04- Support Vector Machines.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support Vector Machines\n",
    "- A Support Vector Machine (SVM) is a powerful and versatile Machine Learning model, **capable of performing linear or nonlinear classification, regression, and even outlier detection.**\n",
    "- It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. \n",
    "- **SVMs are particularly well suited for classification of complex small- or medium-sized datasets.**\n",
    "### TIP\n",
    "- If your SVM model is overfitting, you can try regularizing it by reducing C.\n",
    "#### The following Scikit-Learn code loads the iris dataset, scales the features, and then trains a linear SVM model (using the LinearSVC class with C=1 and the hinge loss function, described shortly) to detect Iris virginica flowers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('linear_svc', LinearSVC(C=1, loss='hinge'))])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.float64) # Iris virginica\n",
    "\n",
    "svm_clf = Pipeline([\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"linear_svc\", LinearSVC(C=1, loss=\"hinge\")),\n",
    "    ])\n",
    "\n",
    "svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf.predict([[5.5, 1.7]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Instead of using the LinearSVC class, we could use the SVC class with a linear kernel. \n",
    "- When creating the SVC model, we would write SVC(kernel=\"linear\", C=1). Or we could use the SGDClassifier class, with SGDClassifier(loss=\"hinge\", alpha=1/(m*C)). \n",
    "    - This applies regular Stochastic Gradient Descent to train a linear SVM classifier. \n",
    "    - It does not converge as fast as the LinearSVC class, but it can be useful to handle online classification tasks or huge datasets that do not fit in memory (out-of-core training).\n",
    "### TIP\n",
    "- The LinearSVC class regularizes the bias term, so **you should center the training set first by subtracting its mean. **\n",
    "    - **This is automatic if you scale the data using the StandardScaler.**\n",
    "    - Also make sure you **set the loss hyperparameter to \"hinge\"**, as it is not the default value. \n",
    "    - Finally, for better performance, you should set the dual hyperparameter to False, unless there are more features than training instances (we will discuss duality later in the chapter)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear SVM Classification\n",
    "- Although linear SVM classifiers are efficient and work surprisingly well in many cases, many datasets are not even close to being linearly separable. \n",
    "- One approach to handling nonlinear datasets is to add more features, such as polynomial features; in some cases this can result in a linearly separable dataset.\n",
    "    - To implement this idea using Scikit-Learn, create a Pipeline containing a PolynomialFeatures transformer, followed by a StandardScaler and a LinearSVC. \n",
    "    - Let’s test this on the moons dataset: this is a toy dataset for binary classification in which the data points are shaped as two interleaving half circles. You can generate this dataset using the make_moons() function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
    "\n",
    "def plot_dataset(X, y, axes):\n",
    "    plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
    "    plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
    "    plt.axis(axes)\n",
    "    plt.grid(True, which='both')\n",
    "    plt.xlabel(r\"$x_1$\", fontsize=20)\n",
    "    plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n",
    "\n",
    "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_predictions(clf, axes):\n",
    "    x0s = np.linspace(axes[0], axes[1], 100)\n",
    "    x1s = np.linspace(axes[2], axes[3], 100)\n",
    "    x0, x1 = np.meshgrid(x0s, x1s)\n",
    "    X = np.c_[x0.ravel(), x1.ravel()]\n",
    "    y_pred = clf.predict(X).reshape(x0.shape)\n",
    "    y_decision = clf.decision_function(X).reshape(x0.shape)\n",
    "    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n",
    "    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\batuh\\Anaconda3\\lib\\site-packages\\sklearn\\svm\\_base.py:977: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('poly_features', PolynomialFeatures(degree=3)),\n",
       "                ('scaler', StandardScaler()),\n",
       "                ('svm_clf', LinearSVC(C=10, loss='hinge', random_state=42))])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "polynomial_svm_clf = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=3)),\n",
    "        (\"scaler\", StandardScaler()),\n",
    "        (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\", random_state=42))\n",
    "    ])\n",
    "\n",
    "polynomial_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_predictions(clf, axes):\n",
    "    x0s = np.linspace(axes[0], axes[1], 100)\n",
    "    x1s = np.linspace(axes[2], axes[3], 100)\n",
    "    x0, x1 = np.meshgrid(x0s, x1s)\n",
    "    X = np.c_[x0.ravel(), x1.ravel()]\n",
    "    y_pred = clf.predict(X).reshape(x0.shape)\n",
    "    y_decision = clf.decision_function(X).reshape(x0.shape)\n",
    "    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n",
    "    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)\n",
    "\n",
    "plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial Kernel\n",
    "- Adding polynomial features is simple to implement and can work great with all sorts of Machine Learning algorithms (not just SVMs). \n",
    "- That said, at a low polynomial degree, this method cannot deal with very complex datasets, and with a high polynomial degree it creates a huge number of features, making the model too slow.\n",
    "- Fortunately, when using SVMs you can apply an almost miraculous mathematical technique called the kernel trick.\n",
    "    - The kernel trick makes it possible to get the same result as if you had added many polynomial features, even with very high-degree polynomials, without actually having to add them. \n",
    "    - So there is no combinatorial explosion of the number of features because you don’t actually add any features. \n",
    "    - This trick is implemented by the SVC class. Let’s test it on the moons dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('svm_clf', SVC(C=5, coef0=1, kernel='poly'))])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "poly_kernel_svm_clf = Pipeline([\n",
    "        (\"scaler\", StandardScaler()),\n",
    "        (\"svm_clf\", SVC(kernel=\"poly\", degree=3, coef0=1, C=5))\n",
    "    ])\n",
    "poly_kernel_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('svm_clf', SVC(C=5, coef0=100, degree=10, kernel='poly'))])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly100_kernel_svm_clf = Pipeline([\n",
    "        (\"scaler\", StandardScaler()),\n",
    "        (\"svm_clf\", SVC(kernel=\"poly\", degree=10, coef0=100, C=5))\n",
    "    ])\n",
    "poly100_kernel_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 756x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=2, figsize=(10.5, 4), sharey=True)\n",
    "\n",
    "plt.sca(axes[0])\n",
    "plot_predictions(poly_kernel_svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.4, -1, 1.5])\n",
    "plt.title(r\"$d=3, r=1, C=5$\", fontsize=18)\n",
    "\n",
    "plt.sca(axes[1])\n",
    "plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.4, -1, 1.5])\n",
    "plt.title(r\"$d=10, r=100, C=5$\", fontsize=18)\n",
    "plt.ylabel(\"\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This code trains an SVM classifier using a third-degree polynomial kernel. It is represented on the left. \n",
    "- On the right is another SVM classifier using a 10th-degree polynomial kernel. \n",
    "- **Obviously, if your model is overfitting, you might want to reduce the polynomial degree.**\n",
    "- **Conversely, if it is underfitting, you can try increasing it.**\n",
    "- The hyperparameter coef0 controls how much the model is influenced by high-degree polynomials versus low-degree polynomials.\n",
    "### TIP\n",
    "- A common approach to finding the right hyperparameter values is to use grid search.\n",
    "- It is often faster to first do a very coarse grid search, then a finer grid search around the best values found. \n",
    "- Having a good sense of what each hyperparameter actually does can also help you search in the right part of the hyperparameter space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Similarity Features\n",
    "- Another technique to tackle nonlinear problems is to add features computed using a similarity function, which measures how much each instance resembles a particular landmark.\n",
    "- The simplest approach is to create a landmark at the location of each and every instance in the dataset. \n",
    "    - Doing that creates many dimensions and thus increases the chances that the transformed training set will be linearly separable. \n",
    "    - The downside is that a training set with m instances and n features gets transformed into a training set with m instances and m features (assuming you drop the original features). \n",
    "    - If your training set is very large, you end up with an equally large number of features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian RBF Kernel\n",
    "- Just like the polynomial features method, the similarity features method can be useful with any Machine Learning algorithm, but it may be computationally expensive to compute all the additional features, especially on large training sets. \n",
    "- Once again the kernel trick does its SVM magic, making it possible to obtain a similar result as if you had added many similarity features. Let’s try the SVC class with the Gaussian RBF kernel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('svm_clf', SVC(C=0.001, gamma=5))])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rbf_kernel_svm_clf = Pipeline([\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"svm_clf\", SVC(kernel=\"rbf\", gamma=5, C=0.001))\n",
    "])\n",
    "rbf_kernel_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 756x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "gamma1, gamma2 = 0.1, 5\n",
    "C1, C2 = 0.001, 1000\n",
    "hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n",
    "\n",
    "svm_clfs = []\n",
    "for gamma, C in hyperparams:\n",
    "    rbf_kernel_svm_clf = Pipeline([\n",
    "            (\"scaler\", StandardScaler()),\n",
    "            (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n",
    "        ])\n",
    "    rbf_kernel_svm_clf.fit(X, y)\n",
    "    svm_clfs.append(rbf_kernel_svm_clf)\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10.5, 7), sharex=True, sharey=True)\n",
    "\n",
    "for i, svm_clf in enumerate(svm_clfs):\n",
    "    plt.sca(axes[i // 2, i % 2])\n",
    "    plot_predictions(svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "    plot_dataset(X, y, [-1.5, 2.45, -1, 1.5])\n",
    "    gamma, C = hyperparams[i]\n",
    "    plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)\n",
    "    if i in (0, 1):\n",
    "        plt.xlabel(\"\")\n",
    "    if i in (1, 3):\n",
    "        plt.ylabel(\"\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Increasing gamma(γ) makes the bell-shaped curve narrower. \n",
    "- As a result, each instance’s range of influence is smaller: the decision boundary ends up being more irregular, wiggling around individual instances. \n",
    "- Conversely, a small gamma value makes the bell-shaped curve wider: instances have a larger range of influence, and the decision boundary ends up smoother. \n",
    "- So γ acts like a regularization hyperparameter: if your model is overfitting, you should reduce it; if it is underfitting, you should increase it (similar to the C hyperparameter)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TIP\n",
    "- With so many kernels to choose from, how can you decide which one to use? \n",
    "- As a rule of thumb, **you should always try the linear kernel first (remember that LinearSVC is much faster** than SVC(kernel=\"linear\")), especially if the training set is very large or if it has plenty of features. \n",
    "- If the training set is not too large, you should also try the Gaussian RBF kernel; it works well in most cases. \n",
    "- Then if you have spare time and computing power, you can experiment with a few other kernels, using cross-validation and grid search. \n",
    "- You’d want to experiment like that especially if there are kernels specialized for your training set’s data structure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational Complexity\n",
    "- The **LinearSVC** class is based on the liblinear library, which implements an optimized algorithm for linear SVMs. \n",
    "    - It does not support the kernel trick, but it scales almost linearly with the number of training instances and the number of features. \n",
    "    - Its training time complexity is roughly O(m × n).\n",
    "    - The algorithm takes longer if you require very high precision. \n",
    "    - This is controlled by the tolerance hyperparameter ϵ (called tol in Scikit-Learn). \n",
    "    - In most classification tasks, the default tolerance is fine.\n",
    "- The **SVC** class is based on the libsvm library, which implements an algorithm that supports the kernel trick. \n",
    "    - The training time complexity is usually between O(m² × n) and O(m³ × n).\n",
    "    - Unfortunately, this means that it gets dreadfully slow when the number of training instances gets large (e.g., hundreds of thousands of instances). \n",
    "    - **This algorithm is perfect for complex small or medium-sized training sets.** \n",
    "    - It scales well with the number of features, especially with sparse features (i.e., when each instance has few nonzero features). \n",
    "    - In this case, the algorithm scales roughly with the average number of nonzero features per instance. \n",
    "    - Table 5-1 compares Scikit-Learn’s SVM classification classes.\n",
    "<img src=\"svm.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SVM Regression\n",
    "- As mentioned earlier, the SVM algorithm is versatile: not only does it support linear and nonlinear classification, but it also supports linear and nonlinear regression. \n",
    "- To use SVMs for regression instead of classification, the trick is to reverse the objective: instead of trying to fit the largest possible street between two classes while limiting margin violations, SVM Regression tries to fit as many instances as possible on the street while limiting margin violations (i.e., instances off the street). The width of the street is controlled by a hyperparameter, ϵ.\n",
    "\n",
    "#### Linear SVR Model example ; "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 50\n",
    "X = 2 * np.random.rand(m, 1)\n",
    "y = (4 + 3 * X + np.random.randn(m, 1)).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVR(epsilon=1.5, random_state=42)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import LinearSVR\n",
    "\n",
    "svm_reg = LinearSVR(epsilon=1.5, random_state=42)\n",
    "svm_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)\n",
    "svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)\n",
    "svm_reg1.fit(X, y)\n",
    "svm_reg2.fit(X, y)\n",
    "\n",
    "def find_support_vectors(svm_reg, X, y):\n",
    "    y_pred = svm_reg.predict(X)\n",
    "    off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)\n",
    "    return np.argwhere(off_margin)\n",
    "\n",
    "svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)\n",
    "svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)\n",
    "\n",
    "eps_x1 = 1\n",
    "eps_y_pred = svm_reg1.predict([[eps_x1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_svm_regression(svm_reg, X, y, axes):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n",
    "    y_pred = svm_reg.predict(x1s)\n",
    "    plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "    plt.plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n",
    "    plt.plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n",
    "    plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')\n",
    "    plt.plot(X, y, \"bo\")\n",
    "    plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "    plt.legend(loc=\"upper left\", fontsize=18)\n",
    "    plt.axis(axes)\n",
    "\n",
    "fig, axes = plt.subplots(ncols=2, figsize=(9, 4), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])\n",
    "plt.title(r\"$\\epsilon = {}$\".format(svm_reg1.epsilon), fontsize=18)\n",
    "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n",
    "#plt.plot([eps_x1, eps_x1], [eps_y_pred, eps_y_pred - svm_reg1.epsilon], \"k-\", linewidth=2)\n",
    "plt.annotate(\n",
    "        '', xy=(eps_x1, eps_y_pred), xycoords='data',\n",
    "        xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),\n",
    "        textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n",
    "    )\n",
    "plt.text(0.91, 5.6, r\"$\\epsilon$\", fontsize=20)\n",
    "plt.sca(axes[1])\n",
    "plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])\n",
    "plt.title(r\"$\\epsilon = {}$\".format(svm_reg2.epsilon), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding more training instances within the margin does not affect the model’s predictions;\n",
    "thus, the model is said to be ϵ-insensitive.\n",
    "#### Nonlinear SVR model example;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 2 * np.random.rand(m, 1) - 1\n",
    "y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=100, degree=2, kernel='poly')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVR\n",
    "\n",
    "svm_poly_reg = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1, gamma=\"scale\")\n",
    "svm_poly_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=0.01, degree=2, kernel='poly')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_poly_reg1 = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1, gamma=\"scale\")\n",
    "svm_poly_reg2 = SVR(kernel=\"poly\", degree=2, C=0.01, epsilon=0.1, gamma=\"scale\")\n",
    "svm_poly_reg1.fit(X, y)\n",
    "svm_poly_reg2.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=2, figsize=(9, 4), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])\n",
    "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg1.degree, svm_poly_reg1.C, svm_poly_reg1.epsilon), fontsize=18)\n",
    "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n",
    "plt.sca(axes[1])\n",
    "plot_svm_regression(svm_poly_reg2, X, y, [-1, 1, 0, 1])\n",
    "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg2.degree, svm_poly_reg2.C, svm_poly_reg2.epsilon), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- To tackle nonlinear regression tasks, you can use a kernelized SVM model. \n",
    "- Plots above shows SVM Regression on a random quadratic training set, using a second-degree polynomial kernel. \n",
    "- There is **little regularization in the left plot (i.e., a large C value)**, and **much more regularization in the right plot (i.e., a small C value)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The SVR class is the regression equivalent of the SVC class, and the LinearSVR class is the regression equivalent of the LinearSVC class. \n",
    "- The LinearSVR class scales linearly with the size of the training set (just like the LinearSVC class), while the SVR class gets much too slow when the training set grows large (just like the SVC class).\n",
    "### NOTE\n",
    "- SVMs can also be used for outlier detection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise solutions\n",
    "### Exercise 8\n",
    "#### Train a LinearSVC on a linearly separable dataset. Then train an SVC and a SGDClassifier on the same dataset. See if you can get them to produce roughly the same model.\n",
    "Let's use the Iris dataset: the Iris Setosa and Iris Versicolor classes are linearly separable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "setosa_or_versicolor = (y == 0) | (y == 1)\n",
    "X = X[setosa_or_versicolor]\n",
    "y = y[setosa_or_versicolor]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearSVC:                    [0.28475098] [[1.05364854 1.09903804]]\n",
      "SVC:                          [0.31896852] [[1.1203284  1.02625193]]\n",
      "SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC, LinearSVC\n",
    "from sklearn.linear_model import SGDClassifier\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "C = 5\n",
    "alpha = 1 / (C * len(X))\n",
    "\n",
    "lin_clf = LinearSVC(loss=\"hinge\", C=C, random_state=42)\n",
    "svm_clf = SVC(kernel=\"linear\", C=C)\n",
    "sgd_clf = SGDClassifier(loss=\"hinge\", learning_rate=\"constant\", eta0=0.001, alpha=alpha, \n",
    "                       max_iter=1000, tol=1e-3, random_state=42)\n",
    "scaler=StandardScaler()\n",
    "X_scaled = scaler.fit_transform(X)\n",
    "\n",
    "lin_clf.fit(X_scaled, y)\n",
    "svm_clf.fit(X_scaled, y)\n",
    "sgd_clf.fit(X_scaled, y)\n",
    "\n",
    "print(\"LinearSVC:                   \", lin_clf.intercept_, lin_clf.coef_)\n",
    "print(\"SVC:                         \", svm_clf.intercept_, svm_clf.coef_)\n",
    "print(\"SGDClassifier(alpha={:.5f}):\".format(sgd_clf.alpha), sgd_clf.intercept_, sgd_clf.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's plot the decision boundaries of these three models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0536485406769318"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-lin_clf.coef_[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H1K5dMloqhBBCCJtIMOpEihQpwhtvvEFhy46kf/75h4iIiIRgde3atWzdujXd93F1hf37zUb6Tp1McLpwITz+uBk93bEjjQa8vEzi0127TFTbp48pN9qgAdSubZKhRkamu59CCCGEyP5kmj4LadiwIUDChqfLly9TpEiRdLd75oyZfZ85Ey5dgqNHTUl7gKgoE3umKTLSRLRTp5pEqF5eZrh1yBB47LF091EIIYQQWZdTTNMrpWYppSKUUgdTON9UKXVDKbXP8vpvknNtlFJHlFLHlVIjM6rPzmb9+vXMnTsXgOjoaCpWrMh7772X7nbLlDHVnM6dg3XrEgNRrU0+06eegiVL4N69VBrJm9cEnr//bkZMu3c3a0vr1DH5pb77zkS2QgghsgRnKT2ZXB/iX+nps6Oez9U1+XZdXdPXbnaWkdP0s4E2aVyzTWv9qOX1AYBSyhWYDLQFqgI9lVJVHdpTJ+Xl5UUFS6QYExPD6NGjadPG/EjDw8Pp3LkzBw4ceOj2PTxMFqd4p0+bNFEbN0K3blC2rKkcGh6eSiNKmeBz1ixz4ddfw61bMHAg+PrCyy9DOvoohBAiY2TF0pO29NlRz5dSWm5J152yDAtGtdZbgdQKVaakHnBca31Sa30XWAR0tmvnsiAvLy9GjBhB48aNATh27BghISF4eHgAcPToUbZt25au5PqPPJIYT1aubN6//76pKPrss3D+fBoNFCgAw4eb4HPbNujY0awFqFnTLFCdNy+NbPxCCCGEyO6cbQNTQ6XUfqXUaqVUNcsxP+BckmtCLceSpZQarJQKUUqFXLp0yZF9dSpNmjTh3LlzCZWevv76a1q3bs3NmzcBuHPnzkO1mz+/iScPHUocIQXzPmk2p1Sn8JUywef8+abK02efQUSE2fhUsiS88QYcOfJQ/RNCCCFE1uZMwejvQBmtdS3gG+Bny/FkVoWQ4nCf1nq61jpAax1QtGhRB3TTebm4JP5xfvLJJ6xdu5a8efMC0KVLl3TlLlUKmjWDH380G54WLYLcuc25yEgzWhoYaHbpp6pIEVMe6siRxOpO33xjhl6bNTPlSO/efeh+CiGEECJrcZpgVGv9j9b6puX9KsBdKVUEMxJaKsmlJYHUVi0KwNvbmyeeeCLhc+vWrWnevDlgKj0FBgayZcuWh2rbzw9atkz8vH49XLhgduQ/+qgZBF24EKKjU2lEKWje3ASfoaHw8cdmkWqPHibx6ciRcPLkQ/VPCCGEEFmH0wSjSqniylKwXSlVD9O3K8AeoIJS6hGlVC6gB7A883qaNb3++usMGTIEgLCwMJYvX85JS7B369YtgoODH3p9adeuZhp/+HDIl88kz+/Vy4yWjh4NMTFpNODjY4LPEydM8tNGjcxUfrly0Lo1/PRTGusAhBBC2FtWLD1pS58d9XwuKURWKR0XGZhnVCn1PdAUKAJcBMYA7gBa66lKqZeBl4AY4DbwhtZ6h+W77YAvAVdgltZ6nDX3zG55Ru0pNjaW2NhYcuXKxcKFC+nVqxfbtm3j8ccfJy4u7r4pf1vcvAkLFsCUKfDnnyauDA5OPK918uk4/iW+ytOMGWbktEQJsyN/4EAT5QohhBAiy0gtz6gkvRfcvHmTX375he7du+Pi4sJHH33E6tWr2bhxY8LufFtpbSo5aW2m7cEEp888Ay+9BP36gaWwVOpiYmD1apNMf/VqE8m2a2dymrZtK4nbhBBCiCzAKZLeC+fl7e1Njx49EkZDS5YsSbVq1RIC0cmTJ7Nq1Sqb2lTKJMyPD0TBjJgeP272L/n5mYqiaf6u4OZmUkKtXAmnTsGoUeZLHTuCvz989FEaiU+FEEII4cxkZFSkKi4ujipVqvD444/z3XffAXDgwAGqV6+Osmq+PVFsLKxaZabw16xJPF63rsnu1KOHlQ3duwfLl5sdU+vWmdHRzp3NaGmLFrIwRwghhHAyMjIqHpqLiwt//fUXn332GQCnT5+mZs2afP311za35epqBjRXrzaVnUaMMLlK9+wBmzb2u7ub+f5ff01saOtWs9mpQgX49FOTx1QIIbIoZynF6SiOKplpy8/Nlj5k9z+PzCbBqEiTm5sbBS0Z7osWLUpQUBBPP/00AJs3b6ZRo0YcP37cpjbLlzcb5sPCICgIXn018dz8+WY56IoVZjQ1zYY+/dRsclq4MDEtVMmSZqh182azcFUIIbKQrFiK0xaOKplpy8/Nlj5k9z+PzCbBqLCJl5cX/fr1o1Qpk/r19u3bxMXF4evrC8CGDRv4+eefibPybxRPT7OZqXLlxGMzZ5pp/E6dzLLQjz+2YqDTwwN69jTB56FDMGwYrF1rEulXqQJffAFXH6YarRBCCCEcSdaMCrvq2rUrhw4d4u+//0YpRVhYGL6+vjatL71yBWbPhm+/NalHwczMP/usWVtap46VDd2+bUpGTZ0KO3eagLV7d7O2tFEjK3NMCSFExkvtr6fs8L9tRz2fLe066lqRPFkzKjLMjz/+yOrVq1FKERcXR6NGjXjxxRdtaqNwYbMM9OjRxBHS2FgzC2/T7xaentCnj8kxtX8/vPgi/Pyz2eJfsyZMmgQ3btj2gEIIIYSwKwlGhV25ubnh7+8PmMT6Y8eOpVevXgD8888/PPXUU2zfvt2qtlxczJ6kZctMZdD//MdUdoo3diy88gocPmxFYzVrwuTJJg3UjBlmlHT4cPD1NYn09+yRX2+FEEKITCDBqHAYd3d3+vXrx1NPPQXAmTNnOH/+PG5uboDZmb9s2TLu3r2bZltlysCHH4K3t/kcHQ1ffQXffANVq5oy94sXW1E11NvbBJ8hISYAff55+P57qFcPAgJg+nRTRkoIITJRVizFaQtHlcy05edmSx+y+59HZpM1oyJDxf/7ppTigw8+YOzYsYSGhlKiRAkiIyPx9va2en3p/v1mXen8+RAVZY75+sLgwRAYaMNfEjdumIz8U6fCgQOQN68Zgg0MhFq1HuIphRBCCJGUlAMVTunevXvs3buXBg0aAPD8889z+vRpgoODbdrwdOMGzJ1rkun//bc5tmMHNGxoY4e0ht9+M8n0//c/uHMH6tc3QWn37pAnj40NCiGEEALsFIwqpfIAjwLFeGB6X2u9NL2ddAQJRrOWBQsWcPXqVYYPHw7A0KFDadWqFV26dLHq+1qbzE4rV8KECYm7H196yUzl9+kD+fNb2ZmrV2HePDNa+vffUKCAaWDIENOYEEIIIayW7mBUKdUC+B4onMxprbVOZ80Ex5BgNOuKjIykXr16DBw4kBEjRhATE8PatWtp1aoV7u7uVrdz9ChUqmTee3lB794mOLV69l1r2LbNBKVLlsDdu/DEEyYofeYZyJ3b9ocTQjit4sWTT2Tu4wMXLmR8f6xhS9ohV9fkk7q7uPy7yIijrgXbfs6OulZkLHsEo38Be4B3tdbhdu6fw0gwmrVprYmJicHd3Z21a9fSpk0bfvrpJ7p06UJMTAyurq5pTuffu2d240+ZAps2JR5v3BiGDoVu3SBXLis7dOmSSYA6bZpJgFq4MPTvbxapVqjw0M8phHAeWTGfpDPk1rT15+Ys/RAZxx7BaBRQU2t9wt6dcyQJRrOPe/fusXbtWlq2bImHhwdTpkzhq6++YseOHRQunNyA/b8dOmQGOOfMgX/+MYOaoaEmprRJXBxs3GgaW7YMYmLgqafMaGnnzjZEt0IIZ5MVgxlnCOwkGBVpsUfS+2Cgkv26JIRt3N3d6dChAx4eHgCULl2axo0bJwSi06ZNY86cOam2UbUqfP01hIWZwc13300MRO/dg759TQXRNCuZurhAixYml9TZs/DRR3D8uNnkVLq0afjUqfQ+shBCCJEjpDgyqpR6LMnHssBHwETgAHBfNket9e8O6l+6yMhoztGsWTPy58/Pzz//DEBISAi1atWyen3p4sWm3ChA+fJmXWm/flCokJUdiI01key0afDLL+ZX8NatzU789u3BkltVCOHcsuLImjOMMsrIqEjLQ03TK6XiAA2klWNHNjCJTKe1JjIyknz58nHlyhVKlCjBm2++yfjx4xPOp7a+NCICvvvOzLyfPWuO5c4NPXuataUByf7nk4Jz50xjM2aYik9+fibR/sCBULJkOp5SCOFoWTGYcYbAToJRkZaHnaZ/BPC3/DO1l7+VnZillIpQSh1M4XwvpdSfltcOpVStJOdOK6UOKKX2KaUkuhT/opQiX758AOTLl4/FixfTv39/APbv30/VqlXZu3dvit8vVgxGjTJlR5cvhzZtTJrRoCBTpMmmv8RKlYL334czZ+Dnn6FGDfjgA1NGqnNnWLUq+e2lQohMl90r7dhSdchR14JtP2dHXSucR4pzh1rrM/HvlVJPAju01jFJr1FKuQGNgDOkbTYwCZibwvlTQBOt9TWlVFtgOlA/yflmWuvLVtxH5HDu7u506tQp4fPt27cpXrw4ZcqUAWD79u0cPXqU3r17k+uBzUaurtCxo3kdP25m3StVSvxt+9w5U4Y0MNBM56fKzc0En507mzWkM2aYEdPly01gOngwDBhgcpEIIZxCVkz/Y8svy7b8Huyoa8G2n7OjrhXOw9rd9LFACa11xAPHCwMR1k7TK6XKAr9orauncV1B4KDW2s/y+TQQYGswKtP0IjnDhg1jyZIlhIaG4ubmxunTp/Hz87Nqfel775n9SmCWhA4bBu3amSDWKnfvmh34U6eaHflubtCli9mJ37x5+gszCyGEEE7IHrvpFWb96IMKA1EP27FUvAisTvJZA78qpfYqpQan9kWl1GClVIhSKuTSpUsO6JrI6iZNmkRISAhulk1FXbp0uW8kNTVPP21Si+bObfYrdeoE/v7w8cdm3WmacuUyO6U2bIAjR+DVV00C1JYtzRDshAkmn6kQQgiRQ6Q6MqqUWm552x5YD0QnOe0KVAcOa63bWHUzK0ZGlVLNgCnA41rrK5ZjvlrrcKVUMWAdMFxrvTWt+8nIqEiL1poVK1bg7u5O27ZtuXv3Ls2bN+ftt99ONUC9csXkv//2W5P/HkyM+cMPD9GJO3dMdadp00y1p1y5THWnwEBT7SmNxP5CCCGEs0vPyOgVy0sB15J8vgKEAlOB3nbsaE1gJtA5PhAFiK/6ZFkm8BNQz173FDmbUopOnTrRtm1bAC5cuIBSKmHU9OLFiwQFBXHz5s37vle4MIwYYcqNrlljRkhfeinxfHAwTJ8OD3wteblzQ69esHUrHDxogtBVq6BJE6hWzSxSvXbNXo8shMgCihc3v4c++Epuibkt1zqqD87UdlbqgzCsXTM6BvhMa52uKfnURkaVUqWBjUAfrfWOJMe9ABetdaTl/TrgA631mrTuJyOjIr2mTZtGYGAghw8fpnLlyty4cQMvL6+EYDUlnTrBihWQL59Jpv/SS1Clig03vnXLDLNOnQq7dpmA9bnnTKBav76MlgqRzTlDOiNHpklyhhRMztCHnCTd5UDt1InvgaZAEeAiMAZwB9BaT1VKzQSeIXFnfozWOkAp5Y8ZDQWz+3+h1nqcNfeUYFSkl9aa/fv38+ijjwLw8ssvs3LlSo4dO5ZqQLpoEUyaZEZI4zVrZnKWdu4MVubiN/btM1P48+ebodaaNU1Q2quXiXaFENmOBKOO5wx9yEkeNun9KZLftPQvWmurco1mNAlGhb2tWbOGw4cP8/rrrwPwyiuvULNmTQYOHJjs9fv3m3Wl8+dDlGVe4dNP4e23H+LmkZHw/fdmtPSPP8DLyyRBHTIE6tR5yCcSQjgjCUYdzxn6kJM87JrRScBky2sOZuf8CWC+5XXCcmy2PTsrhDNr06ZNQiAaExPD/v37OWWpQ6+15ocffiAyMjLh+lq1TOwYFgZff20GNfv0SWxv2TKzmd6qv/jy5jW5Sffuhd27zbT9/PmmPFTduiaHaZQjklsIIYQQjmPtmtHZwFGt9fgHjo8Cqmmt7baJyZ5kZFRkhLi4OFxcXNi7dy8BAQHMmDGDgQMHcu/evfs2Qz0oNtYkzj992qwnHToUXngB8ue34ebXr5uAdOpU+OsvM23/wgtmtLRGDbs8nxAi48nIqOM5Qx9yEnvkGX0aSC5pzY+AdQkahcimXCyJ6h977DGCg4Pp3r07AEuWLDnfgPkAACAASURBVKFUqVKciM/99IC7d6FfPyhRAg4fhuHDTRn7wED4808rb16gALz8Mhw4ANu3m51TM2eaIdjGjWHuXLh92w5PKYTISM5QAtORpTWdoWynM/RBGNaOjJ4H3tNaz3zg+EDgI621UyZCkJFRkZmCg4OZNWsWM2bMwMXFhaCgIC5fvsybb76JSvIr+b17Zrp+yhQzZR9v82aT3clmV67AnDlm09PRo1CwoNnSP2QIVK6c7ucSQgghbJXu3fRKqbeBD4Eg4DfL4QZAX+B9rfWnduqrXUkwKpzJCy+8wNmzZ9myZQsAO3fupEaNGnh7eydcc+iQmXHfvNnsUYovM7poETRsaEraW01r09C0abB0qYl6mzQxQ69du4KHh92eTQghhEiNXVI7KaW6A68C8dkSDwNfaa0fpuZMhpBgVDib27dv4+npye3btylevDjPPvssM2eaCYf4tafmfWKZ+osXoVQps8a0QweztrRlSxvL2EdEQFCQCUxPnYIiRWDAALMhqlw5Oz+lEEIIcT97rBlFa/2D1rqx1rqQ5dXYmQNRIZyRp6cnALlz52blypUJO/PPnj1LqVKlWLduHXB/oHnnjik16uoKy5dDmzZQsSJ8/jlcvWrljYsVg3fegePHTcmoJ54wDZQvD61aJY6cCiGEEBnMlrEVIYSdKKV4/PHHqVatGgBRUVHUrVuXcpZRypCQECZMmEBkZCRlysCCBRAaCuPHQ+nScOIEvPmmGTG1OiAFE+W2bm2Cz7Nn4YMP4O+/4ZlnTMPvvQdnzqTdjshWpCxixnCGEp9COKPUkt7/A/hrrS8rpSJJJQG+1topy8DINL3IqsaNG8cnn3zChQsX8PLy4uTJkxQrVgxvb29iY03p+ilTzGjpL7+Y72gNixebqXzLAKx1YmNh9WqzWHXVKnOsXTuz4aldu8SFqyLbkhQ3GcMZ0jUJkVketgJTX2CR1jpaKdWP1IPROfboqL1JMCqyskuXLlG0aFEAmjdvztWrV9m3b99919y7l1hadOtWsz+pYEGzHDQw0MzC2+TMGZMa6rvv4Px5M/Q6cCC8+KLJOyWyJQl8MoYEoyInc4ra9JlBglGRXQQHB3Pt2jU6dOhAXFwcTz75JAMGDGDAgAEJ12zeDG+9BUn/lW/d2mx4at/exgHOe/dgxQqz4enXX82XO3Y0Ea7Nu6eEs5PAJ2NIMCpysnRvYFJKjVJKNVBKyXydEJmgcePGdOjQAYAbN25QuHDhhM1QkZGRTJw4kWrVLrFnj6kU2q8f5M4Na9dC584mLZRN/wNzd4ennzYNHD9uFqgGB5vdU+XLwyefmG3+QgghRDpZm2d0O1AXuAvsADZbXru11rEO7F+6yMioyAmWLVtGly5dCA4OplGjRly/fh13d3fu3PFi9mz49ltTxn7cOHP9jRtw8CA0apT66Mu/REfDzz8nJkJ1dzf5SgMDoWlTGxsTzkRG4TKGjIyKnCzdI6Na68eBApiyoHuA9sAm4LpSao29OiqEsF3nzp05cuQIDRs2BOCLL77A19eXXLkiGTHCFGEaPTrx+jlz4PHHoXZtmD4dbt608kYeHiaq3bTJ1C99+WVYtw6aNzeVnSZONNWfRJYjZREzhjOU+BTCGdmSZ/S21nodMAmYDCwGcgNPOqhvQggrVaxYMaHEaPv27RkzZgx58+YF4O233+SLL8YlXOviAkWLwv79ZsO8nx+88oqJL60WH3yGhcHcuSaJ/ogRprEXXoDt22X4Jgu5cMH8cT34unAhs3uWvdjyc5Y/E5GTWLtm9Fml1BSl1GHgBDAYOA60BAo6sH9CCBvVq1ePN954AwCtNaGhoVxI8n+wggUXsGfPBRYsgMaN4Z9/4JtvoGpVszTUJp6eJvgMDoY//zQ775cvN0n1a9QwDV+/bsenE0IIkd1Yu2Y0DrgEfA5M0lrfcnTH7EHWjAphaK1RSnH27FnKlCnDp59+yttvv01sbCx79twlKMiT+fNNxdDu3c13zp41m+htzugUFQWLFpmd+Hv2mIC1Rw+ztrRuXVlbKoQQOZA9yoEOAdYBw4FwpdQKpdQIpdRjSsn/WYRwdvH/mZYuXZrDhw8npITasGEDLVsWY+DAPYSHm/1I8caOhTJloFs3s0zU6ll3Ly+Tl3T3bti714yc/vAD1K8Pjz1mgtTISDs/oRBCiKzK2g1MM7TWvbXWpYAAYBlQD/gNsHrHglJqllIqQil1MIXzSin1tVLquFLqT6XUY0nO9VVKHbO8+lp7TyHE/SpXrkyRIkUA8PX1pXfv3tSoUYP8+WHJkkWMHDmS6Oi7xMSY65csMXuUqlY1s+43bthws/jgMzzcbOvX2oyQ+vqaf/7xh/0fUGRZrq7Jl8BMbxEwR7XrLCU7pcyoyOqsTnqvlHLBpHdqCjQHGgO5gL1a64ZWtvEkcBOYq7Wunsz5dpjR13ZAfeArrXV9pVQhIAQTCGtgL1BHa30ttfvJNL0Qthk5ciRr1qzhjz/+QCnFzz/vJji4KgsXehMebq7x8jIFmp577iFuoDXs2mUC1EWL4M4dqFfPBKbPPQd58tj1eUTW4qh0RlmtXUf2w1n6LHIeeyS9XwVcA7YBXYE/gG5AQWsDUQCt9VbgaiqXdMYEqlpr/RtQQClVAmgNrNNaX7UEoOuANtbeVwhhnU8++YQ9e/aglCIuLo5hw7py9GgvTp82de+bNo0jKgpq1kz8zqlTJgWpVZSCBg3M4tTwcPjqKzNlP2CAGS195RX46y9HPJoQQggnZe2a0T+B5zDBZwOt9Uit9RqtdZSd++MHnEvyOdRyLKXj/6KUGqyUClFKhVy6dMnO3RMi+3O3FLt3cXFh3bp1fPjhh7i7Q/Pm1zh40Icvv1xGlSrmWq3h2WehdGmTy/TMGRtuVLBgYvC5daupWTptGlSvbnbjz59vRk6FEEJka9auGXVU8Pmg5CYQdCrH/31Q6+la6wCtdUDRokXt2jkhcpqqVatS0zIMGhUVRceOHXnyydIAHD58mNdf/4Bbt2KIiIDx48Hf35QfXbsW4uKsvIlSJvhcsMDkLZ0wwSRTfOEFs5X/zTdN5n4hhBDZktVJ7zNIKFAqyeeSQHgqx4UQGaRkyZLMmjWL2rVrA7Bjxw6mTfuYTZuusn07dOoUiaurZvlyU8K+YkVTdtQmRYqY4PPIEVi/Hp56ykzlV6pk3v/wA9y9a/+HE0IIkWmcLRhdDvSx7KpvANzQWp8H1gKtlFIFlVIFgVaWY0KITPLiiy9y8eJFfHyK0bgx5Mo1gEKFHmXcuDhKl4YrVzT+/onXh4XZ0LiLS2Lwee6cGXY9edJscipVCkaNMotVRbbiksL/kVI6ntntOkvJTikzKrI6q3fT2+VmSn2P2Y1fBLgIjAHcAbTWUy05SydhNifdAvprrUMs3x0AvGtpapzWOiit+8lueiEyzqFDhzhx4gQdO3YkNhYaNuxH166VGDVqFFFRZn9SpUowdKiJKT09bbxBbCz8+qtZV7pihVmw2qqV2YnfoQO4uTnkuYQQ6RMXF0doaChRUY5e6Scym5eXFyVLlsQlmd/0UttNn6HBaEaTYFSIzBEdHU1gYCCNGjVi0KBBBAfH0KLFPe7cMRFowYJmA/1LL0G5cg9xg9BQk19qxgwz5Orra0qRDhxoRk6FEE4jIiKC6Oho/Pz8kg1SRPYQFxdHWFgYHh4eFCtW7F/n7VGBSQghrObh4UFQUBCDBg0CwMVlD9HRRXj11X0EBMC1a/D551C+PLRtCzdv2niDkiVhzBg4fRqWLYNateDDD6FsWejUCVatMiOpQohMd/36dXx8fCQQzeZcXFzw8fHhhk2VUSzfTemEUipSKfWPNa909V4Ike01bNiQsLDjTJhQjT174I03FqHUHDw84rhyBby9E6+9ft2Ght3cEoPPkydh5EhThrR9e7O1f9w4OH/e7s8jhLBebGxsQso4kb25u7sTE1++zwapLbJ6+eG7I4QQ9ytRokTC+8GDa1Oy5Cr69HHh/Hl47733uHbtGoGB31CnjuLZZ83a0oYNU68Yc5+yZU3wOWYMLF8OU6fCf/4D779v8k0NGWI2RcnojBAZTln9H7LIyh72zznFYFRrPeeheyOEEKmoVKkSlSpVAqBwYZg1K4pbt26xfbsiJsakHF2wwMy+Dx0Kzz9//+hpqnLlgm7dzOvYMZg+3VR8WrLELFAdPBj69wfJQyyEEE5BhgiEEJlu4sSJzJo1i8BA2L8/ElfXT8mT5yb795sBTV/fOEaOfIiGK1QwSfRDQ0106+cH77xj1pz27AlbtkhBbiHEfbZt25bwy7LIGNbWps+llBqrlDqqlLqjlIpN+nJ0J4UQOUf16nk5d64Phw7dtIyO3iQy0oV9+xIrAsfEwL17NjSaO7cZXt2yxZQfDQyENWugaVOoWhW+/BKuXrX7swghnFvZsmVZv379fceeeOIJjhw5kin9uXv3LiNGjKBkyZJ4e3vzyCOP8PrrrwPQunVr/vvf//7rO8uWLaN48eIJazV3795Nu3btKFCgAIUKFaJevXoEBaWZDTNTWTsy+iHQF/gciAPeAiYDV4ChjumaECKnKlGiBGXKFOf552HZsiv06TOR8ePzAbBixQpatZpBmTJxjB0L4bbWYqta1VR1Cgsz0/cFCsDrr5tR0759YedOGS0VQmS4mJgYPv74Y0JCQti9ezeRkZFs2rQpoepdv379mDdvHg+m5Jw3bx69evXCzc2NnTt30rx5c5o0acLx48e5cuUK3377LatXr86MR7Ke1jrNF3AKaGN5HwmUs7x/CVhsTRuZ8apTp44WQmQvX3zxhc6b92dtIkatXV3jdJs2/+iNG7WOi3vIRvft0/qll7TOm9c0WqOG1pMna339ul37LkROdOjQoczuQorKlCmj161bd9+xTZs2aT8/v/uumTBhgq5Ro4bOly+f7t69u759+3bC+RUrVuhatWrp/Pnz64YNG+r9+/cnnPv444+1v7+/9vb21lWqVNFLly5NOBcUFKQbNWqkX3vtNV2wYEE9evRo3b59e/3FF18k29dbt27pfPny6S1btiQcu3r1qvbw8ND79u3TWmvduHFjPXTo0PT9UNIppT9vIESnEK9ZOzLqAxyyvL8JFLC8X4MpzSmEEBnitdde49q1jmzcaPYoxcbGsmZNXpo3N4Oec+c+RO36WrVgyhQzzDp9Ori7w7BhJpn+oEEgxTOEsKumTZsye/ZsAO7du0fTpk2ZP38+ALdu3aJp06b873//A+DGjRs0bdqUpUuXAnD58mWaNm3KihUrALhw4QJNmzZlzZo1AJw7dw57++GHH1izZg2nTp3izz//TOj777//zoABA5g2bRpXrlxhyJAhdOrUiejoaADKlSvHtm3buHHjBmPGjKF3796cT5JubteuXfj7+xMREcHo0aNp0KABEydOZMqUKRw4cOC+UVBPT0+6d+/O3Llz7+tX5cqVqVWrFrdu3WLnzp1069bN7s/vaNYGo2cBX8v740Bry/uGwG17d0oIIVLj6upCs2bw448QEnKZIUMuUKIE/P03DBv2X7788kvgIfLee3ub4HPvXtizx2xyWrgQ6taFgABT8cnmDP1CiKzulVdewdfXl0KFCtGxY0f27dsHwIwZMxgyZAj169fH1dWVvn374uHhwW+//QbAs88+i6+vLy4uLjz33HNUqFCB3bt3J7Tr6+vL8OHDcXNzw9PTk1GjRvHOO++wYMECAgIC8PPzY86cxORGffv25ccff+T2bRN6zZ07l759+wJw7do14uLi7kujl2WkNGSa9AV8DIy2vO8G3MNM3d/F1InP9Cn55F4yTS9EznH3rtZBQZH65Zff1Vu3btVaaz106A3t43NMf/HFRX3nzkM2fP261pMmaV29upnCz5vXTOknmYoTQqQsO0zTJ71mzJgxulevXlprrdu2bas9PT11/vz5E16enp564cKFWmut58yZkzCFnz9/fu3q6qpnzpyptU6cpk/JrVu39KRJk7SLi8t9P8Ny5crp77//Xp84cUK7u7vrCxcuaK21joqK0i4uLnrjxo3p/Kmkj8Om6bXWo7TW4yzvFwOPA98AT2utR9s9QhZCCBu5u0O/ft588804nnjiCbSGpUtduXixPK+/XozSpWHYsOts3Xratobz5zdT9n/+CcHB0KULzJplpvYbNYI5c+C2TBAJkROVKlWK0aNHc/369YTXrVu36NmzJ2fOnGHQoEFMmjSJK1eucP36dapXr37f1HtqSeI9PT0ZNmwYBQsW5NChQwnH+/Tpw9y5c5k3bx6tWrXCx8cHgDx58tCwYUOWLFniuAd2EGtTOz2plEpIkK+13qW1ngisUUo96bDeCSHEQ1IKjh3z4uuv71KzJkREwJQpBWjSpBQdOsTyxx8QFxdnW4ONGsHcuWZt6cSJJh1Uv35mbelrr8Hhww57HiGEY9y7d487d+4kvGwpZzlo0CCmTp3Krl270FoTFRXFypUriYyMJCoqCqUURS0FNoKCgjh48GCq7X355Zds3ryZ27dvExMTw5w5c4iMjEzYUQ8mGF2/fj0zZsxImKKP93//93/Mnj2bCRMmcOXKFQD2799Pjx49rH6mzGDtmtFNQKFkjue3nBNCCKfj7Q3Dh+di3z7Yvh26dLmFm5ti5UpXbt6Ejh078uqrr9qeyalQIZMO6vBh2LQJ2rQxG6CqVoUmTeD778GygUEI4dzatWuHp6dnwuv999+3+rsBAQHMmDGDl19+mYIFC1K+fPmEzU1Vq1ZlxIgRNGzYEB8fHw4cOEDjxo1Tbc/T05MRI0ZQvHhxihQpwuTJk1myZAn+/v4J15QtW5ZGjRoRFRVFp06d7vt+o0aN2LhxIxs3bsTf359ChQoxePBg2rVrZ/UzZQalrfhbWCkVB/horS89cLwiZg1APgf1L10CAgJ0iOyCFUIkcfEiLF0KQ4Zo3nnnbfz8/Ni27TXy5dPAFN5440lq1Khhe8MRETB7NkybBidPQpEipuzo4MFQvry9H0OILOPw4cNUqVIls7shMkhKf95Kqb1a64DkvpNqMKqUWm552x5YDyT9Vd8VqA4c1lq3edhOO5IEo0KItJw/b6qDxs/YP/LIZf773yJ07HiL69fPU65cOdsajIuDDRtg6lRYtsxs6W/RwtQ17dzZLG4VIgeRYDRneZhgNK1p+iuWlwKuJfl8BQgFpgK909FnIYTIVCVKwJEjMGIEFCigOXWqCP37Q5kyrpQv/xMbNhywrUEXF2jZEpYsgbNn4cMP4ehRePZZKF0aRo+G06cd8ixCCJEVWTtNPwb4TGsd5fgu2Y+MjAohbHH7NvzvfzB5sslz7+oaS1iYCz4+ik8++YSQkBAWLVqEm5tb2o0lFRsLa9aYKfyVK03xqDZtIDAQ2rUDW9sTIguRkdGcxREjowBorcdqraOUUgFKqeeUUl6Whr2S7rJPi1KqjVLqiFLquFJqZDLnv1BK7bO8jiqlric5F5vk3PIHvyuEEOnl6Wk2x+/ZA7t3w5Qprvj4mNQrWruydetHTJjgRkSESTa9Z88e6xp2dYX27WH5cjh1Cv7zH9i3z0zbP/IIjB0LYWGOezAhhHBi1o6M+gDLgbqABiporU8qpaYBd7TWr1rRhitwFGiJmeLfA/TUWh9K4frhQG2t9QDL55taa2/rHsuQkVEhhL2sXAkdOpj3uXJplFpC69bH+fnnkSgF4eHh+Pr6pt5IUvfuwS+/mNHStWtNwNqhgxktbdXKTPcLkQ3IyGjO4rCRUeAL4AJQGLiV5PiPWF+bvh5wXGt9Umt9F1gEdE7l+p7A91a2LYQQDtW2LaxeDR07wr17iujobixfPpLatWHcuEv4+ZW9r2xfmtzdoWtXM31/4gS89Rbs2GFuVK4cfPyx2fovhBDZnLXB6FOYcqDXHjh+AihtZRt+wLkkn0Mtx/5FKVUGeATYmORwbqVUiFLqN6VUl5RuopQabLku5NKlSyldJoQQNnFxMcs8ly83mZtGjYKiRWH/fpgxoxDjxn1A8+bNAdi8eTPdunUjPDzcusb9/U3wGRpqFq0+8gi8+67Z5t+9u9mdb0uCfiGEyEKsDUY9MXXoH1QUuGNlG8nVvEppjUAPYLHWOjbJsdKW4d3ngS+VUsnmW9FaT9daB2itA+KrHgghhD2VLQvjx8O5czB/PnzyiSvvvjuSUqVKER4Ow4dXIji4BN7eBQEIDg5OqNCSqly5TPC5cSP8/Te88ooJRFu0gMqV4fPP4fJlxz+gEEJkIGuD0a1AvySftWUN6DvABivbCAVKJflcEkhp2KAHD0zRa63DLf88CWwGav/7a0IIkXE8PKBXL0haaW/mTDh4sAQXLnxDlSqejB0LI0d+Tb9+/RKuuXnzZtqNV6pkgs+wMJg3D3x84M03wc8PeveGbduwvXSUEEI4H2uD0beBQUqpdYAH8DlwCGgMjLKyjT1ABaXUI0qpXJiA81+74pVSlYCCwM4kxwoqpTws74tY7pvsxichhMhMr74KX39tBjLDw+H992HnzkWUKrWTLVsUcXFxVK1alXfeece6BnPnTgw+DxwwFZ1++QWefBKqVzc3u3497XaEEMnavn07jRo1In/+/BQqVIjGjRuzbds2vLy8iIyM/Nf1tWvXZtKkSQDcvXuX999/nwoVKuDl5UXZsmUZMGAApyWXsE2sTe10CKiJCRB/BXJjNi/V1lqfsLKNGOBlYC1wGPhBa/2XUuoDpVTS4qo9gUX6/vmsKkCIUmo/sAn4JKVd+EIIkZny54fhw+HQITPb3q0bgGLdugJ8+SVER0cTGBhIs2bNALh+/To9e/bkzz//TLvx6tXhm2/MaOl334G3t4l+fX1hwADYtUtGS4WwwT///EOHDh0YPnw4V69eJSwsjDFjxpA/f35KlizJkiVL7rv+4MGDHDp0iJ49ewLQrVs3li9fzsKFC7lx4wb79++nTp06bNhg7aSxACtTO2VVktpJCOEMwsJgxgxo1gyaNDHHtmyB77+HRo32MWJES1atWkXdunU5d+4cFy5cICAgAKWSW2r/gN9/N+mhFiyAqCh49FFTerRXL8ib17EPJoQVnDm1U0hICC1atOB6MrML48ePZ/369WzcmLiX+u233+b48eMsXbqU9evX07FjR44ePUqpUqX+9f2cyu6pnZRSeZRSk5VSYUqpCKXUQss0uRBCCCv5+Znp+vhAFMzs+rRp0Lfvo1SseJGjRwOIjoZvv/2Whg0bEp8NJCYmJvXGH3vMNBQeDt9+a0ZGX3rJjJYOGQJ//OG4BxPiISmV8mv69MTrpk9P/dqk6tRJ/nhqKlasiKurK3379mX16tVcu5aYNOiFF15g27ZtnD17FoC4uDgWLlxInz59AFi/fj316tWTQNQO0pqmH4vZuLQSkxe0JfCtg/skhBDZ3ocfmun8fPlgxw4XevdWlCoFd+78l5kz11GsWDHA/A+xm5nrT12+fCZh/h9/wG+/wbPPmo1Pjz0G9erBrFlm5FQIkSBfvnxs374dpRSDBg2iaNGidOrUiYsXL1KqVCmaNGnC/PnzAdiwYQN37tyhffv2AFy5coUSJUpkZvezjbSC0aeBF7XWg7XWrwDtgS6WnfRCCCEeUtWqZnQ0LAymToWaNeHSJfjii9ycOtUs4bo6deoQEJA4szVq1Ci2bduWcsNKQf36JvgMDzc3iYqCF180o6XDh8PBg458NCHSpHXKr8GDE68bPDj1a5Pauzf542mpUqUKs2fPJjQ0lIMHDxIeHs5rr70GQN++fZk7dy4A8+bN4/nnn8fd3R2AwoULc/78+Yf+GYhEaQWjpYCEv/W01ruBGMCGmndCCCFS4u1tZtP37YPt2+H552HQoMTzxYq9ibv7SK5ehcuXLzNz5kzi18LHxMQQEhKScv7SAgUSg89t20z5qOnToUYNePxxM3J6x9pU0UJkf5UrV6Zfv34ctPzC9vTTTxMWFsamTZtYunRpwhQ9QIsWLdi9ezehoaGZ1d1sI61g1JV/J7uPAdwc0x0hhMiZlILGjc0+pJIlzbG4OPjgg8T0om+/XYTly8MZMmQIAL/++it169bl119/BUg5KFXKBJ/z55uh2M8+g4gI6NPHNDxiBBw5khGPKYRT+fvvv/n8888TAspz587x/fff06BBAwC8vLzo1q0b/fv3p0yZMvfNUrRo0YKWLVvStWtX9u7dS0xMDJGRkUydOpVZs2ZlyvNkVWkFowqYr5RaHv/CpHWa8cAxIYQQDjBxIrRubQYwg4KgUSN3mjbNw+zZULt2I2bOnJmQJmrKlCk0bdo02dyICYoUSQw+N2yAp55KTIzavLkpR3o3uYJ7QmQ/efPmZdeuXdSvXx8vLy8aNGhA9erV+fzzzxOu6du3L2fOnLlvVDTe4sWLadeuHc899xz58+enevXqCTv0hfVSTe2klAqyphGtdX+79ciOJLWTECK7OHbMbJqfNQviN/wuXQpduyZeM3v2bFasWJGQG3H+/PkULVqU1q1bp974hQsm0p0+HU6fhmLFoH9/s2DP398xDyRyDGdO7STs72FSO0meUSGEyEJu34ZFi0wg+tNP4GZZNDVxIpQvD+3bg6urmbKvUaMGlSpVSghOT5w4gb+/f8r5S+Pi4NdfTdS7YgXExkKrVmaXfocOYNm4IYQtJBjNWeyeZ1QIkXkuXlzAzp1l2bzZhZ07y3Lx4oLM7pJwAp6eZtByxYrEQPTyZRg1Cjp3NgOZH38Mly4pfv/9dyZPngzApUuXqFy5Mp9++mnKjbu4QJs2Jso9cwbGjjWlpJ5+GsqUgf/+Fyw5F4UQwl4kGBXCCV28uIAjRwYTHX0G0ERHn+HIkcESkIpkeXjA+PFQrpyJFd99F0qVggEDcnHyZHG0Bk9PTyZPnkxXy7z+H3/8QfPmzfn777+Tb9TPzwSfp07B8uVQuzZ89BE88ojZHsyVWAAAIABJREFUlf/LL2bkVAgh0kmCUSGc0MmTo4mLu3Xfsbi4W5w8OTqTeiScWd68Zk/S0aOwZo2JFe/dMzvzGzc2y0C9vb0ZPHgwlSpVAsxI6cWLFylatCgAu3btYvXq1cQ+GGC6uZkGV66EkyfNEGxIiDnm728C1PDwDH5iIUR2IsGoEE4oOjr5qdCUjgsBZpa9dWszkBkfN/bqZQYzwSQDHz8eDh+GVq1a8ddff1G4cGEAvvrqK1588cWEtq5evfrvVFFly5rg8+xZWLwYKlaE996D0qXhmWfMetO4uAx6WiFEdiHBqBBOyMOjtE3HhXhQ2bIm8LRUMgRg504YPdpUf3rqKViyxIyggtmJv27dOlxdXdFa06RJk2RT2QBmI9Mzz8C6dWab/xtvwNatJhKuUAE+/dTkMRVCCCtIMCqEE/L3H4eLS577jrm45MHff1wm9UhkB8WKmWxNefLAxo3QrZsJWseOhcuXc1GtWjUA4uLiGDZsGM888wwA0dHRdOnSha1bt/670fLl4f/+D0JDYeFCs1h15EiTub9HD9i82fb6jEKIHEWCUSGckI9PLypVmo6HRxlA4eFRhkqVpuPj0yuzuyaysPLlTdam+JL1lSub9++/D489BjEx5jpXV1cCAwPp0qULAKdOneLAgQPcvn0bgIsXL7J27Vpi4r8AZhdVz54m+Dx0CIYNg7VroVkzqFIFvvgCrl7N2AcWQmQJEowK4aR8fHrRsOFpmjaNo2HD0xKICrvJn9+UrD90KHGEdMCAxFRRkZEwaRLcuGE+V65cmePHj9OyZUsAFi5cSJs2bTh58iQAd+7cuX99aXzwGR4Oc+ZAoUJmKt/X15QgDQ6W0VIhknj//ffp3bu3w9qvVq0amzdvBkwO4v79+1OwYEHq1avHtm3bEjY2ZhYJRoUQIodSygxc/vgjjEuyAmTePBOs/n97dx5e07U+cPy7MkjISJAmEYmY6TUUNaR61VTTDW1pDW21iqumolwttxWtVlulbquttil+rlkHsxZFXVerQcMVQww1JcQYEtKIZP3+WCdHZCDTySDv53nOI2fvtfde+xzDa+213tfPz+S737cPlFLY2Zl/MoYOHcqmTZuoVasWAKNHj6Zly5akZly8VLasCT537IC9e+Gll2DFCnjkEWjQ4M6IV4gisn37dlq1aoWHhwcVKlQgODiY8PBwAM6ePcugQYPw9fXF1dWVoKAgXnjhBWtKtBMnTqCUwtXVFVdXV7y9venWrRsbN27MdJ1FixbRtGlTXF1d8fHxoXPnzmzfvr1Q7jEyMpI2bdpY73fjxo2cOXOG3377jdatW3P48OFC6Ud2JBgVQghB+qJMNWuaIPX6dfNYv2FDEz8uXgxJSeDk5ES7du2s7Vu2bEmXLl2swerEiRNZuXLlnRdo0AA+/dSMln71lXmsP2KEGS0dOBDCw2W0VBS6a9eu0a1bN0aMGMHly5eJjo5m0qRJODk5cenSJVq1asWNGzf4z3/+Q3x8PHv27OGvf/1rpmAzLi6OhIQE9u7dS4cOHXjiiSeYN2+edf+MGTMYNWoUEyZMIDY2llOnTjF06NDMf04KwcmTJwkMDMTFxSXf57pjqk5+aK0L7QV0Ag4DR4HXstj/AnABiLC8Bqbb1x84Ynn1z8n1mjRpooUoDc6dW6B37AjQW7YovWNHgD53bkFRd0ncByIjtR4xQmt3d61NpKh1t253PyYxMVHXrFlTT5w4UWutdWpqqt68ebO+detW5sbh4VoPHKh1uXLm5A89pPUXX2gdH2+DuxFF5cCBA0XdhWyFh4drDw+PLPdNnDhRN2jQQKekpGR7/B9//KEBnZycfMf2adOm6cqVK+uUlBQdFxenXVxc9LJly7I9z6RJk3S/fv2s73v27Km9vb21u7u7bt26td6/f79139q1a3XdunW1q6ur9vX11dOmTdNaa33hwgXdtWtX7eHhocuXL68feeQRa98DAgL0xo0bdVhYmHZyctJ2dnbaxcVFv/nmm3rLli3az8/Pev7o6Gj95JNP6ooVK+rAwED9r3/9645+PvXUU7pfv37azc1Nf/XVV5nuJbvvG9ils4nXHAompL03pZQ98CnQATgDhCulVmmtD2RoulRrPTzDsRWASUBTQAO7LcdeKYSuC1GspVVrSkuSn1atCZB5piJf6tUzC53efdck0P/0U7NGKU1UlCnQ1KGDyXEK4OzszOHDh/nzzz8Bk0y/bdu2zJ8/n+eee47U1FTrCCpNm5rXhx+aC8yeDX//O4wdaxKkDhlihmXF/WXUKIiIsO01GjWCmTPv2axWrVrY29vTv39/evfuTYsWLShfvjwAmzZt4oknnrj9+zUXnnzyScaNG8fhw4c5efIkf/75p7X6WU507tyZOXPmUKZMGcaPH0+/fv2IsHxmL730EsuWLaN169ZcuXKFP/74A4Dp06dTpUoVLly4AMCvv/6KSv/Iw3Ksvb09YWFh1ikCaXNJwWTS+Nvf/kb37t1ZvHgxZ86coX379tSuXZvHH38cgJUrV7J8+XLmz59PUlJSrj+brBTmY/qHgaNa6+Na65vAEqB7Do99HNiotb5sCUA3YkZZhSj1pFqTsDVXVxMj7t1rsjWlmT7dlLKvVcv8nLZYXilF2bJlAWjUqBHffPMN3bubv+6XLFlCw4YNiUlftcnDA4YONRfYsQOefBLmzTMBRYsW5ucbd/4eF6IguLu7s337dpRSDBo0iEqVKhESEkJsbCwXL17kgQcesLZdtWoVnp6euLm50bFjx7ue19fXFzDFIy5dukTFihVxcMj5+N+AAQNwc3PDycmJ0NBQ9u7dy1XL/GpHR0cOHDjAtWvXKF++PA899JB1+9mzZzl58iSOjo60bt06UzB6L+Hh4Vy4cIE333yTMmXKEBQUxKBBg1iyZIm1TcuWLenRowd2dnbWP+f5VWgjo4AfcDrd+zNA8yzaPaWUehSIAkZrrU9nc6xfVhdRSg0GBgNUrSoJwsX9T6o1icKi1J1zS+vWNcWXjh0zg5n//KcZOR061Ax4ghkpTctXCuYf/6CgIOs/8kuWLCElJYV+/fqZk7dsaV4zZpiVVLNnw4svwujRZjHU3/9uhmxFyZWDEcvCVLduXev8zkOHDvHss88yatQovLy8OHv2rLVdSEgIcXFxhIWFsSB9NYksREdHA1ChQgXi4+O5ePEit27dylFAmpKSwsSJE1m+fDkXLlywjsxevHgRDw8Pvv32W6ZMmcJrr71GgwYNeO+992jZsiXjxo0jNDTUGigPHjyY1157LVefxcmTJ4mJicHT0/OO/rRu3dr63t/fP1fnzInCHBnNKjzPOFt9NRCotW4AbAL+LxfHmo1af6m1bqq1bppWc1mI+5lUaxJFZdQoU3Z05UpTfOnPP2HuXGjWDKZOzfqYbt268f3331v/gZ0zZw5hYWHW/QcOHCAlJcWkg3rlFZN/6uefoXNnE5jWrw+PPmoS7BfQI0Ih0tSpU4cXXniB/fv3065dO1asWJE5S0QOfP/991SuXJnatWvTsmVLnJ2dWbFiRY6OXbRoEStXrmTTpk1cvXqVEydOAFjTpzVr1oyVK1dy/vx5evTowdNPPw2Am5sb06dP5/jx46xevZoZM2bw008/5arf/v7+VKtWjbi4OOsrPj6edevWWdvkdrQ1JwozGD0DpA+nqwAx6RtorS9prdP+dvkKaJLTY4UoraRakyhK9vYQEgI//GAqg776KpQvD9263W6za5cZPc3KDz/8wPLlywG4ceMGzZs359VXX73dQKnbweeZM6baU0yMmVPq5wfjxpkLC5EHhw4dYvr06Zw5cwaA06dPs3jxYlq0aMGYMWO4cuUKzz33HMeOHUNrTXx8vHXuZlZiY2OZNWsWkydPZurUqdjZ2eHh4cFbb73FsGHDWLFiBTdu3CA5OZn169fzj3/8I9M54uPjcXJywsvLixs3bjBhwgTrvps3b7Jw4UKuXr2Ko6Mj7u7u2NvbA7BmzRqOHj2K1tq6PW1fTj388MO4u7vz/vvvk5iYSEpKCvv377emurKVwgxGw4GaSqlqSqkyQG9gVfoGSimfdG9DgIOWn38EOiqlyiulygMdLduEKPWkWpMoLmrUMGuRzp6Fv/zl9vYRI8y+zp1h9WpISbm9z87OjooVKwLg4ODA3LlzefHFFwGTw7Fx48bs3LnTNK5UyQSfUVGwcSO0aWOS69eqBe3bwzffQHJyId2tuB+4ubmxc+dOmjdvjouLCy1atODBBx9k+vTpVKxYkV9//RVnZ2ceeeQR3NzcaNSoEfHx8Xz++ed3nMfT0xMXFxf+8pe/sG7dOpYvX86AAQOs+8eMGcOMGTOYMmUKlSpVwt/fn1mzZlmrnKX3/PPPExAQgJ+fH/Xq1aNFixZ37P/3v/9NYGAg7u7uzJ492zpl4MiRI7Rv3x5XV1datmzJ0KFDrblFc8re3p7Vq1cTERFBtWrVqFixIgMHDrTOV7UVlTbsWxiUUl2AmYA9MEdr/Y5S6i3Mcv9VSqmpmCD0FnAZeFlrfchy7AAg7b8H72it597rek2bNtW7du2yxa0IIYTIgaQksyh+yRLzGB/MPNMhQ0wO/MqVsz82PDyc4cOHs3TpUgIDA/n99985cOAAPXv2xMnJyTQ6exbmzIEvv4RTp8Db25x40CAIDLT5/Yl7O3jwIHXr1i3qbohCkt33rZTarbVumtUxhRqMFjYJRoUQoni4dMksiv/889uP7B0dYd06M6iZE2PGjCEsLIxz585Rrlw5YmNjqVixonkUmZICP/5o5pWuXWvSonbqZBY8de16u9apKHQSjJYueQlGpQKTEEIIm/PyMvNJo6LM/NKQEHBxMZmb0vz6KyQkZH+ODz/8kF27dlGunJkj/cwzz9ChQwez094eunSBVavgxAl44w2TKqpHDzNCGhpq5pwKIYodCUaFEEIUGjs7s/J+5Uo4edLkMAWTRrRLF7MmaeRIOHgwq2PtqFWrlvX9sGHDePnllwGTrLtbt25mxbK/P0yebC7w/fdmAutbb0FAAHTvDuvX3zlxVQhRpCQYFSILsbEL+eWXQLZuteOXXwKJjV1YIOeNiGjP1q3K+oqIyP75ZG76YKv+2vrconRzd7/987lzJn3otWvwySfm53bt4Ntvs1+T1KtXL3r16gWYVcyxsbEkJiYCpub4omXLuNGxowk+jx2D8ePN8GuXLlC9uiktde6crW9TCHEPEowKkUFaec2kpJOAtpbXzG8QFhHRnri4O3O+xcX9lGVAmps+2Kq/tj63EOkFBcH27aZK5ODBUK4cbN4MPXuap+zpco9nycfHh/DwcHpbSkStWrWKfv368b///Q+AG97epE6ZAqdPw7JlJhidONGMovbqBT/9BHnIJymEyD8JRoXIwFblNTMGonfbnps+2LIcqJQaFYWtYUP44guTSvTjj6FOHbNAPl1VRn7/3axPykpaQu6+ffuyfft2Hn74YQDeffddqlevzp+pqbeDz8OHTWL9zZvNKqratU1uqosXbX2bQoh0JBgVIoPiUF4zN32wZX+Lw2chSicPD5Of9MAB85Q9rejL4cPw0EOmENOsWZBd+kM7OzuCg4OtwWmrVq14/vnncXZ2BmDSpEl8/Z//mOAzOhoWLDAR77hxZuJqv36wbVv2Ua8QosBIMCpEBsWhvGZu+mDL/haHz0KUbkqZkdE0f/wBPj5mgdOIESZuHDIE9u27+3m6dOnC5MmTAVNWcfPmzezevdvsdHbmBy8vEjdsgP37TTqotWvhr381Ue+//gVXrtjoDoUQEowKkYGtymt6erbL8fbc9MGW5UCl1Kgobjp1Movkly+Hxx6D69fNY/2GDaFDh5wNZCql+M9//sPMmTMBiIqKonPnzqaqTv36pM6cSeqZMyaZvrs7jBoFvr7wwgtmAZSMlpYaCxcupGPHjkXdjWzVr1+frVu35uscbdq0ISwsrGA6lEcSjAqRga3KazZqtClT4Onp2Y5GjTblqw+2LAcqpUZFceToaBY2bd4MkZEwfDi4uUGVKrcf5ycnm4JMd1OmTBkAatSowebNm3n22WcB2LBhA4H16nGgeXMTfP7+uwlEv/0WWraERo1M9v5r12x4l6IwBAYGsmlT5r+D0/Tr148NGzYUYo9yJzIyMtclP4sjKUkhRBa8vfvZJODKKvAsiD7Yqr+2PrcQ+VWvnkkFNXXqnQnzV66EZ56Bbt1g6FAzamqXzfCLnZ0djz32mPW9m5sbzZs3p3r16gB8d/w4p+vUYfjp09gvW2aqPA0dauaX9u1rHus3aWLL2yyVHngAYmMzb/f2LpyMXLdu3cKhiCt3FYc+ZKcg+yYjo0IIIUo8V9c7V9wfPWqKMq1aZR7t164NM2bA5cv3PldwcDDLly/HyckJgDVr1jBnzhzsPT1h8GD2zpnDnz//bKLdBQugaVNo1gy+/trMGxAFIqtA9G7b82vevHkEBwczevRoKlSoQGhoKPPmzeORRx4BzFzj0aNHU7lyZTw8PGjQoAH79+/PdJ4lS5bQtOmdVS8/+ugjQkJCAEhKSmLs2LFUrVoVb29vhgwZYs2Pu3XrVqpUqcL777/PAw88wIsvvsjFixfp1q0bnp6eVKhQgdatW5NqSUOWfmQ3JSXFmjXCzc2NJk2acPr0aQB27NhBs2bN8PDwoFmzZuzYsSPLzyA1NZUpU6YQEBBA5cqVef7557lqWSV44sQJlFJ8/fXXVK1albZt2+b3I7eSYFQIIcR957XXTErRd9+FqlVNcPrqq2bB06RJuTvXnDlz2LZtG2BGgzp17swLn31mgs+YGPTHH0NiIgwcaOaWDh8OlvymomTZuXMnQUFBnD9/nokT70xht2HDBrZt20ZUVBRxcXEsXboULy+vTOcICQnh8OHDHDlyxLpt0aJF9O3bF4Dx48cTFRVFREQER48eJTo6mrfeesva9ty5c1y+fJmTJ0/y5ZdfMn36dKpUqcKFCxeIjY3l3XfftWaJSG/GjBksXryYdevWce3aNebMmUO5cuW4fPkyXbt2ZeTIkVy6dIkxY8bQtWtXLl26lOkc8+bNY968eWzZsoXjx4+TkJDA8OHD72jz888/c/DgQX788cfcfbh3IcGoEEKI+5K3N7z+Ohw/fnuE9M8/oXz5222uXjVx5L14eHgA5pH+woULefXVVwG4lJJC7U8+Yf0HH5is/SEhEBYGDRpAcDDMn5+zC4hiwdfXlxEjRuDg4EDZsmXv2Ofo6Eh8fDyHDh1Ca03dunXx8fHJdI5y5crRvXt3Fi9eDMCRI0c4dOgQISEhaK356quv+Oijj6hQoQJubm5MmDCBJUuWWI+3s7Nj8uTJODk5UbZsWRwdHTl79iwnT57E0dGR1q1bZxmMhoWFMWXKFGrXro1SioYNG+Ll5cXatWupWbMmzz33HA4ODvTp04c6deqwevXqTOdYuHAhY8aMISgoCFdXV6ZOncqSJUu4deuWtU1oaCguLi6ZPp/8kGBUiCxERQ1l61YHS9lOB6Kihmbb1lYlPnNDSnYKkT17e/jb30y+0iNH4MUXb++bNs2Mlo4da0ZP78XOzo62bdvSrFkzAC5fvkz16tXx8fWF4GAOTZzIV6Gh/PnuuyZ5fv/+5gKjR8OhQza6Q1FQ/P39s93Xtm1bhg8fzrBhw/D29mbw4MFcy2YRW9++fa3B6KJFi+jRowflypXjwoUL3LhxgyZNmuDp6YmnpyedOnXiwoUL1mMrVapkzYcLMG7cOGrUqEHHjh0JCgrivffey/Kap0+fts5zTi8mJoaAgIA7tgUEBBAdHX3PtgEBAdy6dYvYdHMj7vYZ5ZUEo0JkEBU1lJiYz4EUy5YUYmI+zzIgtVWJz9yQkp1C5FyNGiahfpqICJNCdPp0qFkTOneG1ashJSX7c6RXs2ZN1q9fT6NGjQAzv3ToG2+QMGgQHDrExWXLSGnXDj79FOrWhTZtYMkSSEoq+JsT+ZbViGN6I0eOZPfu3URGRhIVFcW0adOybNexY0cuXrxIREQEixcvtj6ir1ixImXLliUyMpK4uDji4uK4evUqCelW32Xsg5ubG9OnT+f48eOsXr2aGTNm8NNPmSv3+fv7c+zYsUzbfX19OXny5B3bTp06hZ+f3z3bnjp1CgcHB7zTJfu912eUFxKMCpFBTMyXOd5uqxKfuSElO4XIuzVr4LffTOYmZ2f44QfzpL16dVixIvfnGzt2LMeOHaNixYqgFIMXL+bB/fvRp0/De++ZfFN9+pg8VOPHQxbBgzDSFzvIyXZbCw8PZ+fOnSQnJ+Pi4oKzszP29vZZtnVwcKBnz56MGzeOy5cv06FDB8CMrA8aNIjRo0dz/vx5AKKjo+86/3LNmjUcPXoUrTXu7u7Y29tned2BAwfyxhtvcOTIEbTW7Nu3j0uXLtGlSxeioqJYtGgRt27dYunSpRw4cIBu3bplOkefPn346KOP+OOPP0hISGDChAk888wzNl/RL8GoEJlkNySSw6GSbNiqtKaU7BQif5o1g7lz4cwZUx20enWTWD/9CGp8fM5z3VetertC2YgRI3jzzTdR3t4wfjw9HnyQ9a+8Aq1bm+HYGjWgY0f47juTHFVYnTtnPvOMr8JI65SVa9euMWjQIMqXL09AQABeXl6MHTs22/Z9+/Zl06ZN9OrV645g7v3336dGjRq0aNECd3d32rdvz+HDh7M9z5EjR2jfvj2urq60bNmSoUOHZplbdMyYMTz99NN07NgRd3d3XnrpJRITE/Hy8mLNmjVMnz4dLy8vPvjgA9asWWP+w5TBgAEDeO6553j00UepVq0azs7OfPLJJ7n7oPJA6fu4kkTTpk31rl27irobooTZutWBrANPe9q0uZWhbfaPK9q0ufPP1i+/BFoepd/JySmAli1P5KGntj2vEKVVaips3WoqPKU9kQwJMYOaQ4ea1KKurrk/b0JCAk899RQ9evTg5Zdf5uaJE0SMGEGT33/HPjra5KYaONC8MszxK8kOHjxI3bp1i7obopBk930rpXZrrZtmcUjhjowqpToppQ4rpY4qpV7LYv8YpdQBpdQ+pdRPSqmAdPtSlFIRlteqwuy3KF18fQfneLutSnzmhpTsFKJg2dlB27a3A9GEBAgPh717TX57Pz8YOTL365FcXV358ccfefnllwH4+cgRmq9Zw4bZs2H1am41aoR+5x2oVs1k68/N5FUhSrBCC0aVUvbAp0BnoB7QRylVL0Oz34GmWusGwDfAB+n2JWqtG1leIYXSaVEq1ar1Gb6+LwNpc3Ls8fV9mVq1PsvU1lYlPnNDSnYKYVuurnDiBCxcCK1amSqgn3xi1iO1bQsHDuTtvB06dGDv3r106NQJunXj4w4daOjmxvXRo2HPHjMcW60avPUWZLHyWYj7RaE9pldKtQRCtdaPW96/DqC1nppN+8bALK11sOV9gtY6Vw9G5DG9EEKIghYRYUrTL1gAN2+a5Ppp1Z9u3gRLyftc+/XXX1m3bp1JgJ6czDf9+/PQrl0EHTlyOz/VkCF3r21aDMlj+tKluD+m9wNOp3t/xrItOy8B69O9d1ZK7VJK/aqU6mGLDgohhBD30qgRfPEFxMSYZPppgWhKCjz4IPTqBVu25HzBU5oWLVrcrsTj6Mh3wBvNmpkEqGPHkrRli8ncX6OGWZlvq7qYQhSywgxGs1rpkeUfVaXUs0BTIH0Cr6qWiLovMFMplTmzqzl2sCVo3ZU+iawQQghRkDw8TF7SNBERptrTN9+Yx/f168OsWabKU14sWrSI+fPnQ/XqXHj1VcrHx7O4e3ezuOn119H+/vDMM3mLfIUoRgozGD0DpE/bXwWIydhIKdUemAiEaK2tWYG11jGWX48DW4HGWV1Ea/2l1rqp1rpppUqVCq73QgghxF00aWJSQk2aBD4+cPAgjBhhFjwNGZK3oDQtn2SlSpX4Zc8eWs+aBVu2sG/pUj6zsyN5/XoT+dapAzNmQBb1xoUo7gpzzqgDEAW0A6KBcKCv1joyXZvGmIVLnbTWR9JtLw/c0FonKaUqAr8A3bXWd502LnNGS57Y2IUcPz6RpKRTODlVJSjonQJZiGOqKn2JSdlkj6/v4CwXJKXZubM+iYm3f3uVLVuP5s0js2y7dWsZIH1+QEfatLmZTdtyQPo61WVp0+ZGlm3/+18/kpNv/3/N0dGX4OCsFzHY6nOz9bmFuF8lJ8PKlfDZZ2bgsmpVM2qalqs8NTV/0z4jIyN5//33+fj99/HcuJEr771H+YMH0U5OqF69TPTbqtXtlABFSOaMli7Fes6o1voWMBz4ETgILNNaRyql3lJKpa2Onwa4AsszpHCqC+xSSu0FtgDv3SsQFSWPrcpa5qa8J2QORAESEw+wc2f9TG0zB6IAyZbtGdtmDEQBEi3b75QxEAVITo7hv//NPM3aluVApdSoEHnj6Ag9e8LmzRAZCV99dTsQjY01T9onTDAjqXlRv3595s+fj6ePDzz/PNOffJLHfXzgpZfMRNZHHuFWvXpmnkBcXMHdmBA2UKjL8bTW67TWtbTW1bXW71i2vam1XmX5ub3W2jtjCiet9Q6t9V+01g0tv35dmP0WhcNWZS1zU94TyBSI3n17dhVTstqeMRDNfnvGQPRu221ZDlRKjQqRf/XqmSJLab77zlR7mjoVgoKge3f48UczWppXU6ZM4fujR1GffoqOjuafDzzA0ehoM0/A1xc9YICpeypzS3Nl4cKFdEz/5QmbKDm5IcR9z3ZlLW1T3rO4sGU5UCk1KkTBGzIEtm83lZzs7c1AZqdOULs2zJyZ93ixXDnLUxYXF3quX0/chg2waxe3evfmxrx50Ly5mdj6xRemvqkgMDCQTZsy54VO069fPzZs2FBo/VFKcfTo0UK7XnEhwagoNpycquZqe87Z53J7yWK7z8225xaitFIKgoNNEv3Tp+Gdd8Df32SsQvX1AAATLUlEQVRw2rTp9jTPvAalSikaNWpEixYtoEkTLrzzDq/07EnU6NEm/9SQISRVrEhi//4mBUAxFhu7kF9+CWTrVjt++SWwUKcI3bp1696NRIGQYFQUG7Yqa5mb8p5gFivlfLtjNlfNanvZbNpm3u7o6Jv1WbPYbstyoFJqVAjb8vY2c0f/+MMseHrjjdv7tm0zg5n/93+QmN0snxzw8fEhbNkyas2YARER/DBpEotv3sRp6VJo3JibjRtzfdYsuJH1YsqiUthz1ufNm0dwcDCjR4+mQoUKhIaGMm/ePB555BEAtNaMHj2aypUr4+HhQYMGDdi/f3+25woKCsLNzY1q1aqxcOHtPs+ZM4e6detSvnx5Hn/8cU5aJg4/+uijADRs2BBXV1eWLl0KwFdffUWNGjWoUKECISEhxMTE3LM/a9eupXHjxri7u+Pv709oaKhNPrOCIsGoKDZsVdYyN+U9AZo3j8wUeGa3mt6sms8YeGa9mt6sms8YeGa9mj44ODpT4JndanpblgOVUqNCFA57e1P9s3nz29vmzjXTPF94AapUgXHj4NixfF5IKTqFhtIlNha7s2dh5kwunjiBy4gRaF9fGDnSrLgqBopizvrOnTsJCgri/PnzTJx453U2bNjAtm3biIqKIi4ujqVLl+Ll5ZXpHNevX2fkyJGsX7+e+Ph4duzYQaNGjQBYsWIF7777Lt999x0XLlygdevW9OnTB4Bt27YBsHfvXhISEnjmmWfYvHkzr7/+OsuWLePs2bMEBATQu3fve/bHxcWF+fPnExcXx9q1a/n8889ZsWKFzT63fNNa37evJk2aaCGEEKIkun5d6zlztG7SRGvz0N68OnXSesOGgrvO73v26A3//KfWfftqXaaM1qBPBgRovWCB1omJ+T7/gQMH8nTcli1Kb9lCFi+V7z6lCQgI0Bs3btRaaz137lzt7+9/x/65c+fq4OBgrbXWP/30k65Zs6b+5ZdfdEpKSrbnTEhI0B4eHvqbb77RN27cuGNfp06ddFhYmPV9SkqKLlu2rD5x4oTWWmtAHzlyxLp/wIABety4cdb38fHx2sHBQf/xxx857o/WWr/yyit61KhRd21TULL7voFdOpt4TUZGhRBCiGKoXDl48UXYtev2CKmzM/zwA2zdWnDXadS4MR3efhsWLiTl1CkWNm6MW0ICPPssukoVdrVpQ0xBXjCHimLOur+/f7b72rZty/Dhwxk2bBje3t4MHjyYa9euZWrn4uLC0qVLmT17Nj4+PnTt2pVDhw4BcPLkSV555RU8PT3x9PSkQoUKaK2Jjs46h3RMTAwBAQHW966urnh5eREdHX3X/uzcuZPHHnuMSpUq4eHhwezZs7l48WJ+PhqbkmBUCCGEKOaaNTOP7c+cgQ8/hL///fa+2bOhXz/YsSP/mZvsvb3pt2cP5c+fh02buNq4MQ1//hnfxx6Ddu24uWABV2Jj83eRHCqKOevqHkUCRo4cye7du4mMjCQqKopp06Zl2e7xxx9n48aNnD17ljp16jBo0CDABLtffPEFcXFx1ldiYiKtWrXK8jy+vr7WOaVgpgBcunQJPz+/u/anb9++hISEcPr0aa5evcqQIUPQxTitlwSjQgghRAnh5QWvvmoqOoEJPj/5BBYtMiv0GzeGL7+EhIR8XsjODtq1w3PjRmLDw7kZGgrHjlHmuee4+cADXBo82Ky6sqHiNmc9PDycnTt3kpycjIuLC87OztZyrenFxsayatUqrl+/jpOTE66urtZ2Q4YMYerUqURa5uVevXqV5cuXW4/19vbm+PHj1vd9+/Zl7ty5REREkJSUxIQJE2jevDmBgYF37U98fDwVKlTA2dmZ3377jUWLFtnyo8k3CUZFiVWUKT/Si4oaytatDmzdqti61SHbyk65bSuEEPeiFKxdC6+/DpUqwd69ZtTUz8+sRSqIlJVVmjalzKRJcOwYp2bP5krt2lT4+muoXp0TdeoQ1q0bOjm7AiD54+3dj5YtT9CmTSotW54o0sWT165dY9CgQZQvX56AgAC8vLwYO3ZspnapqalMnz4dX19fKlSowM8//8xnn5kFs0888QTjx4+nd+/euLu78+CDD7J+/XrrsaGhofTv3x9PT0+WLVtGu3btePvtt3nqqafw8fHh2LFjLFmy5J79+eyzz3jzzTdxc3Pjrbfe4umnny6ETyjvCq02fVGQ2vT3r7SUH+lXWtrZlSv0/zXfLjV6p6xW6+emrRBC5FZSEnz7LXz6qXlkD7B0KdgkDjlzBsLCiJs+Hc+EBPD1hYED+dHfn9rt2xMYGGhtKrXpS5diXZteiIJUXMpU5qbUaG7LkgohRG44OZmqTv/9L/z+O4waBT163N7/+usQGgoxWVcbzp0qVSA0FM8rV9Dffw8NG6Lffpv2gwZxtU0bWLcOUlJIyPd8AVEaSDAqSqTiU6YyN6VG7++ypEKI4qNRI/joIyhTxry/csWUGp082cw37dULtmwpgFL1Dg6oHj1g3TrU8eMkDBvGg9evQ9euJFetyrTy5UmUgFTcgwSjokQqPmUqc1Nq9P4uSyqEKL48Pc1gZc+e5v0330DbtlC/PsyaBVlkKMq9wEA8Zs3CPjoali/nVrVqTL51i7KXLsGxY9w4d45Tp05JmU2RiQSjokQqLmUqc1NqNLdlSYUQoqAoBY89BsuXw8mTMGkS+PjAwYMwYkQBPbpPU6YM9OxJ2e3bISoK3NzQ165R7swZvM+fx+7CBUhO5vr16yQlJRXghUVRy+s6JAlGRYlUXFJ+5KbUaG7LkgohhC34+Zm5oydPmuB07FioU8fs0xoGD4bFi82CqHyrWRP7SpVIrlsXqlWjjKsrdtHRsG8fKUeOEBMVZZ0rcD8vqC4tkpOTcXBwyPVxsppeCCGEEICp9NS8ufm5cmUYONCkiqqajxlQ58+fJykpCT8/P+zs7CAxES5cQF+6hEpJAWdndMWKHDx/ngqVK/PAAw8UzM2IQpWamkp0dDROTk5Urlw50/67raaXYFQIIYQQgEmWv3ChSQ/1v/+ZbXZ20K0bDB0KHTqY97mRmprKmTNnuH79esYdcOOGuWhSEhpIcXbGwdOTVEdH4uLicHd3z9NImygaLi4uVKlSxfynIwMJRoUQQgiRY1qbXKWffWYe5Scnm0VQ0dFQrty9j8+1vXvhiy9gwQKIjye+WjUmnjrFiz/9ROO//pWzZ8+SnJxM1fwM0YoiJcGoEEIIIfIkNhbmzDEjouPHm23Xr5uypAMHQtMsw4s8SkgwE1Znz4Y9e9DlyqH69uXjpCTGLV3K+fPn8fDwQGt9zzryongpNknvlVKdlFKHlVJHlVKvZbHfSSm11LJ/p1IqMN2+1y3bDyulHi/MfgshhBCllbe3SZifFogCLFpkBjKbNYOHH4Z588xU0HxzdYVBg2D3bggPR/XpA4sWMfLf/ybGzw+PZcsgIYH+/fszYsSIArigKA4KLRhVStkDnwKdgXpAH6VUvQzNXgKuaK1rAB8B71uOrQf0BuoDnYDPLOcTQgghRCFr186MjJYvD+Hh8OKLpijTuHFw7FgBXaRpUwgLM3mnZs3Cy8XFLPX39eXv+/ZRL12+0g8++IDIyMgCurAobIU5MvowcFRrfVxrfRNYAnTP0KY78H+Wn78B2ikzDt8dWKK1TtJa/wEctZxPCCGEEIUsKAg+/NDMIZ0718SNly+bbX37FvDFPDxg2DDYt8/UOu3Rg+BDh3h59mxo1YorM2fyzj//yaZNmwCTXuj06dMF3AlhS4U2Z1Qp1RPopLUeaHn/HNBcaz08XZv9ljZnLO+PAc2BUOBXrfUCy/avgfVa62+yuM5gIC2L+IPAfpvdlLClisDFou6EyDP5/kou+e5KNvn+Srb7+fsL0FpXympHYeZLyGqmccZIOLs2OTnWbNT6S+BLAKXUruwmy4riTb67kk2+v5JLvruSTb6/kq20fn+F+Zj+DOCf7n0VIGMBMmsbpZQD4AFczuGxQgghhBCihCnMYDQcqKmUqqaUKoNZkLQqQ5tVQH/Lzz2BzdrMI1gF9Lastq8G1AR+K6R+CyGEEEIIGym0x/Ra61tKqeHAj5ji3HO01pFKqbeAXVrrVcDXwL+VUkcxI6K9LcdGKqWWAQeAW8AwrXVKDi77pS3uRRQK+e5KNvn+Si757ko2+f5KtlL5/d3XSe+FEEIIIUTxVqhJ74UQQgghhEhPglEhhBBCCFFk7stg9F5lR0XxpZSao5Q6b8k5K0oQpZS/UmqLUuqgUipSKfVKUfdJ5JxSylkp9ZtSaq/l+5tc1H0SuaOUsldK/a6UWlPUfRG5o5Q6oZT6n1IqQim1q6j7U9juuzmjljKhUUAHTEqocKCP1vpAkXZM5IhS6lEgAZivtX6wqPsjck4p5QP4aK33KKXcgN1AD/mzVzJYqt25aK0TlFKOwHbgFa31r0XcNZFDSqkxQFPAXWvdraj7I3JOKXUCaKq1vl8T3t/V/TgympOyo6KY0lpvw2RSECWM1vqs1nqP5ed44CDgV7S9EjmljQTLW0fL6/4arbiPKaWqAF2BsKLuixC5dT8Go35A+qK0Z5B/EIUoVEqpQKAxsLNoeyJyw/KYNwI4D2zUWsv3V3LMBP4BpBZ1R0SeaGCDUmq3pax5qXI/BqM5Lh0qhCh4SilX4FtglNb6WlH3R+Sc1jpFa90IU+XuYaWUTJUpAZRS3YDzWuvdRd0XkWfBWuuHgM7AMMuUtVLjfgxGpXSoEEXEMtfwW2Ch1vq7ou6PyButdRywFehUxF0RORMMhFjmHS4B2iqlFhRtl0RuaK1jLL+eB77HTDksNe7HYDQnZUeFEAXMsgDma+Cg1npGUfdH5I5SqpJSytPyc1mgPXCoaHslckJr/brWuorWOhDzb95mrfWzRdwtkUNKKRfLok+UUi5AR6BUZZS574JRrfUtIK3s6EFgmdY6smh7JXJKKbUY+AWorZQ6o5R6qaj7JHIsGHgOMyoTYXl1KepOiRzzAbYopfZh/lO/UWstKYKEsD1vYLtSai/wG7BWa/1DEfepUN13qZ2EEEIIIUTJcd+NjAohhBBCiJJDglEhhBBCCFFkJBgVQgghhBBFRoJRIYQQQghRZCQYFUIIIYQQRUaCUSGEKAJKqReUUgn3aHNCKTW2sPp0N0qpQKWUVko1Leq+CCHuLxKMCiFKLaXUPEuApZVSyUqp40qpDy2Jp3NzjvsqH+f9eE9CiOLLoag7IIQQRWwTJlm/I9AaCANcgJeLslNCCFFayMioEKK0S9Jan9Nan9ZaLwIWAj3Sdiql6iml1iql4pVS55VSi5VSD1j2hQL9ga7pRljbWPa9p5Q6rJRKtDxu/0Ap5ZyfjiqlPJRSX1r6Ea+U+jn9Y/O0R/9KqXZKqf1KqetKqS1KqWoZzvO6UirW0na+UmqSpa75Xe/JIkAptVEpdUMpdUAp1SE/9ySEEBKMCiHEnRIxo6QopXyAbZg60Q9j6rW7AquUUnbAh8AyzOiqj+W1w3Ke68AAoC4wFFMzfGJeO6WUUsBawA/oBjS29G2zpZ9pnIDXLdduCXgCs9OdpzcwydKXhzBlk8ekO/5u9wTwDvAx0BBTNnSJUso1r/clhBDymF4IISyUUg8DfYGfLJteBvZqrcena/M8cBloqrX+TSmViGV0Nf25tNZvp3t7Qin1LjAWeCOP3XsMaARU0lonWra9oZT6G2aawQeWbQ7AMK31YUt/PwTmKqXstNapwCvAPK11mKX9VKXUY0AtS78TsronEwsD8JHWerVl2wTgeUu/tufxvoQQpZwEo0KI0q6TZVW7A2ZEdCUwwrKvCfBoNqveqwO/ZXdSpVRPYBRQAzOaam955VUToBxwIV1gCOBs6UuapLRA1CIGc1+emCC6DvBVhnPvxBKM5sC+DOcGqJzDY4UQIhMJRoUQpd02YDCQDMRorZPT7bPDPBrPKr1SbHYnVEq1AJYAk4HRQBwQgnkEnld2lmu2zmLftXQ/38qwT6c7PuO2vLB+PlprbQmMZcqXECLPJBgVQpR2N7TWR7PZtwd4GjiZIUhN7yaZRzyDgej0j+qVUgH57OcewBtI1Vofz8d5DmHmv85Nt+3hDG2yuichhLAJ+d+sEEJk71PAA1iqlGqulApSSrW3rGh3s7Q5ATyolKqtlKqolHIEogA/pVQ/yzEvA33y2ZdNwH+BlUqpzkqpakqplkqpyUqprEZLs/Mv4AWl1AClVE2l1D+A5tw5WprVPQkhhE1IMCqEENnQWsdgRjlTgR+ASEyAmmR5gZl/eRDYBVwAgi0LfKYBMzFzLDsAb+azLxroAmy2XPMwZtV7bW7P3czJeZYAbwPvAb8DD2JW2/+Zrlmme8pP34UQ4m6U+ftNCCFEaaWU+h5w0Fr/raj7IoQofWTOqBBClCJKqXKYlFU/YBY7PQV0t/wqhBCFTkZGhRCiFFFKlQVWY5LmlwWOAB9orRcWaceEEKWWBKNCCCGEEKLIyAImIYQQQghRZCQYFUIIIYQQRUaCUSGEEEIIUWQkGBVCCCGEEEVGglEhhBBCCFFk/h8sXpcCHQ9dDwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 792x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the slope and bias of each decision boundary\n",
    "w1 = -lin_clf.coef_[0, 0]/lin_clf.coef_[0, 1]\n",
    "b1 = -lin_clf.intercept_[0]/lin_clf.coef_[0, 1]\n",
    "w2 = -svm_clf.coef_[0, 0]/svm_clf.coef_[0, 1]\n",
    "b2 = -svm_clf.intercept_[0]/svm_clf.coef_[0, 1]\n",
    "w3 = -sgd_clf.coef_[0, 0]/sgd_clf.coef_[0, 1]\n",
    "b3 = -sgd_clf.intercept_[0]/sgd_clf.coef_[0, 1]\n",
    "\n",
    "# Transform the decision boundary lines back to the original scale\n",
    "line1 = scaler.inverse_transform([[-10, -10 * w1 + b1], [10, 10 * w1 + b1]])\n",
    "line2 = scaler.inverse_transform([[-10, -10 * w2 + b2], [10, 10 * w2 + b2]])\n",
    "line3 = scaler.inverse_transform([[-10, -10 * w3 + b3], [10, 10 * w3 + b3]])\n",
    "\n",
    "# Plot all three decision boundaries\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.plot(line1[:, 0], line1[:, 1], \"k:\", label=\"LinearSVC\")\n",
    "plt.plot(line2[:, 0], line2[:, 1], \"b--\", linewidth=2, label=\"SVC\")\n",
    "plt.plot(line3[:, 0], line3[:, 1], \"r-\", label=\"SGDClassifier\")\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris versicolor\") \n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris setosa\") \n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"lower right\", fontsize=12)\n",
    "plt.axis([0, 5.5, 0, 2])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 9. Train an SVM classifier on the MNIST dataset. \n",
    "- Since SVM classifiers are binary classifiers, you will need to use one-versus-the-rest to classify all 10 digits. \n",
    "- You may want to tune the hyperparameters using small validation sets to speed up the process.\n",
    "- What accuracy can you reach?\n",
    "#### First, let's load the dataset and split it into a training set and a test set. We could use train_test_split() but people usually just take the first 60,000 instances for the training set, and the last 10,000 instances for the test set (this makes it possible to compare your model's performance with others):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "mnist = fetch_openml('mnist_784', version=1, cache=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'categories', 'feature_names', 'target_names', 'DESCR', 'details', 'url'])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = mnist[\"data\"]\n",
    "y = mnist[\"target\"]\n",
    "\n",
    "X_train = X[:60000]\n",
    "y_train = y[:60000]\n",
    "X_test = X[60000:]\n",
    "y_test = y[60000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Many training algorithms are sensitive to the order of the training instances, so it's generally good practice to shuffle them first. However, the dataset is already shuffled, so we do not need to do it.\n",
    "- Let's start simple, with a **linear SVM classifier.** \n",
    "    - **It will automatically use the One-vs-All (also called One-vs-the-Rest, OvR) strategy, so there's nothing special we need to do.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\batuh\\Anaconda3\\lib\\site-packages\\sklearn\\svm\\_base.py:977: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearSVC(random_state=42)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_clf = LinearSVC(random_state=42)\n",
    "lin_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's make predictions on the training set and measure the accuracy (we don't want to measure it on the test set yet, since we have not selected and trained the final model yet):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8348666666666666"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "y_pred = lin_clf.predict(X_train)\n",
    "accuracy_score(y_train, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, 83.4% accuracy on MNIST is pretty bad. This linear model is certainly too simple for MNIST, but perhaps we just needed to scale the data first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "X_train_scaled = scaler.fit_transform(X_train.astype(np.float32))\n",
    "X_test_scaled = scaler.transform(X_test.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\batuh\\Anaconda3\\lib\\site-packages\\sklearn\\svm\\_base.py:977: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearSVC(random_state=42)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_clf = LinearSVC(random_state=42)\n",
    "lin_clf.fit(X_train_scaled, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9217333333333333"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = lin_clf.predict(X_train_scaled)\n",
    "accuracy_score(y_train, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's much better, but still not great at all for MNIST. If we want to use an SVM, we will have to use a kernel. \n",
    "#### Let's try an SVC with an RBF kernel (the default)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC()"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf = SVC(gamma=\"scale\")\n",
    "svm_clf.fit(X_train_scaled[:10000], y_train[:10000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's promising, we get better performance even though we trained the model on 6 times less data. Let's tune the hyperparameters by doing a randomized search with cross validation. We will do this on a small dataset just to speed up the process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9455333333333333"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = svm_clf.predict(X_train_scaled)\n",
    "accuracy_score(y_train, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 3 folds for each of 10 candidates, totalling 30 fits\n",
      "[CV] C=7.689240596630997, gamma=0.053497702356221796 .................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] .. C=7.689240596630997, gamma=0.053497702356221796, total=   1.5s\n",
      "[CV] C=7.689240596630997, gamma=0.053497702356221796 .................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    1.4s remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] .. C=7.689240596630997, gamma=0.053497702356221796, total=   1.5s\n",
      "[CV] C=7.689240596630997, gamma=0.053497702356221796 .................\n",
      "[CV] .. C=7.689240596630997, gamma=0.053497702356221796, total=   1.5s\n",
      "[CV] C=3.3018526824155527, gamma=0.009962922677707813 ................\n",
      "[CV] . C=3.3018526824155527, gamma=0.009962922677707813, total=   1.4s\n",
      "[CV] C=3.3018526824155527, gamma=0.009962922677707813 ................\n",
      "[CV] . C=3.3018526824155527, gamma=0.009962922677707813, total=   1.4s\n",
      "[CV] C=3.3018526824155527, gamma=0.009962922677707813 ................\n",
      "[CV] . C=3.3018526824155527, gamma=0.009962922677707813, total=   1.4s\n",
      "[CV] C=6.720041992091831, gamma=0.034443559676607075 .................\n",
      "[CV] .. C=6.720041992091831, gamma=0.034443559676607075, total=   1.5s\n",
      "[CV] C=6.720041992091831, gamma=0.034443559676607075 .................\n",
      "[CV] .. C=6.720041992091831, gamma=0.034443559676607075, total=   1.5s\n",
      "[CV] C=6.720041992091831, gamma=0.034443559676607075 .................\n",
      "[CV] .. C=6.720041992091831, gamma=0.034443559676607075, total=   1.5s\n",
      "[CV] C=1.4360377175443375, gamma=0.09752164572338576 .................\n",
      "[CV] .. C=1.4360377175443375, gamma=0.09752164572338576, total=   1.5s\n",
      "[CV] C=1.4360377175443375, gamma=0.09752164572338576 .................\n",
      "[CV] .. C=1.4360377175443375, gamma=0.09752164572338576, total=   1.5s\n",
      "[CV] C=1.4360377175443375, gamma=0.09752164572338576 .................\n",
      "[CV] .. C=1.4360377175443375, gamma=0.09752164572338576, total=   1.5s\n",
      "[CV] C=5.69944513990943, gamma=0.0036234367402567607 .................\n",
      "[CV] .. C=5.69944513990943, gamma=0.0036234367402567607, total=   1.3s\n",
      "[CV] C=5.69944513990943, gamma=0.0036234367402567607 .................\n",
      "[CV] .. C=5.69944513990943, gamma=0.0036234367402567607, total=   1.3s\n",
      "[CV] C=5.69944513990943, gamma=0.0036234367402567607 .................\n",
      "[CV] .. C=5.69944513990943, gamma=0.0036234367402567607, total=   1.3s\n",
      "[CV] C=9.83494022266259, gamma=0.031292304511228025 ..................\n",
      "[CV] ... C=9.83494022266259, gamma=0.031292304511228025, total=   1.5s\n",
      "[CV] C=9.83494022266259, gamma=0.031292304511228025 ..................\n",
      "[CV] ... C=9.83494022266259, gamma=0.031292304511228025, total=   1.5s\n",
      "[CV] C=9.83494022266259, gamma=0.031292304511228025 ..................\n",
      "[CV] ... C=9.83494022266259, gamma=0.031292304511228025, total=   1.5s\n",
      "[CV] C=10.530718470239531, gamma=0.004586702893394872 ................\n",
      "[CV] . C=10.530718470239531, gamma=0.004586702893394872, total=   1.4s\n",
      "[CV] C=10.530718470239531, gamma=0.004586702893394872 ................\n",
      "[CV] . C=10.530718470239531, gamma=0.004586702893394872, total=   1.4s\n",
      "[CV] C=10.530718470239531, gamma=0.004586702893394872 ................\n",
      "[CV] . C=10.530718470239531, gamma=0.004586702893394872, total=   1.4s\n",
      "[CV] C=6.527649668354899, gamma=0.013950344686768637 .................\n",
      "[CV] .. C=6.527649668354899, gamma=0.013950344686768637, total=   1.5s\n",
      "[CV] C=6.527649668354899, gamma=0.013950344686768637 .................\n",
      "[CV] .. C=6.527649668354899, gamma=0.013950344686768637, total=   1.4s\n",
      "[CV] C=6.527649668354899, gamma=0.013950344686768637 .................\n",
      "[CV] .. C=6.527649668354899, gamma=0.013950344686768637, total=   1.4s\n",
      "[CV] C=10.803315837160456, gamma=0.0014147917283055171 ...............\n",
      "[CV]  C=10.803315837160456, gamma=0.0014147917283055171, total=   1.1s\n",
      "[CV] C=10.803315837160456, gamma=0.0014147917283055171 ...............\n",
      "[CV]  C=10.803315837160456, gamma=0.0014147917283055171, total=   1.1s\n",
      "[CV] C=10.803315837160456, gamma=0.0014147917283055171 ...............\n",
      "[CV]  C=10.803315837160456, gamma=0.0014147917283055171, total=   1.1s\n",
      "[CV] C=4.056970192871819, gamma=0.002408918252446824 .................\n",
      "[CV] .. C=4.056970192871819, gamma=0.002408918252446824, total=   1.2s\n",
      "[CV] C=4.056970192871819, gamma=0.002408918252446824 .................\n",
      "[CV] .. C=4.056970192871819, gamma=0.002408918252446824, total=   1.2s\n",
      "[CV] C=4.056970192871819, gamma=0.002408918252446824 .................\n",
      "[CV] .. C=4.056970192871819, gamma=0.002408918252446824, total=   1.2s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  30 out of  30 | elapsed:   41.6s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "RandomizedSearchCV(cv=3, estimator=SVC(),\n",
       "                   param_distributions={'C': <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001EAE68D6388>,\n",
       "                                        'gamma': <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001EAE68D6808>},\n",
       "                   verbose=2)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import RandomizedSearchCV\n",
    "from scipy.stats import reciprocal, uniform\n",
    "\n",
    "param_distributions = {\"gamma\": reciprocal(0.001, 0.1), \"C\": uniform(1, 10)}\n",
    "rnd_search_cv = RandomizedSearchCV(svm_clf, param_distributions, n_iter=10, verbose=2, cv=3)\n",
    "rnd_search_cv.fit(X_train_scaled[:1000], y_train[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=10.803315837160456, gamma=0.0014147917283055171)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnd_search_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8639927352502204"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnd_search_cv.best_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks pretty low but remember we only trained the model on 1,000 instances. Let's retrain the best estimator on the whole training set (run this at night, it will take hours):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=10.803315837160456, gamma=0.0014147917283055171)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnd_search_cv.best_estimator_.fit(X_train_scaled, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9994666666666666"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = rnd_search_cv.best_estimator_.predict(X_train_scaled)\n",
    "accuracy_score(y_train, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks good! Let's select this model. Now we can test it on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9724"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = rnd_search_cv.best_estimator_.predict(X_test_scaled)\n",
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Not too bad, but apparently the model is overfitting slightly. \n",
    "- It's tempting to tweak the hyperparameters a bit more (e.g. decreasing C and/or gamma), but we would run the risk of overfitting the test set. \n",
    "- Other people have found that the hyperparameters C=5 and gamma=0.005 yield even better performance (over 98% accuracy). By running the randomized search for longer and on a larger part of the training set, you may be able to find this as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 10. Train an SVM regressor on the California housing dataset.\n",
    "Let's load the dataset using Scikit-Learn's fetch_california_housing() function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_california_housing\n",
    "\n",
    "housing = fetch_california_housing()\n",
    "X = housing[\"data\"]\n",
    "y = housing[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split it into a training set and a test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't forget to scale the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_train_scaled = scaler.fit_transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train a simple **LinearSVR** first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\batuh\\Anaconda3\\lib\\site-packages\\sklearn\\svm\\_base.py:977: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearSVR(random_state=42)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import LinearSVR\n",
    "\n",
    "lin_svr = LinearSVR(random_state=42)\n",
    "lin_svr.fit(X_train_scaled, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Let's see how it performs on the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9641780189948642"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "y_pred = lin_svr.predict(X_train_scaled)\n",
    "mse = mean_squared_error(y_train, y_pred)\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the RMSE:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9819256687727764"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- In this training set, the targets are tens of thousands of dollars. \n",
    "- The RMSE gives a rough idea of the kind of error you should expect (with a higher weight for large errors): so with this model we can expect errors somewhere around 10,000USD. \n",
    "- Not great. Let's see if we can do better with an RBF Kernel. \n",
    "    - We will use randomized search with cross validation to find the appropriate hyperparameter values for C and gamma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 3 folds for each of 10 candidates, totalling 30 fits\n",
      "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  11.9s\n",
      "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:   11.8s remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  11.9s\n",
      "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n",
      "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  12.1s\n",
      "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
      "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=  11.3s\n",
      "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
      "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=  11.0s\n",
      "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
      "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=  11.2s\n",
      "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
      "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=  10.4s\n",
      "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
      "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=  10.6s\n",
      "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
      "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=  10.8s\n",
      "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
      "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=  10.8s\n",
      "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
      "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=  10.4s\n",
      "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
      "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=  11.5s\n",
      "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
      "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=  11.8s\n",
      "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
      "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=  12.0s\n",
      "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
      "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=  12.1s\n",
      "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
      "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=  10.8s\n",
      "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
      "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=  10.8s\n",
      "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
      "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=  11.0s\n",
      "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
      "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=  11.3s\n",
      "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
      "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=  11.2s\n",
      "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
      "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=  11.0s\n",
      "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
      "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=  10.6s\n",
      "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
      "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=  11.2s\n",
      "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
      "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=  10.9s\n",
      "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
      "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=  10.9s\n",
      "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
      "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=  11.0s\n",
      "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
      "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=  11.0s\n",
      "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
      "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=  10.8s\n",
      "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
      "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=  11.2s\n",
      "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
      "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=  10.9s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  30 out of  30 | elapsed:  5.6min finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "RandomizedSearchCV(cv=3, estimator=SVR(),\n",
       "                   param_distributions={'C': <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001EA95945448>,\n",
       "                                        'gamma': <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001EA82BBF6C8>},\n",
       "                   random_state=42, verbose=2)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVR\n",
    "from sklearn.model_selection import RandomizedSearchCV\n",
    "from scipy.stats import reciprocal, uniform\n",
    "\n",
    "param_distributions = {\"gamma\": reciprocal(0.001, 0.1), \"C\": uniform(1, 10)}\n",
    "rnd_search_cv = RandomizedSearchCV(SVR(), param_distributions, n_iter=10, verbose=2, cv=3, random_state=42)\n",
    "rnd_search_cv.fit(X_train_scaled, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=4.745401188473625, gamma=0.07969454818643928)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnd_search_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's measure the RMSE on the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.572752477078536"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = rnd_search_cv.best_estimator_.predict(X_train_scaled)\n",
    "mse = mean_squared_error(y_train, y_pred)\n",
    "np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks much better than the linear model. Let's select this model and evaluate it on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5929168385528742"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = rnd_search_cv.best_estimator_.predict(X_test_scaled)\n",
    "mse = mean_squared_error(y_test, y_pred)\n",
    "np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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