test2.svg)\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Validation\n", "\n", "An important piece of machine learning is **model validation**: that is, determining how well your model will generalize from the training data to future unlabeled data. Let's look at an example using the *nearest neighbor classifier*. This is a very simple classifier: it simply stores all training data, and for any unknown quantity, simply returns the label of the closest training point.\n", "\n", "With the iris data, it very easily returns the correct prediction for each of the input points:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] } ], "source": [ "import sklearn.datasets as ds\n", "from sklearn.neighbors import KNeighborsClassifier\n", "\n", "iris = ds.load_iris()\n", "X, y = iris.data, iris.target\n", "clf = KNeighborsClassifier(n_neighbors=1)\n", "clf.fit(X, y)\n", "y_pred = clf.predict(X)\n", "print(np.all(y == y_pred))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A more useful way to look at the results is to view the **confusion matrix**, or the matrix showing the frequency of inputs and outputs:" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "\n", "confmat = confusion_matrix(y, y_pred)\n", "\n", "fig, ax = plt.subplots(figsize=(5, 5))\n", "ax.matshow(confmat, cmap=plt.cm.Blues, alpha=0.3)\n", "for i in range(confmat.shape[0]):\n", " for j in range(confmat.shape[1]):\n", " ax.text(x=j, y=i, s=confmat[i, j], va='center', ha='center')\n", "\n", "plt.xlabel('predicted label')\n", "plt.ylabel('true label')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For each class, all 50 training samples are correctly identified. But this **does not mean that our model is perfect!** In particular, such a model generalizes extremely poorly to new data. We can simulate this by splitting our data into a *training set* and a *testing set*. Scikit-learn contains some convenient routines to do this:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.cross_validation import train_test_split\n", "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y)\n", "clf.fit(Xtrain, ytrain)\n", "ypred = clf.predict(Xtest)\n", "\n", "confmat = confusion_matrix(ytest, ypred)\n", "\n", "fig, ax = plt.subplots(figsize=(5, 5))\n", "ax.matshow(confmat, cmap=plt.cm.Blues, alpha=0.3)\n", "for i in range(confmat.shape[0]):\n", " for j in range(confmat.shape[1]):\n", " ax.text(x=j, y=i, s=confmat[i, j], va='center', ha='center')\n", "\n", "plt.xlabel('predicted label')\n", "plt.ylabel('true label')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This paints a better picture of the true performance of our classifier: apparently there is some confusion between the second and third species, which we might anticipate given what we've seen of the data above.\n", "\n", "This is why it's **extremely important** to use a train/test split when evaluating your models. We'll go into more depth on model evaluation later in this tutorial." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Overfitting, Underfitting and Model Selection\n", "Now that we've gone over the basics of validation, and cross-validation, it's time to go into even more depth regarding model selection.\n", "\n", "The issues associated with validation and \n", "cross-validation are some of the most important\n", "aspects of the practice of machine learning. Selecting the optimal model\n", "for your data is vital, and is a piece of the problem that is not often\n", "appreciated by machine learning practitioners.\n", "\n", "Of core importance is the following question:\n", "\n", "**If our estimator is underperforming, how should we move forward?**\n", "\n", "- Use simpler or more complicated model?\n", "- Add more features to each observed data point?\n", "- Add more training samples?\n", "\n", "The answer is often counter-intuitive. In particular, **Sometimes using a\n", "more complicated model will give _worse_ results.** Also, **Sometimes adding\n", "training data will not improve your results.** The ability to determine\n", "what steps will improve your model is what separates the successful machine\n", "learning practitioners from the unsuccessful." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Illustration of the Bias-Variance Tradeoff\n", "\n", "For this section, we'll work with a simple 1D regression problem. This will help us to\n", "easily visualize the data and the model, and the results generalize easily to higher-dimensional\n", "datasets. We'll explore a simple **linear regression** problem.\n", "This can be accomplished within scikit-learn with the `sklearn.linear_model` module.\n", "\n", "We'll create a simple nonlinear function that we'd like to fit" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def test_func(x, err=0.5):\n", " y = 10 - 1. / (x + 0.1)\n", " if err > 0:\n", " y = np.random.normal(y, err)\n", " return y" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_data(N=40, error=1.0, random_seed=1):\n", " # randomly sample the data\n", " np.random.seed(1)\n", " X = np.random.random(N)[:, np.newaxis]\n", " y = test_func(X.ravel(), error)\n", " \n", " return X, y" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MMAoAQDLCKAAAyQijAAAkI4wCAJCMMAoAQDLCKAAAyQijAAAkI4wCAJCMMAoA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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X, y = make_data(40, error=1)\n", "plt.scatter(X.ravel(), y);" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sQo/+RhgFAD8TbJesB+qimfaqzoJCi4o7V3Umxign06yZF8cpLNQ/qzqB/kIY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\nMPXp00cFBQVOHxa3ITLysiRb7Qup/d/tAAAA5vC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n", "\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import mean_squared_error\n", "model = LinearRegression()\n", "model.fit(X, y)\n", "y_test = model.predict(X_test)\n", "\n", "plt.scatter(X.ravel(), y)\n", "plt.plot(X_test.ravel(), y_test)\n", "plt.title(\"mean squared error: {0:.3g}\".format(mean_squared_error(model.predict(X), y)));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have fit a straight line to the data, but clearly this model is not a good choice. We say that this model is **biased**, or that it **under-fits** the data.\n", "\n", "Let's try to improve this by creating a more complicated model. We can do this by adding degrees of freedom, and computing a polynomial regression over the inputs. Scikit-learn makes this easy with the ``PolynomialFeatures`` preprocessor, which can be pipelined with a linear regression.\n", "\n", "Let's make a convenience routine to do this:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.pipeline import make_pipeline\n", "\n", "def PolynomialRegression(degree=2, **kwargs):\n", " return make_pipeline(PolynomialFeatures(degree),\n", " LinearRegression(**kwargs))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll use this to fit a quadratic curve to the data." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0eZnE9QxjcO9wYiMCO9zcXnEehVERcXsKKUccrKoja0cJWTtL2LS7jIrq+mMe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\njJ45c0azZs3SwIEDNWjQIL300ku6cOHCNff/7LPPNGbMGN1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = PolynomialRegression(2)\n", "model.fit(X, y)\n", "y_test = model.predict(X_test)\n", "\n", "plt.scatter(X.ravel(), y)\n", "plt.plot(X_test.ravel(), y_test)\n", "plt.title(\"mean squared error: {0:.3g}\".format(mean_squared_error(model.predict(X), y)));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This reduces the mean squared error, and makes a much better fit. What happens if we use an even higher-degree polynomial?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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W+SWdz9ZfNzMYFTKjNpgzSnVGHRsFoyLHf791FIsSYpKCskaUVHJz8G5NHGL2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = PolynomialRegression(30)\n", "model.fit(X, y)\n", "y_test = model.predict(X_test)\n", "\n", "plt.scatter(X.ravel(), y)\n", "plt.plot(X_test.ravel(), y_test)\n", "plt.title(\"mean squared error: {0:.3g}\".format(mean_squared_error(model.predict(X), y)))\n", "plt.ylim(-4, 14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we increase the degree to this extent, it's clear that the resulting fit is no longer reflecting the true underlying distribution, but is more sensitive to the noise in the training data. For this reason, we call it a **high-variance model**, and we say that it **over-fits** the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, let's use IPython's interact capability (only in IPython 2.0+) to explore this interactively:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kkUeUmZmpH/7wh8rKyvLLwAEAo4svy9pPp7y8QsXFm2WzxQblo0ebWrtUVt2g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\no7eDX38N1F9F9DLrf9sBAADMoYzeBsLCLkiy/7H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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.html.widgets import interact\n", "\n", "def plot_fit(degree=1, Npts=50):\n", " X, y = make_data(Npts, error=1)\n", " X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n", " \n", " model = PolynomialRegression(degree=degree)\n", " model.fit(X, y)\n", " y_test = model.predict(X_test)\n", "\n", " plt.scatter(X.ravel(), y)\n", " plt.plot(X_test.ravel(), y_test)\n", " plt.ylim(-4, 14)\n", " plt.title(\"mean squared error: {0:.2f}\".format(mean_squared_error(model.predict(X), y)))\n", " \n", "interact(plot_fit, degree=[1, 30], Npts=[2, 100]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Detecting Over-fitting with Validation Curves\n", "\n", "Clearly, computing the error on the training data is not enough (we saw this previously). As above, we can use **cross-validation** to get a better handle on how the model fit is working. The following figures demonstrate how validation curves can aid in understanding generalization performance." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make things more clear, we'll use the slightly larger dataset visualized in the following figure:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CgA/5ba5jOt+P30J5Jk2ZMlobNvy3WlrmKF67nJwHNGXK6KSu09Nc0/nzR/OzyXIBy7I6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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X, y = make_data(120, error=1.0)\n", "plt.scatter(X, y);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.learning_curve import validation_curve\n", "\n", "def rms_error(model, X, y):\n", " y_pred = model.predict(X)\n", " return np.sqrt(np.mean((y - y_pred) ** 2))\n", "\n", "degree = np.arange(0, 18)\n", "val_train, val_test = validation_curve(PolynomialRegression(), X, y,\n", " 'polynomialfeatures__degree', degree, cv=7,\n", " scoring=rms_error)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the validation curves:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8lQA4/g7C0XjGtgq5IiIiIvlNIXcnE0q7Fp95XN5vyLz4TDW5IiIiIvlNIXcn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\nPG7ZmHDsOF5cHw2q3mPlxhplb2e28bYr3MbN/Cd/m+L3He1pGN1udFC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_with_err(x, data, **kwargs):\n", " mu, std = data.mean(1), data.std(1)\n", " lines = plt.plot(x, mu, '-', **kwargs)\n", " plt.fill_between(x, mu - std, mu + std, edgecolor='none',\n", " facecolor=lines[0].get_color(), alpha=0.2)\n", "\n", "plot_with_err(degree, val_train, label='training scores')\n", "plot_with_err(degree, val_test, label='validation scores')\n", "plt.xlabel('degree'); plt.ylabel('rms error')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the trend here, which is common for this type of plot.\n", "\n", "1. For a small model complexity, the training error and validation error are very similar. This indicates that the model is **under-fitting** the data: it doesn't have enough complexity to represent the data. Another way of putting it is that this is a **high-bias** model.\n", "\n", "2. As the model complexity grows, the training and validation scores diverge. This indicates that the model is **over-fitting** the data: it has so much flexibility, that it fits the noise rather than the underlying trend. Another way of putting it is that this is a **high-variance** model.\n", "\n", "3. Note that the training score (nearly) always improves with model complexity. This is because a more complicated model can fit the noise better, so the model improves. The validation data generally has a sweet spot, which here is around 5 terms.\n", "\n", "Here's our best-fit model according to the cross-validation:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rd/t7nf39UIFAL50FA7+H3W43b28p5S8b9uJyu7EA1yycypfOGqfyT17y69JO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\nCRQKo0Hi/Y7aouPSY5mQGefj1oiIiIgMjsJoECi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = PolynomialRegression(4).fit(X, y)\n", "plt.scatter(X, y)\n", "plt.plot(X_test, model.predict(X_test));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Detecting Data Sufficiency with Learning Curves\n", "\n", "As you might guess, the exact turning-point of the tradeoff between bias and variance is highly dependent on the number of training points used. Here we'll illustrate the use of *learning curves*, which display this property.\n", "\n", "The idea is to plot the mean-squared-error for the training and test set as a function of *Number of Training Points*" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.learning_curve import learning_curve\n", "\n", "def plot_learning_curve(degree=3):\n", " train_sizes = np.linspace(0.05, 1, 20)\n", " N_train, val_train, val_test = learning_curve(PolynomialRegression(degree),\n", " X, y, train_sizes, cv=5,\n", " scoring=rms_error)\n", " plot_with_err(N_train, val_train, label='training scores')\n", " plot_with_err(N_train, val_test, label='validation scores')\n", " plt.xlabel('Training Set Size'); plt.ylabel('rms error')\n", " plt.ylim(0, 3)\n", " plt.xlim(5, 80)\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what the learning curves look like for a linear model:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uHyc9s7rTI7Mbm8u/5oMdn7DHu5fyYAULt77Hkl3LGN9lNEfn9kuqj/81ZUFE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_learning_curve(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows a typical learning curve: for very few training points, there is a large separation between the training and test error, which indicates **over-fitting**. Given the same model, for a large number of training points, the training and testing errors converge, which indicates potential **under-fitting**.\n", "\n", "As you add more data points, the training error will never increase, and the testing error will never decrease (why do you think this is?)\n", "\n", "It is easy to see that, in this plot, if you'd like to reduce the MSE down to the nominal value of 1.0 (which is the magnitude of the scatter we put in when constructing the data), then adding more samples will *never* get you there. For $d=1$, the two curves have converged and cannot move lower. What about for a larger value of $d$?" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4sMHj5s6di759+2LAgAHB23bu3IlRo0aF/FyaqkFpIDzGheqSAlXVoMj1/5Dk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_learning_curve(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see that by adding more model complexity, we've managed to lower the level of convergence to an rms error of 1.0!\n", "\n", "What if we get even more complex?" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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IFQmRk+/ILefxayZXRETkZCnkikQpr+nDsk6m0UFEREQUckXC4STCqmVZeE1f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_learning_curve(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For an even more complex model, we still converge, but the convergence only happens for *large* amounts of training data.\n", "\n", "So we see the following:\n", "\n", "- you can **cause the lines to converge** by adding more points or by simplifying the model.\n", "- you can **bring the convergence error down** only by increasing the complexity of the model.\n", "\n", "Thus these curves can give you hints about how you might improve a sub-optimal model. If the curves are already close together, you need more model complexity. If the curves are far apart, you might also improve the model by adding more data.\n", "\n", "To make this more concrete, imagine some telescope data in which the results are not robust enough. You must think about whether to spend your valuable telescope time observing *more objects* to get a larger training set, or *more attributes of each object* in order to improve the model. The answer to this question has real consequences, and can be addressed using these metrics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The holdout method" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Get Data" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "\n", "if Version(sklearn_version) < '0.18':\n", " from sklearn.cross_validation import StratifiedKFold\n", "else:\n", " from sklearn.model_selection import StratifiedKFold\n", "\n", "if Version(sklearn_version) < '0.18':\n", " from sklearn.cross_validation import train_test_split\n", "else:\n", " from sklearn.model_selection import train_test_split\n", "\n", "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases'\n", " '/breast-cancer-wisconsin/wdbc.data', header=None)\n", "\n", "from sklearn.preprocessing import LabelEncoder\n", "\n", "X = df.loc[:, 2:].values\n", "y = df.loc[:, 1].values\n", "le = LabelEncoder()\n", "y = le.fit_transform(y)\n", "le.transform(['M', 'B'])\n", "\n", "X_train, X_test, y_train, y_test = \\\n", " train_test_split(X, y, test_size=0.20, random_state=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Combining transformers and estimators in a pipeline" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test Accuracy: 0.947\n" ] } ], "source": [ "from sklearn.preprocessing import StandardScaler\n", "from sklearn.decomposition import PCA\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.pipeline import Pipeline\n", "\n", "pipe_lr = Pipeline([('scl', StandardScaler()),\n", " ('pca', PCA(n_components=2)),\n", " ('clf', LogisticRegression(random_state=1))])\n", "\n", "pipe_lr.fit(X_train, y_train)\n", "print('Test Accuracy: %.3f' % pipe_lr.score(X_test, y_test))\n", "y_pred = pipe_lr.predict(X_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## K-fold cross-validation" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fold: 1, Class dist.: [256 153], Acc: 0.891\n", "Fold: 2, Class dist.: [256 153], Acc: 0.978\n", "Fold: 3, Class dist.: [256 153], Acc: 0.978\n", "Fold: 4, Class dist.: [256 153], Acc: 0.913\n", "Fold: 5, Class dist.: [256 153], Acc: 0.935\n", "Fold: 6, Class dist.: [257 153], Acc: 0.978\n", "Fold: 7, Class dist.: [257 153], Acc: 0.933\n", "Fold: 8, Class dist.: [257 153], Acc: 0.956\n", "Fold: 9, Class dist.: [257 153], Acc: 0.978\n", "Fold: 10, Class dist.: [257 153], Acc: 0.956\n", "\n", "CV accuracy: 0.950 +/- 0.029\n" ] } ], "source": [ "if Version(sklearn_version) < '0.18':\n", " kfold = StratifiedKFold(y=y_train, \n", " n_folds=10,\n", " random_state=1)\n", "else:\n", " kfold = StratifiedKFold(n_splits=10,\n", " random_state=1).split(X_train, y_train)\n", "\n", "scores = []\n", "for k, (train, test) in enumerate(kfold):\n", " pipe_lr.fit(X_train[train], y_train[train])\n", " score = pipe_lr.score(X_train[test], y_train[test])\n", " scores.append(score)\n", " print('Fold: %s, Class dist.: %s, Acc: %.3f' % (k+1,\n", " np.bincount(y_train[train]), score))\n", " \n", "print('\\nCV accuracy: %.3f +/- %.3f' % (np.mean(scores), np.std(scores)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## We can also use the built-in CV function" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CV accuracy scores: [ 0.89130435 0.97826087 0.97826087 0.91304348 0.93478261 0.97777778\n", " 0.93333333 0.95555556 0.97777778 0.95555556]\n", "CV accuracy: 0.950 +/- 0.029\n" ] } ], "source": [ "if Version(sklearn_version) < '0.18':\n", " from sklearn.cross_validation import cross_val_score\n", "else:\n", " from sklearn.model_selection import cross_val_score\n", "\n", "scores = cross_val_score(estimator=pipe_lr,\n", " X=X_train,\n", " y=y_train,\n", " cv=10,\n", " n_jobs=1)\n", "print('CV accuracy scores: %s' % scores)\n", "print('CV accuracy: %.3f +/- %.3f' % (np.mean(scores), np.std(scores)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimizing the precision and recall of a classification model" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Precision: 0.974\n", "Recall: 0.881\n", "F1: 0.925\n" ] } ], "source": [ "from sklearn.metrics import precision_score, recall_score, f1_score\n", "\n", "print('Precision: %.3f' % precision_score(y_true=y_test, y_pred=y_pred))\n", "print('Recall: %.3f' % recall_score(y_true=y_test, y_pred=y_pred))\n", "print('F1: %.3f' % f1_score(y_true=y_test, y_pred=y_pred))" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.982798668208\n", "{'clf__kernel': 'linear', 'clf__C': 0.1}\n" ] } ], "source": [ "from sklearn.svm import SVC\n", "\n", "from sklearn.metrics import make_scorer\n", "if Version(sklearn_version) < '0.18':\n", " from sklearn.grid_search import GridSearchCV\n", "else:\n", " from sklearn.model_selection import GridSearchCV\n", " \n", "pipe_svc = Pipeline([('scl', StandardScaler()),\n", " ('clf', SVC(random_state=1))])\n", "\n", "scorer = make_scorer(f1_score, pos_label=0)\n", "\n", "c_gamma_range = [0.01, 0.1, 1.0, 10.0]\n", "\n", "param_grid = [{'clf__C': c_gamma_range,\n", " 'clf__kernel': ['linear']},\n", " {'clf__C': c_gamma_range,\n", " 'clf__gamma': c_gamma_range,\n", " 'clf__kernel': ['rbf']}]\n", "\n", "gs = GridSearchCV(estimator=pipe_svc,\n", " param_grid=param_grid,\n", " scoring=scorer,\n", " cv=10,\n", " n_jobs=-1)\n", "gs = gs.fit(X_train, y_train)\n", "print(gs.best_score_)\n", "print(gs.best_params_)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test accuracy: 0.965\n" ] } ], "source": [ "clf = gs.best_estimator_\n", "clf.fit(X_train, y_train)\n", "print('Test accuracy: %.3f' % clf.score(X_test, y_test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm selection with nested cross-validation" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CV accuracy: 0.960 +/- 0.026\n" ] } ], "source": [ "gs = GridSearchCV(estimator=pipe_svc,\n", " param_grid=param_grid,\n", " scoring='accuracy',\n", " cv=2)\n", "\n", "# Note: Optionally, you could use cv=2 \n", "# in the GridSearchCV above to produce\n", "# the 5 x 2 nested CV that is shown in the figure.\n", "\n", "scores = cross_val_score(gs, X_train, y_train, scoring='accuracy', cv=5)\n", "print('CV accuracy: %.3f +/- %.3f' % (np.mean(scores), np.std(scores)))" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CV accuracy: 0.921 +/- 0.029\n" ] } ], "source": [ "from sklearn.tree import DecisionTreeClassifier\n", "\n", "gs = GridSearchCV(estimator=DecisionTreeClassifier(random_state=0),\n", " param_grid=[{'max_depth': [1, 2, 3, 4, 5, 6, 7, None]}],\n", " scoring='accuracy',\n", " cv=2)\n", "scores = cross_val_score(gs, X_train, y_train, scoring='accuracy', cv=5)\n", "print('CV accuracy: %.3f +/- %.3f' % (np.mean(scores), np.std(scores)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting a receiver operating characteristic" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ji4e3BMDVBJ3riqyMKz00rmhMzObNG5CZmQl3d3dKVgkhRE/lynIAwJTg8XAV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\nWLBgATNmzMPCwpJvvvmakyf/ZO3an/Dyq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import roc_curve, auc\n", "from scipy import interp\n", "\n", "pipe_lr = Pipeline([('scl', StandardScaler()),\n", " ('pca', PCA(n_components=2)),\n", " ('clf', LogisticRegression(penalty='l2', \n", " random_state=0, \n", " C=100.0))])\n", "\n", "X_train2 = X_train[:, [4, 14]]\n", "\n", "\n", "if Version(sklearn_version) < '0.18':\n", " cv = StratifiedKFold(y_train, \n", " n_folds=3, \n", " random_state=1)\n", " \n", "else:\n", " cv = list(StratifiedKFold(n_splits=3, \n", " random_state=1).split(X_train, y_train))\n", "\n", "fig = plt.figure(figsize=(7, 5))\n", "\n", "mean_tpr = 0.0\n", "mean_fpr = np.linspace(0, 1, 100)\n", "all_tpr = []\n", "\n", "for i, (train, test) in enumerate(cv):\n", " probas = pipe_lr.fit(X_train2[train],\n", " y_train[train]).predict_proba(X_train2[test])\n", "\n", " fpr, tpr, thresholds = roc_curve(y_train[test],\n", " probas[:, 1],\n", " pos_label=1)\n", " mean_tpr += interp(mean_fpr, fpr, tpr)\n", " mean_tpr[0] = 0.0\n", " roc_auc = auc(fpr, tpr)\n", " plt.plot(fpr,\n", " tpr,\n", " lw=1,\n", " label='ROC fold %d (area = %0.2f)'\n", " % (i+1, roc_auc))\n", "\n", "plt.plot([0, 1],\n", " [0, 1],\n", " linestyle='--',\n", " color=(0.6, 0.6, 0.6),\n", " label='random guessing')\n", "\n", "mean_tpr /= len(cv)\n", "mean_tpr[-1] = 1.0\n", "mean_auc = auc(mean_fpr, mean_tpr)\n", "plt.plot(mean_fpr, mean_tpr, 'k--',\n", " label='mean ROC (area = %0.2f)' % mean_auc, lw=2)\n", "plt.plot([0, 0, 1],\n", " [0, 1, 1],\n", " lw=2,\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", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/roc.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pipe_lr = pipe_lr.fit(X_train2, y_train)\n", "y_pred2 = pipe_lr.predict(X_test[:, [4, 14]])" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ROC AUC: 0.662\n", "Accuracy: 0.711\n" ] } ], "source": [ "from sklearn.metrics import roc_auc_score, accuracy_score\n", "print('ROC AUC: %.3f' % roc_auc_score(y_true=y_test, y_score=y_pred2))\n", "print('Accuracy: %.3f' % accuracy_score(y_true=y_test, y_pred=y_pred2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "We've gone over several useful tools for model validation\n", "\n", "- The **Training Score** shows how well a model fits the data it was trained on. This is not a good indication of model effectiveness\n", "- The **Validation Score** shows how well a model fits hold-out data. The most effective method is some form of cross-validation, where multiple hold-out sets are used.\n", "- **Validation Curves** are a plot of validation score and training score as a function of **model complexity**:\n", " + when the two curves are close, it indicates *underfitting*\n", " + when the two curves are separated, it indicates *overfitting*\n", " + the \"sweet spot\" is in the middle\n", "- **Learning Curves** are a plot of the validation score and training score as a function of **Number of training samples**\n", " + when the curves are close, it indicates *underfitting*, and adding more data will not generally improve the estimator.\n", " + when the curves are far apart, it indicates *overfitting*, and adding more data may increase the effectiveness of the model.\n", " \n", "These tools are powerful means of evaluating your model on your data." ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }