05_06_linear_regression.ipynb

{
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/frkr/mlearn/blob/master/05_06_linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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        "id": "6ZTouyCMTOjJ"
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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)!*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UyyjTBvnTOjT"
      },
      "source": [
        "# In Depth: Linear Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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        "id": "W5duC4YFTOjT"
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      "source": [
        "Just as naive Bayes (discussed earlier in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) is a good starting point for classification tasks, linear regression models are a good starting point for regression tasks.\n",
        "Such models are popular because they can be fit very quickly, and are very interpretable.\n",
        "You are probably familiar with the simplest form of a linear regression model (i.e., fitting a straight line to data) but such models can be extended to model more complicated data behavior.\n",
        "\n",
        "In this section we will start with a quick intuitive walk-through of the mathematics behind this well-known problem, before seeing how before moving on to see how linear models can be generalized to account for more complicated patterns in data.\n",
        "\n",
        "We begin with the standard imports:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
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        "id": "Ot7Jf-j8TOjU"
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      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns; sns.set()\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "cMIDwBFsTOjW"
      },
      "source": [
        "## Simple Linear Regression\n",
        "\n",
        "We will start with the most familiar linear regression, a straight-line fit to data.\n",
        "A straight-line fit is a model of the form\n",
        "$$\n",
        "y = ax + b\n",
        "$$\n",
        "where $a$ is commonly known as the *slope*, and $b$ is commonly known as the *intercept*.\n",
        "\n",
        "Consider the following data, which is scattered about a line with a slope of 2 and an intercept of -5:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "cjvWr4lETOjX",
        "outputId": "cf92ffc7-f37d-4913-81ca-dc6ecf2946d5"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "rng = np.random.RandomState(1)\n",
        "x = 10 * rng.rand(50)\n",
        "y = 2 * x - 5 + rng.randn(50)\n",
        "plt.scatter(x, y);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "pEjaQlh1TOjZ"
      },
      "source": [
        "We can use Scikit-Learn's ``LinearRegression`` estimator to fit this data and construct the best-fit line:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "POyuDuODTOja",
        "outputId": "99efa90c-11ad-4b6e-fa86-4502841b851f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "model = LinearRegression(fit_intercept=True)\n",
        "\n",
        "model.fit(x[:, np.newaxis], y)\n",
        "\n",
        "xfit = np.linspace(0, 10, 1000)\n",
        "yfit = model.predict(xfit[:, np.newaxis])\n",
        "\n",
        "plt.scatter(x, y)\n",
        "plt.plot(xfit, yfit);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "SKKJRw3LTOjb"
      },
      "source": [
        "The slope and intercept of the data are contained in the model's fit parameters, which in Scikit-Learn are always marked by a trailing underscore.\n",
        "Here the relevant parameters are ``coef_`` and ``intercept_``:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yWmIOuEOTOjc",
        "outputId": "9637a96b-03bc-45d9-a6ad-d2c0ad358ee5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model slope:     2.0272088103606953\n",
            "Model intercept: -4.998577085553204\n"
          ]
        }
      ],
      "source": [
        "print(\"Model slope:    \", model.coef_[0])\n",
        "print(\"Model intercept:\", model.intercept_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "xcuifUS7TOjc"
      },
      "source": [
        "We see that the results are very close to the inputs, as we might hope."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "a7SgMAvSTOjd"
      },
      "source": [
        "The ``LinearRegression`` estimator is much more capable than this, however—in addition to simple straight-line fits, it can also handle multidimensional linear models of the form\n",
        "$$\n",
        "y = a_0 + a_1 x_1 + a_2 x_2 + \\cdots\n",
        "$$\n",
        "where there are multiple $x$ values.\n",
        "Geometrically, this is akin to fitting a plane to points in three dimensions, or fitting a hyper-plane to points in higher dimensions.\n",
        "\n",
        "The multidimensional nature of such regressions makes them more difficult to visualize, but we can see one of these fits in action by building some example data, using NumPy's matrix multiplication operator:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8aJkT2ttTOje",
        "outputId": "320d3c16-f1cb-4ade-b2b6-cd292a425450"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5000000000000056\n",
            "[ 1.5 -2.   1. ]\n"
          ]
        }
      ],
      "source": [
        "rng = np.random.RandomState(1)\n",
        "X = 10 * rng.rand(100, 3)\n",
        "y = 0.5 + np.dot(X, [1.5, -2., 1.])\n",
        "\n",
        "model.fit(X, y)\n",
        "print(model.intercept_)\n",
        "print(model.coef_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "s6iiSSlTTOjf"
      },
      "source": [
        "Here the $y$ data is constructed from three random $x$ values, and the linear regression recovers the coefficients used to construct the data.\n",
        "\n",
        "In this way, we can use the single ``LinearRegression`` estimator to fit lines, planes, or hyperplanes to our data.\n",
        "It still appears that this approach would be limited to strictly linear relationships between variables, but it turns out we can relax this as well."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "OiLw-WI6TOjg"
      },
      "source": [
        "## Basis Function Regression\n",
        "\n",
        "One trick you can use to adapt linear regression to nonlinear relationships between variables is to transform the data according to *basis functions*.\n",
        "We have seen one version of this before, in the ``PolynomialRegression`` pipeline used in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) and [Feature Engineering](05.04-Feature-Engineering.ipynb).\n",
        "The idea is to take our multidimensional linear model:\n",
        "$$\n",
        "y = a_0 + a_1 x_1 + a_2 x_2 + a_3 x_3 + \\cdots\n",
        "$$\n",
        "and build the $x_1, x_2, x_3,$ and so on, from our single-dimensional input $x$.\n",
        "That is, we let $x_n = f_n(x)$, where $f_n()$ is some function that transforms our data.\n",
        "\n",
        "For example, if $f_n(x) = x^n$, our model becomes a polynomial regression:\n",
        "$$\n",
        "y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\cdots\n",
        "$$\n",
        "Notice that this is *still a linear model*—the linearity refers to the fact that the coefficients $a_n$ never multiply or divide each other.\n",
        "What we have effectively done is taken our one-dimensional $x$ values and projected them into a higher dimension, so that a linear fit can fit more complicated relationships between $x$ and $y$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "N9G-RX89TOjg"
      },
      "source": [
        "### Polynomial basis functions\n",
        "\n",
        "This polynomial projection is useful enough that it is built into Scikit-Learn, using the ``PolynomialFeatures`` transformer:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fw9nO7HrTOjh",
        "outputId": "bb1a3741-5510-4fe9-8a75-739beea96449"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.,  4.,  8.],\n",
              "       [ 3.,  9., 27.],\n",
              "       [ 4., 16., 64.]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "x = np.array([2, 3, 4])\n",
        "poly = PolynomialFeatures(3, include_bias=False)\n",
        "poly.fit_transform(x[:, None])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "s_BHiTW_TOjh"
      },
      "source": [
        "We see here that the transformer has converted our one-dimensional array into a three-dimensional array by taking the exponent of each value.\n",
        "This new, higher-dimensional data representation can then be plugged into a linear regression.\n",
        "\n",
        "As we saw in [Feature Engineering](05.04-Feature-Engineering.ipynb), the cleanest way to accomplish this is to use a pipeline.\n",
        "Let's make a 7th-degree polynomial model in this way:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "-71WzD_tTOji"
      },
      "outputs": [],
      "source": [
        "from sklearn.pipeline import make_pipeline\n",
        "poly_model = make_pipeline(PolynomialFeatures(7),\n",
        "                           LinearRegression())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "8kNeoh3pTOji"
      },
      "source": [
        "With this transform in place, we can use the linear model to fit much more complicated relationships between $x$ and $y$. \n",
        "For example, here is a sine wave with noise:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0av2xktkTOji",
        "outputId": "c1abbad3-f59e-4746-fa24-bac9e7de4ab7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "rng = np.random.RandomState(1)\n",
        "x = 10 * rng.rand(50)\n",
        "y = np.sin(x) + 0.1 * rng.randn(50)\n",
        "\n",
        "poly_model.fit(x[:, np.newaxis], y)\n",
        "yfit = poly_model.predict(xfit[:, np.newaxis])\n",
        "\n",
        "plt.scatter(x, y)\n",
        "plt.plot(xfit, yfit);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "UMC8LciUTOjj"
      },
      "source": [
        "Our linear model, through the use of 7th-order polynomial basis functions, can provide an excellent fit to this non-linear data!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "-4AyZ4eiTOjj"
      },
      "source": [
        "### Gaussian basis functions\n",
        "\n",
        "Of course, other basis functions are possible.\n",
        "For example, one useful pattern is to fit a model that is not a sum of polynomial bases, but a sum of Gaussian bases.\n",
        "The result might look something like the following figure:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "yuQLve8pTOjk"
      },
      "source": [
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.06-gaussian-basis.png?raw=1)\n",
        "[figure source in Appendix](#Gaussian-Basis)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "W9qVnL45TOjm"
      },
      "source": [
        "The shaded regions in the plot are the scaled basis functions, and when added together they reproduce the smooth curve through the data.\n",
        "These Gaussian basis functions are not built into Scikit-Learn, but we can write a custom transformer that will create them, as shown here and illustrated in the following figure (Scikit-Learn transformers are implemented as Python classes; reading Scikit-Learn's source is a good way to see how they can be created):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U56logsaTOjm",
        "outputId": "59736787-5e25-463c-ea24-0bb4aa2a7189"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from sklearn.base import BaseEstimator, TransformerMixin\n",
        "\n",
        "class GaussianFeatures(BaseEstimator, TransformerMixin):\n",
        "    \"\"\"Uniformly spaced Gaussian features for one-dimensional input\"\"\"\n",
        "    \n",
        "    def __init__(self, N, width_factor=2.0):\n",
        "        self.N = N\n",
        "        self.width_factor = width_factor\n",
        "    \n",
        "    @staticmethod\n",
        "    def _gauss_basis(x, y, width, axis=None):\n",
        "        arg = (x - y) / width\n",
        "        return np.exp(-0.5 * np.sum(arg ** 2, axis))\n",
        "        \n",
        "    def fit(self, X, y=None):\n",
        "        # create N centers spread along the data range\n",
        "        self.centers_ = np.linspace(X.min(), X.max(), self.N)\n",
        "        self.width_ = self.width_factor * (self.centers_[1] - self.centers_[0])\n",
        "        return self\n",
        "        \n",
        "    def transform(self, X):\n",
        "        return self._gauss_basis(X[:, :, np.newaxis], self.centers_,\n",
        "                                 self.width_, axis=1)\n",
        "    \n",
        "gauss_model = make_pipeline(GaussianFeatures(20),\n",
        "                            LinearRegression())\n",
        "gauss_model.fit(x[:, np.newaxis], y)\n",
        "yfit = gauss_model.predict(xfit[:, np.newaxis])\n",
        "\n",
        "plt.scatter(x, y)\n",
        "plt.plot(xfit, yfit)\n",
        "plt.xlim(0, 10);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "8q2C7pyDTOjn"
      },
      "source": [
        "We put this example here just to make clear that there is nothing magic about polynomial basis functions: if you have some sort of intuition into the generating process of your data that makes you think one basis or another might be appropriate, you can use them as well."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "GcftcPVpTOjn"
      },
      "source": [
        "## Regularization\n",
        "\n",
        "The introduction of basis functions into our linear regression makes the model much more flexible, but it also can very quickly lead to over-fitting (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this).\n",
        "For example, if we choose too many Gaussian basis functions, we end up with results that don't look so good:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "id": "sQw7zKS3TOjn",
        "outputId": "7a4de12a-4c2b-4e57-fd0d-ef2f7c6a11fa"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "model = make_pipeline(GaussianFeatures(30),\n",
        "                      LinearRegression())\n",
        "model.fit(x[:, np.newaxis], y)\n",
        "\n",
        "plt.scatter(x, y)\n",
        "plt.plot(xfit, model.predict(xfit[:, np.newaxis]))\n",
        "\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(-1.5, 1.5);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "pMskNz1GTOjo"
      },
      "source": [
        "With the data projected to the 30-dimensional basis, the model has far too much flexibility and goes to extreme values between locations where it is constrained by data.\n",
        "We can see the reason for this if we plot the coefficients of the Gaussian bases with respect to their locations:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "-GPqks5YTOjr",
        "outputId": "5d115fd7-8d30-4829-cc7e-f812fb8ce22d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def basis_plot(model, title=None):\n",
        "    fig, ax = plt.subplots(2, sharex=True)\n",
        "    model.fit(x[:, np.newaxis], y)\n",
        "    ax[0].scatter(x, y)\n",
        "    ax[0].plot(xfit, model.predict(xfit[:, np.newaxis]))\n",
        "    ax[0].set(xlabel='x', ylabel='y', ylim=(-1.5, 1.5))\n",
        "    \n",
        "    if title:\n",
        "        ax[0].set_title(title)\n",
        "\n",
        "    ax[1].plot(model.steps[0][1].centers_,\n",
        "               model.steps[1][1].coef_)\n",
        "    ax[1].set(xlabel='basis location',\n",
        "              ylabel='coefficient',\n",
        "              xlim=(0, 10))\n",
        "    \n",
        "model = make_pipeline(GaussianFeatures(30), LinearRegression())\n",
        "basis_plot(model)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "vPYclqYXTOjs"
      },
      "source": [
        "The lower panel of this figure shows the amplitude of the basis function at each location.\n",
        "This is typical over-fitting behavior when basis functions overlap: the coefficients of adjacent basis functions blow up and cancel each other out.\n",
        "We know that such behavior is problematic, and it would be nice if we could limit such spikes expliticly in the model by penalizing large values of the model parameters.\n",
        "Such a penalty is known as *regularization*, and comes in several forms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "KTwSGQBQTOjs"
      },
      "source": [
        "### Ridge regression ($L_2$ Regularization)\n",
        "\n",
        "Perhaps the most common form of regularization is known as *ridge regression* or $L_2$ *regularization*, sometimes also called *Tikhonov regularization*.\n",
        "This proceeds by penalizing the sum of squares (2-norms) of the model coefficients; in this case, the penalty on the model fit would be \n",
        "$$\n",
        "P = \\alpha\\sum_{n=1}^N \\theta_n^2\n",
        "$$\n",
        "where $\\alpha$ is a free parameter that controls the strength of the penalty.\n",
        "This type of penalized model is built into Scikit-Learn with the ``Ridge`` estimator:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XeTDjbvZTOjt",
        "outputId": "92f19f6e-d117-4ceb-9ed6-c8f708e68499"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from sklearn.linear_model import Ridge\n",
        "model = make_pipeline(GaussianFeatures(30), Ridge(alpha=0.1))\n",
        "basis_plot(model, title='Ridge Regression')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "BjQE-pGpTOjt"
      },
      "source": [
        "The $\\alpha$ parameter is essentially a knob controlling the complexity of the resulting model.\n",
        "In the limit $\\alpha \\to 0$, we recover the standard linear regression result; in the limit $\\alpha \\to \\infty$, all model responses will be suppressed.\n",
        "One advantage of ridge regression in particular is that it can be computed very efficiently—at hardly more computational cost than the original linear regression model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "5-LtLOW6TOjw"
      },
      "source": [
        "### Lasso regression ($L_1$ regularization)\n",
        "\n",
        "Another very common type of regularization is known as lasso, and involves penalizing the sum of absolute values (1-norms) of regression coefficients:\n",
        "$$\n",
        "P = \\alpha\\sum_{n=1}^N |\\theta_n|\n",
        "$$\n",
        "Though this is conceptually very similar to ridge regression, the results can differ surprisingly: for example, due to geometric reasons lasso regression tends to favor *sparse models* where possible: that is, it preferentially sets model coefficients to exactly zero.\n",
        "\n",
        "We can see this behavior in duplicating the ridge regression figure, but using L1-normalized coefficients:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n0ewhcDdTOjx",
        "outputId": "a98f31ed-5749-45d6-a40d-4ce90f90562b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/sklearn/linear_model/_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 2.136e-03, tolerance: 2.065e-03\n",
            "  model = cd_fast.enet_coordinate_descent(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from sklearn.linear_model import Lasso\n",
        "model = make_pipeline(GaussianFeatures(30), Lasso(alpha=0.001))\n",
        "basis_plot(model, title='Lasso Regression')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "rOXOTcDxTOjx"
      },
      "source": [
        "With the lasso regression penalty, the majority of the coefficients are exactly zero, with the functional behavior being modeled by a small subset of the available basis functions.\n",
        "As with ridge regularization, the $\\alpha$ parameter tunes the strength of the penalty, and should be determined via, for example, cross-validation (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Z0pH5qcPTOjy"
      },
      "source": [
        "## Example: Predicting Bicycle Traffic"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "N_qYN9SmTOjy"
      },
      "source": [
        "As an example, let's take a look at whether we can predict the number of bicycle trips across Seattle's Fremont Bridge based on weather, season, and other factors.\n",
        "We have seen this data already in [Working With Time Series](03.11-Working-with-Time-Series.ipynb).\n",
        "\n",
        "In this section, we will join the bike data with another dataset, and try to determine the extent to which weather and seasonal factors—temperature, precipitation, and daylight hours—affect the volume of bicycle traffic through this corridor.\n",
        "Fortunately, the NOAA makes available their daily [weather station data](http://www.ncdc.noaa.gov/cdo-web/search?datasetid=GHCND) (I used station ID USW00024233) and we can easily use Pandas to join the two data sources.\n",
        "We will perform a simple linear regression to relate weather and other information to bicycle counts, in order to estimate how a change in any one of these parameters affects the number of riders on a given day.\n",
        "\n",
        "In particular, this is an example of how the tools of Scikit-Learn can be used in a statistical modeling framework, in which the parameters of the model are assumed to have interpretable meaning.\n",
        "As discussed previously, this is not a standard approach within machine learning, but such interpretation is possible for some models.\n",
        "\n",
        "Let's start by loading the two datasets, indexing by date:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "OMF_2voSTOjz",
        "outputId": "362eeba1-01de-4efa-bcb5-253bd2a8bf0c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
            "                                 Dload  Upload   Total   Spent    Left  Speed\n",
            "100 2725k    0 2725k    0     0   981k      0 --:--:--  0:00:02 --:--:--  980k\n",
            "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
            "                                 Dload  Upload   Total   Spent    Left  Speed\n",
            "100  229k  100  229k    0     0  1820k      0 --:--:-- --:--:-- --:--:-- 1820k\n"
          ]
        }
      ],
      "source": [
        " !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD\n",
        " !curl -o BicycleWeather.csv https://raw.githubusercontent.com/jakevdp/PythonDataScienceHandbook/master/notebooks/data/BicycleWeather.csv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bynqdjp4TOjz"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "counts = pd.read_csv('FremontBridge.csv', index_col='Date', parse_dates=True)\n",
        "weather = pd.read_csv('BicycleWeather.csv', index_col='DATE', parse_dates=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "yppGDCq4TOjz"
      },
      "source": [
        "Next we will compute the total daily bicycle traffic, and put this in its own dataframe:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "dHcA_YPjTOjz"
      },
      "outputs": [],
      "source": [
        "daily = counts.resample('d').sum()\n",
        "daily['Total'] = daily.sum(axis=1)\n",
        "daily = daily[['Total']] # remove other columns"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "3rKhvssGTOj0"
      },
      "source": [
        "We saw previously that the patterns of use generally vary from day to day; let's account for this in our data by adding binary columns that indicate the day of the week:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "3gFUr3ykTOj0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24d4078e-81eb-4d43-8e02-7ed87422497d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-29-991c749c3333>:3: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  daily[days[i]] = (daily.index.dayofweek == i).astype(float)\n"
          ]
        }
      ],
      "source": [
        "days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']\n",
        "for i in range(7):\n",
        "    daily[days[i]] = (daily.index.dayofweek == i).astype(float)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "acOvHWmpTOj0"
      },
      "source": [
        "Similarly, we might expect riders to behave differently on holidays; let's add an indicator of this as well:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "MT7pDZoMTOj0"
      },
      "outputs": [],
      "source": [
        "from pandas.tseries.holiday import USFederalHolidayCalendar\n",
        "cal = USFederalHolidayCalendar()\n",
        "holidays = cal.holidays('2012', '2016')\n",
        "daily = daily.join(pd.Series(1, index=holidays, name='holiday'))\n",
        "daily['holiday'].fillna(0, inplace=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Bn8VD-T1TOj0"
      },
      "source": [
        "We also might suspect that the hours of daylight would affect how many people ride; let's use the standard astronomical calculation to add this information:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "DTN4A6JTTOj1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "9259f98f-b04b-416a-ee3b-2a3ddd16a942"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(8.0, 17.0)"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def hours_of_daylight(date, axis=23.44, latitude=47.61):\n",
        "    \"\"\"Compute the hours of daylight for the given date\"\"\"\n",
        "    days = (date - pd.datetime(2000, 12, 21)).days\n",
        "    m = (1. - np.tan(np.radians(latitude))\n",
        "         * np.tan(np.radians(axis) * np.cos(days * 2 * np.pi / 365.25)))\n",
        "    return 24. * np.degrees(np.arccos(1 - np.clip(m, 0, 2))) / 180.\n",
        "\n",
        "daily['daylight_hrs'] = list(map(hours_of_daylight, daily.index))\n",
        "daily[['daylight_hrs']].plot()\n",
        "plt.ylim(8, 17)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "zdBK2-KKTOj1"
      },
      "source": [
        "We can also add the average temperature and total precipitation to the data.\n",
        "In addition to the inches of precipitation, let's add a flag that indicates whether a day is dry (has zero precipitation):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "uYP5luPPTOj1"
      },
      "outputs": [],
      "source": [
        "# temperatures are in 1/10 deg C; convert to C\n",
        "weather['TMIN'] /= 10\n",
        "weather['TMAX'] /= 10\n",
        "weather['Temp (C)'] = 0.5 * (weather['TMIN'] + weather['TMAX'])\n",
        "\n",
        "# precip is in 1/10 mm; convert to inches\n",
        "weather['PRCP'] /= 254\n",
        "weather['dry day'] = (weather['PRCP'] == 0).astype(int)\n",
        "\n",
        "daily = daily.join(weather[['PRCP', 'Temp (C)', 'dry day']])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "c10ZrIoyTOj1"
      },
      "source": [
        "Finally, let's add a counter that increases from day 1, and measures how many years have passed.\n",
        "This will let us measure any observed annual increase or decrease in daily crossings:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Kr05prpbTOj2"
      },
      "outputs": [],
      "source": [
        "daily['annual'] = (daily.index - daily.index[0]).days / 365."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "-fB3SUvwTOj2"
      },
      "source": [
        "Now our data is in order, and we can take a look at it:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "87ghGDZSTOj2",
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          "height": 238
        },
        "outputId": "890b62c1-fd5e-4763-8587-8af5966b9286"
      },
      "outputs": [
        {
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          "data": {
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              "             Total  Mon  Tue  Wed  Thu  Fri  Sat  Sun  holiday  daylight_hrs  \\\n",
              "Date                                                                           \n",
              "2012-10-03  7042.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0      0.0     11.277359   \n",
              "2012-10-04  6950.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0      0.0     11.219142   \n",
              "2012-10-05  6296.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0      0.0     11.161038   \n",
              "2012-10-06  4012.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0      0.0     11.103056   \n",
              "2012-10-07  4284.0  0.0  0.0  0.0  0.0  0.0  0.0  1.0      0.0     11.045208   \n",
              "\n",
              "            PRCP  Temp (C)  dry day    annual  \n",
              "Date                                           \n",
              "2012-10-03   0.0     13.35      1.0  0.000000  \n",
              "2012-10-04   0.0     13.60      1.0  0.002740  \n",
              "2012-10-05   0.0     15.30      1.0  0.005479  \n",
              "2012-10-06   0.0     15.85      1.0  0.008219  \n",
              "2012-10-07   0.0     15.85      1.0  0.010959  "
            ],
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            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "daily.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "62tJyHodTOj2"
      },
      "source": [
        "With this in place, we can choose the columns to use, and fit a linear regression model to our data.\n",
        "We will set ``fit_intercept = False``, because the daily flags essentially operate as their own day-specific intercepts:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "TwqYLo75TOj3"
      },
      "outputs": [],
      "source": [
        "# Drop any rows with null values\n",
        "daily.dropna(axis=0, how='any', inplace=True)\n",
        "\n",
        "column_names = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun', 'holiday',\n",
        "                'daylight_hrs', 'PRCP', 'dry day', 'Temp (C)', 'annual']\n",
        "X = daily[column_names]\n",
        "y = daily['Total']\n",
        "\n",
        "model = LinearRegression(fit_intercept=False)\n",
        "model.fit(X, y)\n",
        "daily['predicted'] = model.predict(X)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "pQuYKOsqTOj3"
      },
      "source": [
        "Finally, we can compare the total and predicted bicycle traffic visually:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "u5YlD_dCTOj3",
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          "height": 296
        },
        "outputId": "403308eb-1f94-4aa3-e550-03f48f1dd56c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "daily[['Total', 'predicted']].plot(alpha=0.5);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "DtmRMv2HTOj3"
      },
      "source": [
        "It is evident that we have missed some key features, especially during the summer time.\n",
        "Either our features are not complete (i.e., people decide whether to ride to work based on more than just these) or there are some nonlinear relationships that we have failed to take into account (e.g., perhaps people ride less at both high and low temperatures).\n",
        "Nevertheless, our rough approximation is enough to give us some insights, and we can take a look at the coefficients of the linear model to estimate how much each feature contributes to the daily bicycle count:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "eGQ-HlcHTOj4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "96ae825b-b0a3-4291-ad00-acd7aad1d5af"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Mon             1009.765512\n",
              "Tue             1220.467872\n",
              "Wed             1185.347283\n",
              "Thu              964.716230\n",
              "Fri              355.960691\n",
              "Sat            -2206.603421\n",
              "Sun            -2267.134492\n",
              "holiday        -2374.802762\n",
              "daylight_hrs     257.703022\n",
              "PRCP           -1329.669764\n",
              "dry day         1095.397185\n",
              "Temp (C)         130.325582\n",
              "annual            53.885426\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "params = pd.Series(model.coef_, index=X.columns)\n",
        "params"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bXWBLBa1TOj4"
      },
      "source": [
        "These numbers are difficult to interpret without some measure of their uncertainty.\n",
        "We can compute these uncertainties quickly using bootstrap resamplings of the data:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "XceiZuk_TOj4"
      },
      "outputs": [],
      "source": [
        "from sklearn.utils import resample\n",
        "np.random.seed(1)\n",
        "err = np.std([model.fit(*resample(X, y)).coef_\n",
        "              for i in range(1000)], 0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "ZMV94ZzjTOj5"
      },
      "source": [
        "With these errors estimated, let's again look at the results:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "HlX3hHN1TOj5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2bae60de-fdf1-4caf-bf2e-809fe8cd1cfd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              effect  error\n",
            "Mon           1010.0  173.0\n",
            "Tue           1220.0  166.0\n",
            "Wed           1185.0  166.0\n",
            "Thu            965.0  170.0\n",
            "Fri            356.0  162.0\n",
            "Sat          -2207.0  159.0\n",
            "Sun          -2267.0  166.0\n",
            "holiday      -2375.0  326.0\n",
            "daylight_hrs   258.0   18.0\n",
            "PRCP         -1330.0  125.0\n",
            "dry day       1095.0   66.0\n",
            "Temp (C)       130.0    7.0\n",
            "annual          54.0   35.0\n"
          ]
        }
      ],
      "source": [
        "print(pd.DataFrame({'effect': params.round(0),\n",
        "                    'error': err.round(0)}))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "jNV3QkmMTOj5"
      },
      "source": [
        "We first see that there is a relatively stable trend in the weekly baseline: there are many more riders on weekdays than on weekends and holidays.\n",
        "We see that for each additional hour of daylight, 129 ± 9 more people choose to ride; a temperature increase of one degree Celsius encourages 65 ± 4 people to grab their bicycle; a dry day means an average of 548 ± 33 more riders, and each inch of precipitation means 665 ± 62 more people leave their bike at home.\n",
        "Once all these effects are accounted for, we see a modest increase of 27 ± 18 new daily riders each year.\n",
        "\n",
        "Our model is almost certainly missing some relevant information. For example, nonlinear effects (such as effects of precipitation *and* cold temperature) and nonlinear trends within each variable (such as disinclination to ride at very cold and very hot temperatures) cannot be accounted for in this model.\n",
        "Additionally, we have thrown away some of the finer-grained information (such as the difference between a rainy morning and a rainy afternoon), and we have ignored correlations between days (such as the possible effect of a rainy Tuesday on Wednesday's numbers, or the effect of an unexpected sunny day after a streak of rainy days).\n",
        "These are all potentially interesting effects, and you now have the tools to begin exploring them if you wish!"
      ]
    }
  ],
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      "nbconvert_exporter": "python",
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    "colab": {
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    },
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