09-06-linear-regression.ipynb

{
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  {
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   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "# In Depth: Linear Regression\n",
    "\n",
    "\n",
    "\n",
    "![image.png](./images/author.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Naive Bayes (discussed earlier in **In Depth: Naive Bayes Classification**) is a good starting point for classification tasks.\n",
    "\n",
    "**Linear regression models** are a good starting point for regression tasks.\n",
    "- can be fit very quickly,  \n",
    "- are very interpretable.\n",
    "    \n",
    "The simplest form of a linear regression model (i.e., fitting a straight line to data) \n",
    "- Extended to model more complicated data behavior.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:32:17.018584Z",
     "start_time": "2021-05-21T07:32:15.341430Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:05.272374Z",
     "start_time": "2021-05-21T07:40:05.065155Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate training set\n",
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "# generate test set\n",
    "xtest = np.linspace(0, 10, 1000)\n",
    "ytest = 2*xtest -5\n",
    "# plot training set\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can use Scikit-Learn's ``LinearRegression`` estimator to fit this data and construct the best-fit line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:06.825852Z",
     "start_time": "2021-05-21T07:40:06.607563Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "model = LinearRegression(fit_intercept=True)\n",
    "model.fit(x[:, np.newaxis], y)\n",
    "# predict ypred for the test set.\n",
    "ypred = model.predict(xtest[:, np.newaxis])\n",
    "# plot training set as scatter plot\n",
    "plt.scatter(x, y)\n",
    "# plot the predicted result as a strait line\n",
    "plt.plot(xtest, ypred);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:56:15.572436Z",
     "start_time": "2020-08-12T02:56:15.567831Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model slope:     2.027208810360695\n",
      "Model intercept: -4.998577085553202\n"
     ]
    }
   ],
   "source": [
    "print(\"Model slope:    \", model.coef_[0])\n",
    "print(\"Model intercept:\", model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We see that the results are very close to the inputs, as we might hope."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Model evaluation for regression**\n",
    "\n",
    "- RMSE\n",
    "- R Square\n",
    "\n",
    "https://scikit-learn.org/stable/modules/model_evaluation.html#scoring-parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:52:52.257586Z",
     "start_time": "2020-08-12T02:52:52.254704Z"
    },
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Root mean square error 均方根误差,亦称标准误差\n",
    "# https://en.wikipedia.org/wiki/Root-mean-square_deviation\n",
    "def rmse(y_test, y_pred): \n",
    "    mse = np.mean((y_test - y_pred) ** 2)\n",
    "    rmse = mse ** 0.5 \n",
    "    return rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:55:13.323756Z",
     "start_time": "2020-08-12T02:55:13.320453Z"
    },
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# R square\n",
    "# https://en.wikipedia.org/wiki/Coefficient_of_determination\n",
    "def R2(y_test, y_pred): \n",
    "    residuals_sum_of_squares = np.sum((y_pred - y_test)**2)\n",
    "    total_sum_of_squares = np.sum((y_test - np.mean(y_test))**2)\n",
    "    return 1 - residuals_sum_of_squares/total_sum_of_squares\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:56:23.054793Z",
     "start_time": "2020-08-12T02:56:23.050662Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.1584\n",
      "R2 score: 0.9992\n"
     ]
    }
   ],
   "source": [
    "print('RMSE: %.4f' % rmse(ytest, ypred))\n",
    "print('R2 score: %.4f' % R2(ytest, ypred)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:12.265816Z",
     "start_time": "2021-05-21T07:40:12.263094Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score, explained_variance_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:57:24.326023Z",
     "start_time": "2020-08-12T02:57:24.320219Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.1584\n",
      "R2 score: 0.9992\n",
      "Variance score: 0.9998\n"
     ]
    }
   ],
   "source": [
    "print('RMSE: %.4f' % mean_squared_error(ytest, ypred) ** 0.5)\n",
    "print('R2 score: %.4f' % r2_score(ytest, ypred))\n",
    "print('Variance score: %.4f' % explained_variance_score(ytest, ypred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Building some example data using NumPy**\n",
    "\n",
    "The <font color = 'red'>multidimensional nature of such regressions</font> makes them more difficult to visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:59:38.831449Z",
     "start_time": "2020-08-12T02:59:38.825775Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = 10 * rng.rand(100, 3) #three features\n",
    "y = 0.5 + np.dot(X, [1.5, -2., 1.])\n",
    "# y is constructed from three random X features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "we can use the single ``LinearRegression`` estimator to fit lines, planes, or hyperplanes to our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T02:59:46.439492Z",
     "start_time": "2020-08-12T02:59:46.424332Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5000000000000144\n",
      "[ 1.5 -2.   1. ]\n"
     ]
    }
   ],
   "source": [
    "model.fit(X, y)\n",
    "print(model.intercept_)\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Basis Function Regression 基函数回归\n",
    "\n",
    "One trick you can use to adapt linear regression to nonlinear relationships between variables\n",
    "- to transform the data according to *basis functions*.\n",
    "\n",
    "We have seen one version of this before, in the ``PolynomialRegression`` pipeline used in **Hyperparameters and Model Validation** and **Feature Engineering**.\n",
    "\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 $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "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",
    "\n",
    "Notice that this is *still a linear model*\n",
    "- 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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Polynomial basis functions 多项式基函数\n",
    "\n",
    "> polynomial, Synonym: multinomial, 多项式\n",
    "\n",
    "This polynomial projection is useful enough that it is built into Scikit-Learn, using the ``PolynomialFeatures`` transformer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:17.048470Z",
     "start_time": "2021-05-21T07:40:17.043572Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  4.,  8.],\n",
       "       [ 3.,  9., 27.],\n",
       "       [ 4., 16., 64.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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",
    "- As we saw in **Feature Engineering**, the cleanest way to accomplish this is to use a pipeline.\n",
    "\n",
    "Let's make a 7th-degree polynomial model in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:18.353912Z",
     "start_time": "2021-05-21T07:40:18.350782Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "poly_model = make_pipeline(PolynomialFeatures(7),\n",
    "                           LinearRegression())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With this transform in place, we can use the linear model to fit much more complicated relationships between $x$ and $y$. \n",
    "\n",
    "For example, here is a sine wave with noise:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:40:21.777330Z",
     "start_time": "2021-05-21T07:40:21.560766Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = np.sin(x) + 0.1 * rng.randn(50)\n",
    "xfit = np.linspace(0, 10, 1000)\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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Gaussian basis functions 高斯基函数\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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "<img src = \"img/figures/05.06-gaussian-basis.png\" width = \"400px\">\n",
    "\n",
    "\n",
    "[figure source in Appendix](#Gaussian-Basis)\n",
    "\n",
    "<font size = '4pt'>The shaded regions in the plot are the scaled basis functions, and when added together they reproduce the smooth curve through the data.</font>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "These Gaussian basis functions are not built into Scikit-Learn, \n",
    "- but we can write a custom transformer that will create them\n",
    "- Scikit-Learn transformers are implemented as Python classes; \n",
    "    - reading Scikit-Learn's source is a good way to see how they can be created:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The simplest case of a normal distribution is known as the ''standard normal distribution''.\n",
    "\n",
    "$$\n",
    "f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2} } e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} } \\sim  e^{ -0.5 (\\frac{x-\\mu}{\\sigma})^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:44:11.425428Z",
     "start_time": "2021-05-21T07:44:11.418477Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator, TransformerMixin\n",
    "\n",
    "class GaussianFeatures(BaseEstimator, TransformerMixin):\n",
    "    \"\"\"Uniformly spaced Gaussian features for one-dimensional input\"\"\"\n",
    "    def __init__(self, N, sigma_factor=2.0):\n",
    "        self.N = N\n",
    "        self.sigma_factor = sigma_factor\n",
    "    \n",
    "    @staticmethod\n",
    "    def _gauss_basis(x, mu, sigma, axis=None):\n",
    "        arg = (x - mu) / sigma\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.mu_ = np.linspace(X.min(), X.max(), self.N)\n",
    "        self.sigma_ = self.sigma_factor * (self.mu_[1] - self.mu_[0])\n",
    "        return self\n",
    "        \n",
    "    def transform(self, X):\n",
    "        return self._gauss_basis(X[:, :, np.newaxis], self.mu_,\n",
    "                                 self.sigma_, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:44:13.974864Z",
     "start_time": "2021-05-21T07:44:13.746330Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = np.sin(x) + 0.1 * rng.randn(50)\n",
    "xfit = np.linspace(0, 10, 1000)\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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "There is nothing magic about polynomial basis functions: \n",
    "- You should have some sort of intuition about **the generating process of your data**; \n",
    "- If you think one basis or another might be appropriate, you can use them as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regularization 正则化\n",
    "\n",
    "The introduction of basis functions into our linear regression makes the model much more flexible, \n",
    "- but it also can very quickly lead to over-fitting (refer back to **Hyperparameters and Model Validation** for a discussion of this).\n",
    "\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": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-05-21T07:46:49.061260Z",
     "start_time": "2021-05-21T07:46:48.829505Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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(-5, 1.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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",
    "\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": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T03:15:57.608621Z",
     "start_time": "2020-08-12T03:15:57.251095Z"
    },
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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=(-5, 1.5))\n",
    "    \n",
    "    if title:\n",
    "        ax[0].set_title(title)\n",
    "\n",
    "    ax[1].plot(model.steps[0][1].mu_,\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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This is typical over-fitting behavior when basis functions overlap: \n",
    "- the coefficients of adjacent basis functions blow up and cancel each other out.\n",
    "\n",
    "We know that such behavior is problematic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It would be nice if we could limit such spikes expliticly in the model \n",
    "- by **penalizing large values of the model parameters**.\n",
    "\n",
    "Such a penalty is known as *regularization*, and comes in several forms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ridge regression ($L_2$ Regularization) 岭回归\n",
    "\n",
    "\n",
    "*ridge regression* or $L_2$ *regularization*, sometimes also called *Tikhonov regularization*.\n",
    "- Perhaps the most common form of regularization\n",
    "\n",
    "This proceeds by penalizing the **sum of squares** (2-norms) of the model coefficients; \n",
    "- The penalty on the model fit would be \n",
    "$$\n",
    "P = \\alpha\\sum_{n=1}^N \\theta_n^2\n",
    "$$\n",
    "\n",
    "where $\\alpha$ is a free parameter that controls the strength of the penalty.\n",
    "\n",
    "This type of penalized model is built into Scikit-Learn with the ``Ridge`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:51:22.064426Z",
     "start_time": "2020-05-28T09:51:21.661975Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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; \n",
    "- in the limit $\\alpha \\to \\infty$, all model responses will be suppressed.\n",
    "\n",
    "One advantage of ridge regression in particular is that it can be computed very efficiently\n",
    "- at hardly more computational cost than the original linear regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Lasso regression ($L_1$ regularization) 套索回归\n",
    "\n",
    "Lasso regression 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: \n",
    "- for example, due to geometric reasons lasso regression tends to favor *sparse models* where possible: \n",
    "    - 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": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-12T03:21:31.322971Z",
     "start_time": "2020-08-12T03:21:30.925576Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "model = make_pipeline(GaussianFeatures(30), Lasso(alpha=0.01))\n",
    "basis_plot(model, title='Lasso Regression')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With the lasso regression penalty, **the majority of the coefficients are exactly zero**, \n",
    "- with the functional behavior being modeled by a small subset of the available basis functions.\n",
    "\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** for a discussion of this)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example: Predicting Bicycle Traffic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To predict the number of bicycle trips across Seattle's Fremont Bridge based on weather, season, and other factors.\n",
    "\n",
    "\n",
    "- we will join the bike data with another dataset, and \n",
    "- 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",
    "\n",
    "- the NOAA makes available their daily [weather station data](http://www.ncdc.noaa.gov/cdo-web/search?datasetid=GHCND) (I used station ID USW00024233) \n",
    "- we can easily use Pandas to join the two data sources.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "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",
    "\n",
    "Let's start by loading the two datasets, indexing by date:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:51:22.442283Z",
     "start_time": "2020-05-28T09:51:22.440027Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:35.959546Z",
     "start_time": "2020-05-28T09:52:31.157270Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "counts = pd.read_csv('../data/Fremont_Bridge.csv', index_col='Date', parse_dates=True)\n",
    "weather = pd.read_csv('../data/BicycleWeather.csv', index_col='DATE', parse_dates=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next we will compute the total daily bicycle traffic, and put this in its own dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:39.055553Z",
     "start_time": "2020-05-28T09:52:39.034915Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "daily = counts.resample('d').sum()\n",
    "daily['Total'] = daily.sum(axis=1)\n",
    "daily = daily[['Total']] # remove other columns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 100,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:40.132371Z",
     "start_time": "2020-05-28T09:52:40.122377Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "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)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 101,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:41.139824Z",
     "start_time": "2020-05-28T09:52:41.097242Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 102,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:26.441097Z",
     "start_time": "2020-05-28T09:53:25.954629Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 17)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from datetime import datetime\n",
    "def hours_of_daylight(date, axis=23.44, latitude=47.61):\n",
    "    \"\"\"Compute the hours of daylight for the given date\"\"\"\n",
    "    days = (date - 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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 103,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:30.749580Z",
     "start_time": "2020-05-28T09:53:30.738215Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 104,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:31.910236Z",
     "start_time": "2020-05-28T09:53:31.904789Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "daily['annual'] = (daily.index - daily.index[0]).days / 365."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now our data is in order, and we can take a look at it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:32.995247Z",
     "start_time": "2020-05-28T09:53:32.977299Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Total</th>\n",
       "      <th>Mon</th>\n",
       "      <th>Tue</th>\n",
       "      <th>Wed</th>\n",
       "      <th>Thu</th>\n",
       "      <th>Fri</th>\n",
       "      <th>Sat</th>\n",
       "      <th>Sun</th>\n",
       "      <th>holiday</th>\n",
       "      <th>daylight_hrs</th>\n",
       "      <th>PRCP</th>\n",
       "      <th>Temp (C)</th>\n",
       "      <th>dry day</th>\n",
       "      <th>annual</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-10-03</th>\n",
       "      <td>3521.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.277359</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.35</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-04</th>\n",
       "      <td>3475.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.219142</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.60</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-05</th>\n",
       "      <td>3148.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.161038</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.30</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-06</th>\n",
       "      <td>2006.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.103056</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.85</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.008219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-07</th>\n",
       "      <td>2142.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.045208</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.85</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.010959</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Total  Mon  Tue  Wed  Thu  Fri  Sat  Sun  holiday  daylight_hrs  \\\n",
       "Date                                                                           \n",
       "2012-10-03  3521.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0      0.0     11.277359   \n",
       "2012-10-04  3475.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0      0.0     11.219142   \n",
       "2012-10-05  3148.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0      0.0     11.161038   \n",
       "2012-10-06  2006.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0      0.0     11.103056   \n",
       "2012-10-07  2142.0  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  "
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 106,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:34.084872Z",
     "start_time": "2020-05-28T09:53:34.073512Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, we can compare the total and predicted bicycle traffic visually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:36.008945Z",
     "start_time": "2020-05-28T09:53:35.520348Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "daily[['Total', 'predicted']].plot(alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It is evident that we have missed some key features, especially during the summer time.\n",
    "\n",
    "- Either our features are not complete\n",
    "    - i.e., people decide whether to ride to work based on more than just these\n",
    "- or there are some nonlinear relationships that we have failed to take into account \n",
    "    - e.g., perhaps people ride less at both high and low temperatures\n",
    "\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": 108,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:37.022122Z",
     "start_time": "2020-05-28T09:53:37.016768Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Mon              504.882756\n",
       "Tue              610.233936\n",
       "Wed              592.673642\n",
       "Thu              482.358115\n",
       "Fri              177.980345\n",
       "Sat            -1103.301710\n",
       "Sun            -1133.567246\n",
       "holiday        -1187.401381\n",
       "daylight_hrs     128.851511\n",
       "PRCP            -664.834882\n",
       "dry day          547.698592\n",
       "Temp (C)          65.162791\n",
       "annual            26.942713\n",
       "dtype: float64"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = pd.Series(model.coef_, index=X.columns)\n",
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:39.894650Z",
     "start_time": "2020-05-28T09:53:38.322073Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With these errors estimated, let's again look at the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:41.278481Z",
     "start_time": "2020-05-28T09:53:41.272296Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              effect  error\n",
      "Mon            505.0   86.0\n",
      "Tue            610.0   83.0\n",
      "Wed            593.0   83.0\n",
      "Thu            482.0   85.0\n",
      "Fri            178.0   81.0\n",
      "Sat          -1103.0   80.0\n",
      "Sun          -1134.0   83.0\n",
      "holiday      -1187.0  163.0\n",
      "daylight_hrs   129.0    9.0\n",
      "PRCP          -665.0   62.0\n",
      "dry day        548.0   33.0\n",
      "Temp (C)        65.0    4.0\n",
      "annual          27.0   18.0\n"
     ]
    }
   ],
   "source": [
    "print(pd.DataFrame({'effect': params.round(0),\n",
    "                    'error': err.round(0)}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We first see that there is a relatively stable trend in the weekly baseline: \n",
    "    - 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; \n",
    "- a temperature increase of one degree Celsius encourages 65 ± 4 people to grab their bicycle; \n",
    "- 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",
    "\n",
    "Once all these effects are accounted for, we see a modest increase of 27 ± 18 new daily riders each year.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Our model is almost certainly missing some relevant information. \n",
    "    - For example, nonlinear effects \n",
    "        - such as effects of precipitation *and* cold temperature \n",
    "    - nonlinear trends within each variable \n",
    "        - such as disinclination to ride at very cold and very hot temperatures\n",
    "- Additionally, we have thrown away some of the finer-grained information\n",
    "    - such as the difference between a rainy morning and a rainy afternoon, \n",
    "- and we have ignored correlations between days\n",
    "    - such as the possible effect of a rainy Tuesday on Wednesday's numbers, \n",
    "    - or the effect of an unexpected sunny day after a streak of rainy days.\n",
    "    \n",
    "These are all potentially interesting effects, and you now have the tools to begin exploring them if you wish!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](./images/end.png)\n"
   ]
  }
 ],
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