M05N04_Hyperparameters_and_Model_Validation.ipynb

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      "source": [
        "<!--BOOK_INFORMATION-->\n",
        "<img align=\"left\" style=\"padding-right:10px;\" src=\"https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/PDSH-cover-small.png?raw=1\">\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)!*"
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      "source": [
        "<!--NAVIGATION-->\n",
        "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
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      "source": [
        "# Hyperparameters and Model Validation"
      ]
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        "In the previous section, we saw the basic recipe for applying a supervised machine learning model:\n",
        "\n",
        "1. Choose a class of model\n",
        "2. Choose model hyperparameters\n",
        "3. Fit the model to the training data\n",
        "4. Use the model to predict labels for new data\n",
        "\n",
        "The first two pieces of this—the choice of model and choice of hyperparameters—are perhaps the most important part of using these tools and techniques effectively.\n",
        "In order to make an informed choice, we need a way to *validate* that our model and our hyperparameters are a good fit to the data.\n",
        "While this may sound simple, there are some pitfalls that you must avoid to do this effectively."
      ]
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        "## Thinking about Model Validation\n",
        "\n",
        "In principle, model validation is very simple: after choosing a model and its hyperparameters, we can estimate how effective it is by applying it to some of the training data and comparing the prediction to the known value.\n",
        "\n",
        "The following sections first show a naive approach to model validation and why it\n",
        "fails, before exploring the use of holdout sets and cross-validation for more robust\n",
        "model evaluation."
      ]
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        "### Model validation the wrong way\n",
        "\n",
        "Let's demonstrate the naive approach to validation using the Iris data, which we saw in the previous section.\n",
        "We will start by loading the data:"
      ]
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      "source": [
        "from sklearn.datasets import load_iris\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target"
      ]
    },
    {
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        "Next we choose a model and hyperparameters. Here we'll use a *k*-neighbors classifier with ``n_neighbors=1``.\n",
        "This is a very simple and intuitive model that says \"the label of an unknown point is the same as the label of its closest training point:\""
      ]
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      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "model = KNeighborsClassifier(n_neighbors=1)"
      ]
    },
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      "source": [
        "Then we train the model, and use it to predict labels for data we already know:"
      ]
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      "source": [
        "model.fit(X, y)\n",
        "y_model = model.predict(X)"
      ]
    },
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      "source": [
        "Finally, we compute the fraction of correctly labeled points:"
      ]
    },
    {
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      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(y, y_model)"
      ]
    },
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        "We see an accuracy score of 1.0, which indicates that 100% of points were correctly labeled by our model!\n",
        "But is this truly measuring the expected accuracy? Have we really come upon a model that we expect to be correct 100% of the time?\n",
        "\n",
        "As you may have gathered, the answer is no.\n",
        "In fact, this approach contains a fundamental flaw: *it trains and evaluates the model on the same data*.\n",
        "Furthermore, the nearest neighbor model is an *instance-based* estimator that simply stores the training data, and predicts labels by comparing new data to these stored points: except in contrived cases, it will get 100% accuracy *every time!*"
      ]
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        "### Model validation the right way: Holdout sets\n",
        "\n",
        "So what can be done?\n",
        "A better sense of a model's performance can be found using what's known as a *holdout set*: that is, we hold back some subset of the data from the training of the model, and then use this holdout set to check the model performance.\n",
        "This splitting can be done using the ``train_test_split`` utility in Scikit-Learn:"
      ]
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        "from sklearn.model_selection import train_test_split\n",
        "# split the data with 50% in each set\n",
        "X1, X2, y1, y2 = train_test_split(X, y, random_state=0,\n",
        "                                  train_size=0.5)\n",
        "\n",
        "# fit the model on one set of data\n",
        "model.fit(X1, y1)\n",
        "\n",
        "# evaluate the model on the second set of data\n",
        "y2_model = model.predict(X2)\n",
        "accuracy_score(y2, y2_model)"
      ]
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        "We see here a more reasonable result: the nearest-neighbor classifier is about 90% accurate on this hold-out set.\n",
        "The hold-out set is similar to unknown data, because the model has not \"seen\" it before."
      ]
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        "### Model validation via cross-validation\n",
        "\n",
        "One disadvantage of using a holdout set for model validation is that we have lost a portion of our data to the model training.\n",
        "In the above case, half the dataset does not contribute to the training of the model!\n",
        "This is not optimal, and can cause problems – especially if the initial set of training data is small.\n",
        "\n",
        "One way to address this is to use *cross-validation*; that is, to do a sequence of fits where each subset of the data is used both as a training set and as a validation set.\n",
        "Visually, it might look something like this:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-2-fold-CV.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#2-Fold-Cross-Validation)\n",
        "\n",
        "Here we do two validation trials, alternately using each half of the data as a holdout set.\n",
        "Using the split data from before, we could implement it like this:"
      ]
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      "source": [
        "y2_model = model.fit(X1, y1).predict(X2)\n",
        "y1_model = model.fit(X2, y2).predict(X1)\n",
        "accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)"
      ]
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        "What comes out are two accuracy scores, which we could combine (by, say, taking the mean) to get a better measure of the global model performance.\n",
        "This particular form of cross-validation is a *two-fold cross-validation*—that is, one in which we have split the data into two sets and used each in turn as a validation set.\n",
        "\n",
        "We could expand on this idea to use even more trials, and more folds in the data—for example, here is a visual depiction of five-fold cross-validation:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-5-fold-CV.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#5-Fold-Cross-Validation)\n",
        "\n",
        "Here we split the data into five groups, and use each of them in turn to evaluate the model fit on the other 4/5 of the data.\n",
        "This would be rather tedious to do by hand, and so we can use Scikit-Learn's ``cross_val_score`` convenience routine to do it succinctly:"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "from sklearn.model_selection import cross_val_score\n",
        "cross_val_score(model, X, y, cv=5)"
      ]
    },
    {
      "cell_type": "markdown",
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        "Repeating the validation across different subsets of the data gives us an even better idea of the performance of the algorithm.\n",
        "\n",
        "Scikit-Learn implements a number of useful cross-validation schemes that are useful in particular situations; these are implemented via iterators in the ``cross_validation`` module.\n",
        "For example, we might wish to go to the extreme case in which our number of folds is equal to the number of data points: that is, we train on all points but one in each trial.\n",
        "This type of cross-validation is known as *leave-one-out* cross validation, and can be used as follows:"
      ]
    },
    {
      "cell_type": "code",
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          "data": {
            "text/plain": [
              "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
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          },
          "execution_count": 16,
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      ],
      "source": [
        "from sklearn.model_selection import LeaveOneOut\n",
        "scores = cross_val_score(model, X, y, cv=LeaveOneOut())\n",
        "scores"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "Because we have 150 samples, the leave one out cross-validation yields scores for 150 trials, and the score indicates either successful (1.0) or unsuccessful (0.0) prediction.\n",
        "Taking the mean of these gives an estimate of the error rate:"
      ]
    },
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      "source": [
        "scores.mean()"
      ]
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        "Other cross-validation schemes can be used similarly.\n",
        "For a description of what is available in Scikit-Learn, use IPython to explore the ``sklearn.cross_validation`` submodule, or take a look at Scikit-Learn's online [cross-validation documentation](http://scikit-learn.org/stable/modules/cross_validation.html)."
      ]
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      "source": [
        "## Selecting the Best Model\n",
        "\n",
        "Now that we've seen the basics of validation and cross-validation, we will go into a litte more depth regarding model selection and selection of hyperparameters.\n",
        "These issues are some of the most important aspects of the practice of machine learning, and I find that this information is often glossed over in introductory machine learning tutorials.\n",
        "\n",
        "Of core importance is the following question: *if our estimator is underperforming, how should we move forward?*\n",
        "There are several possible answers:\n",
        "\n",
        "- Use a more complicated/more flexible model\n",
        "- Use a less complicated/less flexible model\n",
        "- Gather more training samples\n",
        "- Gather more data to add features to each sample\n",
        "\n",
        "The answer to this question is often counter-intuitive.\n",
        "In particular, sometimes using a more complicated model will give worse results, and adding more training samples may not improve your results!\n",
        "The ability to determine what steps will improve your model is what separates the successful machine learning practitioners from the unsuccessful."
      ]
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        "### The Bias-variance trade-off\n",
        "\n",
        "Fundamentally, the question of \"the best model\" is about finding a sweet spot in the tradeoff between *bias* and *variance*.\n",
        "Consider the following figure, which presents two regression fits to the same dataset:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-bias-variance.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff)\n",
        "\n",
        "It is clear that neither of these models is a particularly good fit to the data, but they fail in different ways.\n",
        "\n",
        "The model on the left attempts to find a straight-line fit through the data.\n",
        "Because the data are intrinsically more complicated than a straight line, the straight-line model will never be able to describe this dataset well.\n",
        "Such a model is said to *underfit* the data: that is, it does not have enough model flexibility to suitably account for all the features in the data; another way of saying this is that the model has high *bias*.\n",
        "\n",
        "The model on the right attempts to fit a high-order polynomial through the data.\n",
        "Here the model fit has enough flexibility to nearly perfectly account for the fine features in the data, but even though it very accurately describes the training data, its precise form seems to be more reflective of the particular noise properties of the data rather than the intrinsic properties of whatever process generated that data.\n",
        "Such a model is said to *overfit* the data: that is, it has so much model flexibility that the model ends up accounting for random errors as well as the underlying data distribution; another way of saying this is that the model has high *variance*."
      ]
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      "source": [
        "To look at this in another light, consider what happens if we use these two models to predict the y-value for some new data.\n",
        "In the following diagrams, the red/lighter points indicate data that is omitted from the training set:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-bias-variance-2.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff-Metrics)\n",
        "\n",
        "The score here is the $R^2$ score, or [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), which measures how well a model performs relative to a simple mean of the target values. $R^2=1$ indicates a perfect match, $R^2=0$ indicates the model does no better than simply taking the mean of the data, and negative values mean even worse models.\n",
        "From the scores associated with these two models, we can make an observation that holds more generally:\n",
        "\n",
        "- For high-bias models, the performance of the model on the validation set is similar to the performance on the training set.\n",
        "- For high-variance models, the performance of the model on the validation set is far worse than the performance on the training set."
      ]
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      "source": [
        "If we imagine that we have some ability to tune the model complexity, we would expect the training score and validation score to behave as illustrated in the following figure:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-validation-curve.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Validation-Curve)\n",
        "\n",
        "The diagram shown here is often called a *validation curve*, and we see the following essential features:\n",
        "\n",
        "- The training score is everywhere higher than the validation score. This is generally the case: the model will be a better fit to data it has seen than to data it has not seen.\n",
        "- For very low model complexity (a high-bias model), the training data is under-fit, which means that the model is a poor predictor both for the training data and for any previously unseen data.\n",
        "- For very high model complexity (a high-variance model), the training data is over-fit, which means that the model predicts the training data very well, but fails for any previously unseen data.\n",
        "- For some intermediate value, the validation curve has a maximum. This level of complexity indicates a suitable trade-off between bias and variance.\n",
        "\n",
        "The means of tuning the model complexity varies from model to model; when we discuss individual models in depth in later sections, we will see how each model allows for such tuning."
      ]
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        "### Validation curves in Scikit-Learn\n",
        "\n",
        "Let's look at an example of using cross-validation to compute the validation curve for a class of models.\n",
        "Here we will use a *polynomial regression* model: this is a generalized linear model in which the degree of the polynomial is a tunable parameter.\n",
        "For example, a degree-1 polynomial fits a straight line to the data; for model parameters $a$ and $b$:\n",
        "\n",
        "$$\n",
        "y = ax + b\n",
        "$$\n",
        "\n",
        "A degree-3 polynomial fits a cubic curve to the data; for model parameters $a, b, c, d$:\n",
        "\n",
        "$$\n",
        "y = ax^3 + bx^2 + cx + d\n",
        "$$\n",
        "\n",
        "We can generalize this to any number of polynomial features.\n",
        "In Scikit-Learn, we can implement this with a simple linear regression combined with the polynomial preprocessor.\n",
        "We will use a *pipeline* to string these operations together (we will discuss polynomial features and pipelines more fully in [Feature Engineering](05.04-Feature-Engineering.ipynb)):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "SdK_BxnVqmTT"
      },
      "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": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "rH0TDjY0qmTU"
      },
      "source": [
        "Now let's create some data to which we will fit our model:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "04-aQ7vjqmTU"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "def make_data(N, err=1.0, rseed=1):\n",
        "    # randomly sample the data\n",
        "    rng = np.random.RandomState(rseed)\n",
        "    X = rng.rand(N, 1) ** 2\n",
        "    y = 10 - 1. / (X.ravel() + 0.1)\n",
        "    if err > 0:\n",
        "        y += err * rng.randn(N)\n",
        "    return X, y\n",
        "\n",
        "X, y = make_data(40)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "kW7YzttLqmTU"
      },
      "source": [
        "We can now visualize our data, along with polynomial fits of several degrees:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "dHC0tIuqqmTV",
        "outputId": "b7996969-deb3-406b-f68b-9a6e1e1824d7"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn; seaborn.set()  # plot formatting\n",
        "\n",
        "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n",
        "\n",
        "plt.scatter(X.ravel(), y, color='black')\n",
        "axis = plt.axis()\n",
        "for degree in [1, 3, 5]:\n",
        "    y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)\n",
        "    plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))\n",
        "plt.xlim(-0.1, 1.0)\n",
        "plt.ylim(-2, 12)\n",
        "plt.legend(loc='best');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "9oUVR1ydqmTV"
      },
      "source": [
        "The knob controlling model complexity in this case is the degree of the polynomial, which can be any non-negative integer.\n",
        "A useful question to answer is this: what degree of polynomial provides a suitable trade-off between bias (under-fitting) and variance (over-fitting)?\n",
        "\n",
        "We can make progress in this by visualizing the validation curve for this particular data and model; this can be done straightforwardly using the ``validation_curve`` convenience routine provided by Scikit-Learn.\n",
        "Given a model, data, parameter name, and a range to explore, this function will automatically compute both the training score and validation score across the range:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "iEt2HhjXqmTV",
        "outputId": "e4c70f10-c80b-4b20-bc0a-e8e6ef1039d9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from sklearn.model_selection import validation_curve\n",
        "degree = np.arange(0, 21)\n",
        "train_score, val_score = validation_curve(PolynomialRegression(), X, y,\n",
        "                                          param_name='polynomialfeatures__degree', param_range=degree, cv=7)\n",
        "\n",
        "plt.plot(degree, np.median(train_score, 1), color='blue', label='training score')\n",
        "plt.plot(degree, np.median(val_score, 1), color='red', label='validation score')\n",
        "plt.legend(loc='best')\n",
        "plt.ylim(0, 1)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('score');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "y7YxJixnqmTV"
      },
      "source": [
        "This shows precisely the qualitative behavior we expect: the training score is everywhere higher than the validation score; the training score is monotonically improving with increased model complexity; and the validation score reaches a maximum before dropping off as the model becomes over-fit.\n",
        "\n",
        "From the validation curve, we can read-off that the optimal trade-off between bias and variance is found for a third-order polynomial; we can compute and display this fit over the original data as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "DVy5CvsqqmTW",
        "outputId": "22a6701a-2479-4a81-cb72-d0a40dc7c223"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(X.ravel(), y)\n",
        "lim = plt.axis()\n",
        "y_test = PolynomialRegression(3).fit(X, y).predict(X_test)\n",
        "plt.plot(X_test.ravel(), y_test);\n",
        "plt.axis(lim);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "BdUd4sbeqmTW"
      },
      "source": [
        "Notice that finding this optimal model did not actually require us to compute the training score, but examining the relationship between the training score and validation score can give us useful insight into the performance of the model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "KVG34wBKqmTW"
      },
      "source": [
        "## Learning Curves\n",
        "\n",
        "One important aspect of model complexity is that the optimal model will generally depend on the size of your training data.\n",
        "For example, let's generate a new dataset with a factor of five more points:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "sSeJH5h6qmTW",
        "outputId": "4ddbb69f-94a3-4c50-b97b-edf81495c343"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "X2, y2 = make_data(200)\n",
        "plt.scatter(X2.ravel(), y2);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Gq7NXbAVqmTW"
      },
      "source": [
        "We will duplicate the preceding code to plot the validation curve for this larger dataset; for reference let's over-plot the previous results as well:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "3VtA00omqmTX",
        "outputId": "428a1b1e-59d5-4154-f96c-d47ad872caf8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "degree = np.arange(21)\n",
        "train_score2, val_score2 = validation_curve(PolynomialRegression(), X2, y2,\n",
        "                                            param_name='polynomialfeatures__degree', param_range=degree, cv=7)\n",
        "\n",
        "plt.plot(degree, np.median(train_score2, 1), color='blue', label='training score')\n",
        "plt.plot(degree, np.median(val_score2, 1), color='red', label='validation score')\n",
        "plt.plot(degree, np.median(train_score, 1), color='blue', alpha=0.3, linestyle='dashed')\n",
        "plt.plot(degree, np.median(val_score, 1), color='red', alpha=0.3, linestyle='dashed')\n",
        "plt.legend(loc='lower center')\n",
        "plt.ylim(0, 1)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('score');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bOZionIJqmTX"
      },
      "source": [
        "The solid lines show the new results, while the fainter dashed lines show the results of the previous smaller dataset.\n",
        "It is clear from the validation curve that the larger dataset can support a much more complicated model: the peak here is probably around a degree of 6, but even a degree-20 model is not seriously over-fitting the data—the validation and training scores remain very close.\n",
        "\n",
        "Thus we see that the behavior of the validation curve has not one but two important inputs: the model complexity and the number of training points.\n",
        "It is often useful to to explore the behavior of the model as a function of the number of training points, which we can do by using increasingly larger subsets of the data to fit our model.\n",
        "A plot of the training/validation score with respect to the size of the training set is known as a *learning curve.*\n",
        "\n",
        "The general behavior we would expect from a learning curve is this:\n",
        "\n",
        "- A model of a given complexity will *overfit* a small dataset: this means the training score will be relatively high, while the validation score will be relatively low.\n",
        "- A model of a given complexity will *underfit* a large dataset: this means that the training score will decrease, but the validation score will increase.\n",
        "- A model will never, except by chance, give a better score to the validation set than the training set: this means the curves should keep getting closer together but never cross.\n",
        "\n",
        "With these features in mind, we would expect a learning curve to look qualitatively like that shown in the following figure:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Ty48rZMhqmTX"
      },
      "source": [
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-learning-curve.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Learning-Curve)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "7Cgzwn84qmTX"
      },
      "source": [
        "The notable feature of the learning curve is the convergence to a particular score as the number of training samples grows.\n",
        "In particular, once you have enough points that a particular model has converged, *adding more training data will not help you!*\n",
        "The only way to increase model performance in this case is to use another (often more complex) model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "nfsgFl0JqmTX"
      },
      "source": [
        "### Learning curves in Scikit-Learn\n",
        "\n",
        "Scikit-Learn offers a convenient utility for computing such learning curves from your models; here we will compute a learning curve for our original dataset with a second-order polynomial model and a ninth-order polynomial:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "VszHPGNHqmTX",
        "outputId": "650a82ba-bd5f-474f-bdd9-e609926bd4e0"
      },
      "outputs": [
        {
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            "text/plain": [
              "<Figure size 1600x600 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from sklearn.model_selection import learning_curve\n",
        "\n",
        "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
        "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
        "\n",
        "for i, degree in enumerate([2, 9]):\n",
        "    N, train_lc, val_lc = learning_curve(PolynomialRegression(degree),\n",
        "                                         X, y, cv=7,\n",
        "                                         train_sizes=np.linspace(0.3, 1, 25))\n",
        "\n",
        "    ax[i].plot(N, np.mean(train_lc, 1), color='blue', label='training score')\n",
        "    ax[i].plot(N, np.mean(val_lc, 1), color='red', label='validation score')\n",
        "    ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0], N[-1],\n",
        "                 color='gray', linestyle='dashed')\n",
        "\n",
        "    ax[i].set_ylim(0, 1)\n",
        "    ax[i].set_xlim(N[0], N[-1])\n",
        "    ax[i].set_xlabel('training size')\n",
        "    ax[i].set_ylabel('score')\n",
        "    ax[i].set_title('degree = {0}'.format(degree), size=14)\n",
        "    ax[i].legend(loc='best')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "1SmMxRvHqmTY"
      },
      "source": [
        "This is a valuable diagnostic, because it gives us a visual depiction of how our model responds to increasing training data.\n",
        "In particular, when your learning curve has already converged (i.e., when the training and validation curves are already close to each other) *adding more training data will not significantly improve the fit!*\n",
        "This situation is seen in the left panel, with the learning curve for the degree-2 model.\n",
        "\n",
        "The only way to increase the converged score is to use a different (usually more complicated) model.\n",
        "We see this in the right panel: by moving to a much more complicated model, we increase the score of convergence (indicated by the dashed line), but at the expense of higher model variance (indicated by the difference between the training and validation scores).\n",
        "If we were to add even more data points, the learning curve for the more complicated model would eventually converge.\n",
        "\n",
        "Plotting a learning curve for your particular choice of model and dataset can help you to make this type of decision about how to move forward in improving your analysis."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "BjKGJWRlqmTY"
      },
      "source": [
        "## Validation in Practice: Grid Search\n",
        "\n",
        "The preceding discussion is meant to give you some intuition into the trade-off between bias and variance, and its dependence on model complexity and training set size.\n",
        "In practice, models generally have more than one knob to turn, and thus plots of validation and learning curves change from lines to multi-dimensional surfaces.\n",
        "In these cases, such visualizations are difficult and we would rather simply find the particular model that maximizes the validation score.\n",
        "\n",
        "Scikit-Learn provides automated tools to do this in the grid search module.\n",
        "Here is an example of using grid search to find the optimal polynomial model.\n",
        "We will explore a three-dimensional grid of model features; namely the polynomial degree, the flag telling us whether to fit the intercept, and the flag telling us whether to normalize the problem.\n",
        "This can be set up using Scikit-Learn's ``GridSearchCV`` meta-estimator:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "p4-ye7UYqmTY"
      },
      "outputs": [],
      "source": [
        "from sklearn.model_selection import GridSearchCV\n",
        "\n",
        "param_grid = {'polynomialfeatures__degree': np.arange(21),\n",
        "              'linearregression__fit_intercept': [True, False],\n",
        "              'linearregression__normalize': [True, False]}\n",
        "\n",
        "grid = GridSearchCV(PolynomialRegression(), param_grid, cv=7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "pJucdRfrqmTY"
      },
      "source": [
        "Notice that like a normal estimator, this has not yet been applied to any data.\n",
        "Calling the ``fit()`` method will fit the model at each grid point, keeping track of the scores along the way:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "juUYTjDoqmTY"
      },
      "outputs": [],
      "source": [
        "grid.fit(X, y);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "AiV4Hd2kqmTY"
      },
      "source": [
        "Now that this is fit, we can ask for the best parameters as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "aZcshBAeqmTY",
        "outputId": "3b07723a-f6bc-4caa-9cc6-515bc35aa11b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'linearregression__fit_intercept': False,\n",
              " 'linearregression__normalize': True,\n",
              " 'polynomialfeatures__degree': 4}"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "grid.best_params_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "kFixvas3qmTY"
      },
      "source": [
        "Finally, if we wish, we can use the best model and show the fit to our data using code from before:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "wls3674yqmTY",
        "outputId": "1424781b-600f-421a-f632-b6c4886e988b"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/Users/snesbitt/miniforge3/envs/py3/lib/python3.9/site-packages/sklearn/linear_model/_base.py:141: FutureWarning: 'normalize' was deprecated in version 1.0 and will be removed in 1.2.\n",
            "If you wish to scale the data, use Pipeline with a StandardScaler in a preprocessing stage. To reproduce the previous behavior:\n",
            "\n",
            "from sklearn.pipeline import make_pipeline\n",
            "\n",
            "model = make_pipeline(StandardScaler(with_mean=False), LinearRegression())\n",
            "\n",
            "If you wish to pass a sample_weight parameter, you need to pass it as a fit parameter to each step of the pipeline as follows:\n",
            "\n",
            "kwargs = {s[0] + '__sample_weight': sample_weight for s in model.steps}\n",
            "model.fit(X, y, **kwargs)\n",
            "\n",
            "\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "model = grid.best_estimator_\n",
        "\n",
        "plt.scatter(X.ravel(), y)\n",
        "lim = plt.axis()\n",
        "y_test = model.fit(X, y).predict(X_test)\n",
        "plt.plot(X_test.ravel(), y_test);\n",
        "plt.axis(lim);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "ZmtDUHL0qmTY"
      },
      "source": [
        "The grid search provides many more options, including the ability to specify a custom scoring function, to parallelize the computations, to do randomized searches, and more.\n",
        "For information, see the examples in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) and [Feature Engineering: Working with Images](05.14-Image-Features.ipynb), or refer to Scikit-Learn's [grid search documentation](http://Scikit-Learn.org/stable/modules/grid_search.html)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bEfJeidfqmTZ"
      },
      "source": [
        "## Summary\n",
        "\n",
        "In this section, we have begun to explore the concept of model validation and hyperparameter optimization, focusing on intuitive aspects of the bias–variance trade-off and how it comes into play when fitting models to data.\n",
        "In particular, we found that the use of a validation set or cross-validation approach is *vital* when tuning parameters in order to avoid over-fitting for more complex/flexible models.\n",
        "\n",
        "In later sections, we will discuss the details of particularly useful models, and throughout will talk about what tuning is available for these models and how these free parameters affect model complexity.\n",
        "Keep the lessons of this section in mind as you read on and learn about these machine learning approaches!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "9UYOYZKPqmTZ"
      },
      "source": [
        "<!--NAVIGATION-->\n",
        "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
      ]
    }
  ],
  "metadata": {
    "anaconda-cloud": {},
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3.9.7 ('py3')",
      "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": "3.9.7"
    },
    "vscode": {
      "interpreter": {
        "hash": "7a6b41cc1ffbe7f6292ade58ee9ab0c89bd7fa770a77f101cc95d5710b4e5fa9"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}