андан hw3.ipynb

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   "source": [
    "# HSE 2021: Mathematical Methods for Data Analysis\n",
    "\n",
    "## Homework 3\n",
    "\n",
    "**Warning 1**: some problems require (especially the lemmatization part) significant amount of time, so **it is better to start early (!)**\n",
    "\n",
    "**Warning 2**: it is critical to describe and explain what you are doing and why, use markdown cells\n",
    "\n",
    "### Attention!\n",
    "* For tasks where <ins>text answer</ins> is required **Russian language** is **allowed**.\n",
    "* If a task asks you to describe something (make conclusions) then **text answer** is **mandatory** and **is** part of the task\n",
    "* We **only** accept **ipynb** notebooks. If you use Google Colab then you'll have to download the notebook before passing the homework\n",
    "* **Do not** use python loops instead of NumPy vector operations over NumPy vectors - it significantly decreases performance (see why https://blog.paperspace.com/numpy-optimization-vectorization-and-broadcasting/), will be punished with -0.25 for **every** task. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "F7t9dYtdDvZC"
   },
   "outputs": [],
   "source": [
    "from typing import Tuple, List\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "sns.set(style=\"darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fIHtwV6vDvZD"
   },
   "source": [
    "## PART 1: Logit model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q7XKEWcVDvZD"
   },
   "source": [
    "We consider a binary classification problem. For prediction, we would like to use a logistic regression model. For regularization we add a combination of the $l_2$ and $l_1$ penalties (Elastic Net). \n",
    "\n",
    "Each object in the training dataset is indexed with $i$ and described by pair: features $x_i\\in\\mathbb{R}^{K}$ and binary labels $y_i$. The model is parametrized with bias $w_0\\in\\mathbb{R}$ and weights $w\\in\\mathbb{R}^K$.\n",
    "\n",
    "The optimization problem with respect to the $w_0, w$ is the following (Elastic Net Loss):\n",
    "\n",
    "$$ L(w, w_0) = \\frac{1}{N} \\sum_{i=1}^N \\ln(1+\\exp(-y_i(w^\\top x_i+w_0))) + \\gamma \\|w\\|_1 + \\beta \\|w\\|_2^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j1eSuDKXFVZu"
   },
   "source": [
    "#### 1. [0.5 points]  Find the gradient of the Elastic Net loss and write its formulas (better in latex format) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1zjH-YnPDvZD"
   },
   "source": [
    "снчало надо вспомнить производные $\\ln(1+x)$ и $\\|x\\|$\n",
    "$$ \\ln'(1+x) = \\frac{x'}{1+x} $$\n",
    "$$ \\ln'(1+\\exp(x)) = \\frac{x' \\cdot \\exp(x)}{1+\\exp(x)} $$\n",
    "$$ \\|x\\|' = x'\\operatorname{sign}(x) $$\n",
    "теперь ищем градиет по $w$ и по $w_0$ $%вообще грустно что сделать они отдельные, можно же закинуть в одну переменную🙁$\n",
    "$$ \\nabla_w L(w, w_0) = \\frac{1}{N} \\sum_{i=1}^N \\frac{-y_i x_i \\cdot \\exp(-y_i(w^\\top x_i+w_0))}{1+\\exp(-y_i(w^\\top x_i+w_0))} + \\gamma \\operatorname{sign}(w) + 2\\beta w $$\n",
    "$$ \\nabla_{w_0} L(w, w_0) = \\frac{1}{N} \\sum_{i=1}^N \\frac{-y_i \\cdot \\exp(-y_i(w^\\top x_i+w_0))}{1+\\exp(-y_i(w^\\top x_i+w_0))} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eRQTLbTdiZb5"
   },
   "source": [
    "**Reminder!**\n",
    "Do not use loops in task 2 and task 3. Loss and grad functions should be implemented in matrix form, without loops."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q_lIccN_DvZE"
   },
   "source": [
    "#### 2. [0.5 points] Implement the Elastic Net loss (as a function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "9QNfCtV5DvZE"
   },
   "outputs": [],
   "source": [
    "from numpy.linalg import norm\n",
    "\n",
    "def loss(X, y, w: List[float], w0: float, gamma=1., beta=1.) -> float:\n",
    "    \"\"\"\n",
    "    :param w: np.ndarray of shape (n_feratures,) -- the weights\n",
    "    :param w0: intercept\n",
    "    :param X: np.ndarray of shape (n_objects, n_features) -- matrix objects-features\n",
    "    :param y: np.ndarray of shape (n_objects,) -- vector of the correct answers\n",
    "    :param gamma: penalty hyperparameter of L1-regularization\n",
    "    :param beta: penalty hyperparameter of L2-regularization\n",
    "    \"\"\"\n",
    "    return gamma*norm(w, ord=1) + beta*norm(w) + np.sum(np.log(1 + np.exp(-y*(X @ w.T + w0))))/len(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fIVoC6UmDvZE"
   },
   "source": [
    "#### 3. [0.5 points] Implement the gradient (as a function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "HWqBLGRADvZE"
   },
   "outputs": [],
   "source": [
    "def get_grad(X, y, w: List[float], w0: float, gamma=1., beta=1.) -> Tuple[List[float], float]:\n",
    "    \"\"\"\n",
    "    :param X: np.ndarray of shape (n_objects, n_features) -- matrix objects-features\n",
    "    :param y: np.ndarray of shape (n_objects,) -- vector of the correct answers\n",
    "    :param w: np.ndarray of shape (n_feratures,) -- the weights\n",
    "    :param w0: intercept\n",
    "    :param gamma: penalty hyperparameter of L1-regularization\n",
    "    :param beta: penalty hyperparameter of L2-regularization\n",
    "    \"\"\"\n",
    "    exp = np.exp(-y*(X @ w.T + w0))\n",
    "    grad_w0 = -np.sum(exp / (1+exp) * y)/len(X)\n",
    "    grad_w = -(exp / (1+exp) * y)/len(X) @ X + gamma*np.sign(w) + 2*beta*w\n",
    "    return grad_w, grad_w0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BhOb8HrtDvZF"
   },
   "source": [
    "#### Check yourself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "3FxXTocHDvZF"
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "X = np.random.multivariate_normal(np.arange(5), np.eye(5), size=10)\n",
    "y = np.random.binomial(1, 0.42, size=10)\n",
    "w, w0 = np.random.normal(size=5), np.random.normal()\n",
    "\n",
    "grad_w, grad_w0 = get_grad(X, y, w, w0)\n",
    "assert(np.allclose(grad_w,\n",
    "                   [-2.73262076, -1.87176281, 1.30051144, 2.53598941, -2.71198109],\n",
    "                   rtol=1e-2) & \\\n",
    "       np.allclose(grad_w0,\n",
    "                   -0.2078231418067844, \n",
    "                   rtol=1e-2)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LbqLfcrRDvZF"
   },
   "source": [
    "####  4. [1 point]  Implement gradient descent and plot the decision boundary of the result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iIgiwQkjDvZF"
   },
   "source": [
    "The template provides basic sklearn API class. You are free to modify it in any convenient way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "Thyeux0KDvZG"
   },
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator, ClassifierMixin\n",
    "from sklearn.metrics import roc_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "FFwVym3WiZb7"
   },
   "outputs": [],
   "source": [
    "class Logit(BaseEstimator, ClassifierMixin):\n",
    "    def __init__(self, beta=1.0, gamma=1.0, lr=1e-2, tolerance=1e-8, max_iter=1000):\n",
    "        \"\"\"\n",
    "        betta: penalty hyperparameter of L2-regularization\n",
    "        gamma: penalty hyperparameter of L1-regularization\n",
    "        tolerance: minimal allowed movement in each iteration\n",
    "        lr: determines the step size at each iteration\n",
    "        max_iter: maximum number of iterations taken for the solvers to converge\n",
    "        \"\"\"\n",
    "        self.beta = beta\n",
    "        self.gamma = gamma\n",
    "        self.tolerance = tolerance\n",
    "        self.max_iter = max_iter\n",
    "        self.lr = self.learning_rate = lr\n",
    "        self.classes_ = np.array([-1, 1])\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # add weights and bias and optimize Elastic Net loss over (X,y) dataset\n",
    "        # save history of optimization steps\n",
    "        self.loss_history = []\n",
    "        X = np.array(X)\n",
    "        y = np.array(y)\n",
    "\n",
    "        uniq, inverse = np.unique(y, return_inverse=True)\n",
    "        assert len(uniq) == 2\n",
    "        if not np.array_equal(uniq, [-1, 1]):\n",
    "            y = self.classes_[inverse]\n",
    "            self.classes_ = uniq\n",
    "\n",
    "        self.w0 = 1\n",
    "        self.w = np.ones(X.shape[1])\n",
    "        for _ in range(self.max_iter):\n",
    "            gw, gw0 = self.calc_gradient(X, y)\n",
    "            if np.linalg.norm(gw) < self.tolerance:\n",
    "                break\n",
    "            self.w -= gw * self.learning_rate\n",
    "            self.w0 -= gw0 * self.learning_rate\n",
    "            self.loss_history.append(self.calc_loss(X, y))\n",
    "\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\"\n",
    "        Function that returns the vector of predicted labels for each object from X\n",
    "        \"\"\"\n",
    "        return self.classes_[np.argmax(self.predict_proba(X), axis=1)]\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        \"\"\"\n",
    "        Function that estimates probabilities\n",
    "        \"\"\"\n",
    "        tmp = X @ self.w + self.w0\n",
    "        prob_y_eq_neg1 = 1 / (1 + np.exp(tmp))\n",
    "        prob_y_eq_1 = 1 / (1 + np.exp(-tmp))\n",
    "        return np.column_stack((prob_y_eq_neg1, prob_y_eq_1))\n",
    "    \n",
    "    def calc_gradient(self, X, y):\n",
    "        return get_grad(X, y, self.w, self.w0, self.gamma, self.beta)\n",
    "    \n",
    "    def calc_loss(self, X, y):\n",
    "        return loss(X, y, self.w, self.w0, self.gamma, self.beta)\n",
    "\n",
    "    def decision_function(self, X):\n",
    "        return self.predict_proba(X)[:, 1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "7SJX8Y6EDvZG"
   },
   "outputs": [],
   "source": [
    "# sample data to test your model\n",
    "from sklearn.datasets import make_classification\n",
    "X, y = make_classification(n_samples=180, n_features=2, n_redundant=0, n_informative=2,\n",
    "                               random_state=42, n_clusters_per_class=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "u41kzwGTDvZH"
   },
   "outputs": [],
   "source": [
    "# a function to plot the decision boundary\n",
    "def plot_decision_boundary(model, X, y):\n",
    "    X1min, X2min = X.min(axis=0)\n",
    "    X1max, X2max = X.max(axis=0)\n",
    "    x1, x2 = np.meshgrid(np.linspace(X1min, X1max, 200),\n",
    "                         np.linspace(X2min, X2max, 200))\n",
    "    ypred = model.predict(np.c_[x1.ravel(), x2.ravel()])\n",
    "    ypred = ypred.reshape(x1.shape)\n",
    "    \n",
    "    plt.contourf(x1, x2, ypred-.5, alpha=.4, colors=['red', 'green']) # 🍉\n",
    "    plt.scatter(X[:,0], X[:,1], c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "mNuYbsAoDvZI",
    "outputId": "fef5b1f8-f50c-4683-cd55-04e3926c1d97"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = Logit(0, 0, lr=.5)\n",
    "y[y == 0] = -1\n",
    "model.fit(X, y)\n",
    "plot_decision_boundary(model, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qi4WRhcADvZI"
   },
   "source": [
    "#### 5. [0.5 points] Plot loss diagram for the model, i.e. show the dependence of the loss function from the gradient descent steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "R2uptHxWiZb9",
    "outputId": "72c99675-08f8-4ffe-bf54-d1ca1592dee2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kIgoUDAQAA2JDUddkRU1Di79LISLyG7eBUFFRgW3btgEAXnjhBdx77704fPiw1wvzpbbLVpw8wyufEpF8uQ2EpUuXori4GLt27cKOHTswa9Ys/PnPf/ZFbT7T3xgCAcDJMgYCEcmX20CoqanBvHnz8NVXXyE1NRWzZ8+G2RxY9yHWaVSIi9azh0BEsuY2EKxWK6xWK3bs2IHk5GSYzWY0NQXetX8GxIXieCknlolIvtwGwo033oikpCRERkZixIgRuOOOO5CamuqL2nxqSN9w1Da2wMRbahKRTLm92unixYtx5513IjY2FgCwZs0aDBs2zOuF+dqQfhEAgKPFNdKNc4iI5KRTRxn9+OOPEAQBL7zwAp599tmAO8oIAPoYghGkVeHY6Vp/l0JE5Bc8yqiVQhCQ0DccR39lIBCRPPEoo3aG9AtHSUUjGsxWf5dCRORzPMqonSH9wgEAx9hLICIZ4lFG7QzqEwaNSoFDJ6r8XQoRkc91+iijuLg4AIF7lBHgvPLp0Msi8CMDgYhkyG0gOBwO5OXl4auvvoLNZsP48eORkJAAlcrtS3ulEZdHYXPhMVTWNiM6XOfvcoiIfMbtkNFf/vIXfPPNN7j33ntx3333Ye/evXj++ed9UZtfDB8YBQDsJRCR7Lj9N3/Hjh147733oFarAQCTJ0/GLbfcgieeeMLrxflDn5hgRIRo8OPxKkwc1cff5RAR+YzbHoIoilIYAIBGo3FZDjSCIGDEwGj8eLwKNrvD3+UQEfmM20AYNmwYVq1ahVOnTqG4uBjPPvsshg4d6ova/OaaITFostjw86kaf5dCROQzbgNh2bJlqK2tRXp6Ou644w5UVlbi6aef7tSb5+XlYcaMGZg6dSpycnLO275161bMmjULt9xyC37/+9+jtrZnHP8/fGAUNGoF/n3E5O9SiIh8xu0cQkhICJ577jmP37isrAxr165Fbm4uNBoN0tPTMXbsWCQkJAAAGhoasHz5crz33nuIjY3Fyy+/jHXr1uGpp57yvBXdTKNWYuTAaPz7qAn3TB0KhSD4uyQiIq+7YCCkpaVd9IV5eXkX3V5UVIRx48YhIsJ5FdGUlBTk5+dj0aJFAJxnQC9btky6iuoVV1zh9j196dqhBuw5YsJ/SuqQ0Dfc3+UQEXndBQOhs8NCF1JeXg6DwSAtG41G7N+/X1qOjIzEzTffDABobm7Ghg0b8Nvf/vaSPrM7jUqIhkop4LtDZQwEIpKFCwbCmDFjLumNHQ4HhHZDLaIouiy3qa+vx0MPPYRhw4bhtttu8+gzoqNDulyfwRDqdp+xw+Px3eFyPDT3GqiUbqdberzOtDnQsM3ywDZ3D6+dbhwXF4fdu3dLyyaTCUaj0WWf8vJy/O53v8O4ceO6dF5DZWUDHA7Pb3lpMITCZHJ//+TrhsRg5/4SfPHtSVw9JMbjz+lJOtvmQMI2ywPb3HkKhXDRf6S99m9vcnIydu3ahaqqKpjNZhQUFGDixInSdrvdjgULFmD69Ol48sknO+w9+NuIQVEI1aux82Cpv0shIvI6r/UQYmNjkZWVhYyMDFitVsyZMweJiYnIzMzE4sWLcebMGRw6dAh2ux2fffYZAGDEiBFYuXKlt0rymEqpwNirYrF972k0mK0ICQrcE/KIiARRFD0fc+khvD1kBACnyuqxfNP3mHtDAlLGXObxZ/UU7FbLA9ssD71uyChQXBYbiqH9wrFtz69dCh8iot6CgdAJN13fHxW1zdj3S4W/SyEi8hoGQidcMzQGkaFabN39q79LISLyGgZCJygVCtxwbV/8dLIaJ8/Ia6ySiOSDgdBJU67pB71Whf+387i/SyEi8goGQifpdSrcPLo/9h6twKky9hKIKPAwEDxw8/X9EKRV4cOv2UsgosDDQPCAXqfG1NZewrFfe8a9G4iIugsDwUPTxlyGiBAN/rXtKBy995w+IqLzMBA8pNUocfukwTheWodvD5X5uxwiom7DQOiCpBFxGBAXii1fHENTs9Xf5RARdQsGQhcoBAHzpg1DfaMVW7445u9yiIi6BQOhiwbEhSJlTH98ta8UP52o8nc5RESXjIFwCWZNGAhjZBA2fXoYTc02f5dDRHRJGAiXQKNWIjP1KlTVWfBG/mH04iuJExExEC7V4L7hmD1pEHYfLseXP5T4uxwioi5jIHSDaWMvw/CBUXhr61H8UsIT1oiod2IgdAOFIGB+2lWIDNVg3XsHUFXX7O+SiIg8xkDoJqF6DRbPGQWrzY6X390Ps4WTzETUuzAQulHfmGAsnDUCJRWNePmdfbBY7f4uiYio0xgI3WzEoGhkpl2Fo7/W4pXcA7DaHP4uiYioUxgIXjDmyljcO30YDh6vwivvH2BPgYh6BQaCl0wc1QcZKVfgwC+VWPv2DzxxjYh6PAaCF02+pi8enDUcv5TU4fm3/s2jj4ioR2MgeNmYK2OxeE4iymvMyP6/u/HLaZ6nQEQ9EwPBB0YOisaTv70OWrUCz731b+zYV8LLXBBRj8NA8JG+hhA8fe9oDOkXgU2fHsaGvEOcVyCiHoWB4EMhQWr8ce7VuG3iIHz/UzmWb/qO92Ymoh6DgeBjCoWAtOTLsfQ31wIAnv3nHuR8foRnNhOR3zEQ/CShbzj+dP8Y3HBtPxTu+RVP/f1b7D1i4twCEfkNA8GPgrQq3DN1KJ747XXQ61RYl3sAL779A06V1fu7NCKSIQZCDzC4bziWzRuNu24cghNn6vGnTd/jfz7+CdX1Fn+XRkQyovJ3AeSkUipw8+j+SB4Zh4+LTmLrnmJ8c6gM/2dUPKaPvQwx4UH+LpGIApxXewh5eXmYMWMGpk6dipycnAvu9+ijjyI3N9ebpfQawTo17rwhAasyx2H8yDh89UMJHn/9G/zPJz/hTFWTv8sjogDmtR5CWVkZ1q5di9zcXGg0GqSnp2Ps2LFISEhw2WfZsmXYtWsXxo0b561SeqWYiCDcO20Y0pIvx6ffnsJX+0rw9f5SjBgUhZuu64cRg6KhEAR/l0lEAcRrgVBUVIRx48YhIiICAJCSkoL8/HwsWrRI2icvLw833nijtA+dLypMh3tuHorU5Mvx5d7T+OKH03jpnf0wRgRhyrV9kTQ8DmHBGn+XSUQBwGuBUF5eDoPBIC0bjUbs37/fZZ8HHngAALBnzx5vlREwwoM1uGXCQMxIGoA9P5uwbc+veLvwGN7d/gtGDorG+JFxGJUQA5WSxwkQUdd4LRAcDgeEdkMaoii6LHeH6OiQLr/WYAjtxkp8KzUuHKmTEnDyTB0Kvy/G9n8X44f3KxCqV2P8qL5IHhmPkR2EQ29uc1exzfLANncPrwVCXFwcdu/eLS2bTCYYjcZu/YzKygY4HJ6fyGUwhMJk6v3H+uuVAlLHXYbpY/rhx+PVKDpYii92FyN/1wkE61S4ZogB1w8z4MoBUegTHx4QbfZEoPycPcE2y0NX26xQCBf9R9prgZCcnIx169ahqqoKQUFBKCgowIoVK7z1cbKmVCiQODgaiYOj0WK14+DxKuz5uRx7jpTj6wOl0KqVuHqoAUP7hmHkoGjERPAQViI6n9cCITY2FllZWcjIyIDVasWcOXOQmJiIzMxMLF68GCNHjvTWR8uaRq3EtUMNuHaoAVabAz+drMK+Xypx6EQ1vv3xDAAgLkqPkYOiceXlkRjaLxx6ndrPVRNRTyCIvfjiOXIfMvJETEwIDvxchoP/qcKB/1Ti8Kka2OwOCAJwmTEUV1wWgSv6R2BI/wiEBAVGQMjx58w2y0OvGzKinkUQBMRHByM+Ohg3j+6PFqsd/ympw+FT1ThSXIMv9p5GwffFEAD0MQRjUHwYBvUJw6A+4egbEwyFguc8EAU6BoJMadRKDBsQiWEDIgEAVpsDx0vr8POpahw9XYt/HzFhx/5SAIBWrcSAuFAM6hOGgfFhuMwYAkNkEE+MIwowDAQCAKhVCgztH4Gh/Z0nCYqiiPJqM/5TWof/lDi/tu4uhs3uHKLTqpXoZwhG/9hQ9DeG4DJjCPoZQqDVKP3ZDCK6BAwE6pAgCIiN0iM2So+k4XEAnL2I0xUNKC5rwKnyBhSXN+DbQ2XYvve08zUADBFBiI/WIz4m2PkYHYw+0XpOXBP1AgwE6jS1SoHL48JweVyYtE4URVTWNqO43BkSpysaUVrZiB9PVEm9CcB5pnVbQMRF62GMCIIxMggx4UFQq3h2NVFPwECgSyIIAmIighATEYRrhp69VInd4UBFbTNKK5pQWtmI0krn4zeHylxuFyoAiAzTwhgRBENrSBgizn4F61TdfoY7EXWMgUBeoVQoEBupR2ykHlcPiZHWi6KI+iYrymvMMFWbUV5jRnm1GaYaM/b9Uom6xhaX99FqlIgO0yEqTIuoUB2iw7SICtM514XrEBWq5fWbiLoJA4F8ShAEhAVrEBasQULf8PO2N7fYYKpplkKiqr4ZVXUWVNU149SZetQ1WV3fD0BYsAZRYTpEhmoREaJBeIjzcUDfCMBmR0SoFiFBah4VReQGA4F6FJ1Ghf7GEPQ3dnzyTIvVjup6CyrrmlFZ14zqurPPz1Q14fDJajS1G5Jqo1Q4gyiiNSwiQrQID9EgPFiDUL0GYXoNQvVqhOo1CNIqOUxFssRAoF5Fo1ZKRz9dSIvVjtrGFggqFU78Wo2aBgtqG1tQU29BTWMLTDVmHP21Fg1ma4evVykFhOo1CA1SIzTYGRTtA6NtOUSvRrBODb1WxRP3KCAwECjgaNRK56S0IRQxIRc+3NVqc6C+qQX1TVbUN7WgrvV522N9Ywvqmqwoq2pCfZMVFqu9w/cRAOh1KgTr1AgOantUI8Rl+ez6YJ1KelQqOP9BPQcDgWRLrVIgKkyHqDBdp/a3WO0uAdJgtqLRbENj89nHhtbn5dVmNDZb0dRsw8WuthWkVSJIq5K+9Oc9V7qsC9KqoNed3U+rUXJuhLoNA4Gok7RqJbThznMnOsvhENFkcQ2NRrMVjc02NJqdAWK22GC22GG22FDb0IIzlU1osthgtthgd3PxRgGATquCvjVYwkK0UAjOuRidRgmdWgmdVgmdRgWtWulc17at9Uvbbh2P2JI3BgKRFykUAkKC1M4ryEZ69lpRFGG1OaRwaHs0W+xoarY6H6V1zi+bA6hvtKCiphkWqx3NLTY0W+wX7aW0p1IKUjhoNe0CRO1c1qqdXxq1Apq25yoFtBolNColtO3XqxWtj85lzrP0fAwEoh5KEARoWv+gRoRoO/Waji6LLIoiWmwONLc4A8LSYpeeN0vP7bCcs9zcYoPF6uy5VNdbYGmxwWJ1oMVqR4vN4XF7VEpBCgiNWgmtSgGNpvVRCpGzQaJWKqBWK6BRKaFWKaBWKaBpfVSrlNJziwjU15ld9mNPp2sYCEQBThAE6T/78GBNt7ynQxRhtTpgsdnR0mKHxdYaFFY7LFY7WqyO1ke7FCLOfVtf026f5hbnUWHSa2zObe6Gyy5GIQhQqxVQKxXQqJ0BIj13EzRqlXMflVKASnru/FKrhHbPW7epnPuefe5c3xt7RAwEIvKYQhCcQ0gaJXDhI4Avid3hgNXmQIvNAVvro3PZDqvVAavdgRarA0F6DSqrGqXtVptd2mZt/xrb2fdrNNtQY7O0e83Z/brrlmEKQYBKJbgEijNghHbP27YJUs+mLVBUreHjGjQCdFoVpk/wzjedgUBEPZJSoYBSo4DOTaemO++YJooi7A7n3I3N7oDNLsJqdwaSze5o97yD9XbxnGUHbDbne0nLdkfre4vSfmaLrfX52def/SwRjg4SakDfCPSJ6NzRcZ5gIBARtRIEwTlU1IPmIBwOsV2giBAADL482iu3DWUgEBH1YAqFAK3COQfk9c/y+icQEVGvwEAgIiIADAQiImrFQCAiIgAMBCIiasVAICIiAL38sNNLOTW8N55WfqnYZnlgm+WhK2129xpBFLvrRG0iIurNOGREREQAGAhERNSKgUBERAAYCERE1IqBQEREABgIRETUioFAREQAGAhERNSKgUBERABkGAh5eXmYMWMGpk6dipycHH+X023Wr1+PmTNnYubMmXj++ecBAEVFRUhLS8PUqVOxdu1aad+ffvoJs2fPRkpKCp588knYbDZ/ld0tniD8jewAAAqASURBVHvuOSxduhRA4Le5sLAQs2fPxvTp0/HnP/8ZQOC3+cMPP5R+t5977jkAgdvmhoYGpKam4tdffwXgeTtLSkpwzz33YNq0aVi4cCEaGxs9K0CUkTNnzohTpkwRq6urxcbGRjEtLU08evSov8u6ZDt37hTnzp0rWiwWsaWlRczIyBDz8vLESZMmiadOnRKtVqt4//33i9u3bxdFURRnzpwp7t27VxRFUXz88cfFnJwcf5Z/SYqKisSxY8eKjz32mGg2mwO6zadOnRInTJgglpaWii0tLeJdd90lbt++PaDb3NTUJI4ePVqsrKwUrVarOGfOHHHbtm0B2eYffvhBTE1NFYcPHy4WFxd36fd5/vz54kcffSSKoiiuX79efP755z2qQVY9hKKiIowbNw4RERHQ6/VISUlBfn6+v8u6ZAaDAUuXLoVGo4FarcbgwYNx4sQJDBgwAP3794dKpUJaWhry8/Nx+vRpNDc34+qrrwYAzJ49u9d+D2pqarB27VosWLAAALB///6AbvPnn3+OGTNmIC4uDmq1GmvXrkVQUFBAt9lut8PhcMBsNsNms8FmsyEkJCQg27xlyxYsW7YMRqMRgOe/z1arFd9//z1SUlJc1nuiV1/t1FPl5eUwGAzSstFoxP79+/1YUfcYMmSI9PzEiRP49NNP8Zvf/Oa8tpaVlZ33PTAYDCgrK/Npvd3lmWeeQVZWFkpLSwF0/PMNpDafPHkSarUaCxYsQGlpKSZPnowhQ4YEdJtDQkLwX//1X5g+fTqCgoIwevTogP05r1y50mXZ03ZWV1cjJCQEKpXKZb0nZNVDcDgcEISzl38VRdFlubc7evQo7r//fjz66KPo379/h20NlO/BO++8g/j4eCQlJUnrLtS2QGmz3W7Hrl27sGrVKrz99tvYv38/iouLA7rNhw8fxnvvvYcvvvgCO3bsgEKhwIkTJwK6zW08/X3uqL2etl9WPYS4uDjs3r1bWjaZTFL3rLfbs2cPFi9ejCeeeAIzZ87Ed999B5PJJG1va2tcXJzL+oqKil75Pfjkk09gMpkwa9Ys1NbWoqmpCadPn4ZSqZT2CbQ2x8TEICkpCVFRUQCAm266Cfn5+QHd5q+//hpJSUmIjo4G4BwG+cc//hHQbW5zbnvctTMqKgr19fWw2+1QKpVd+vsmqx5CcnIydu3ahaqqKpjNZhQUFGDixIn+LuuSlZaW4qGHHsKaNWswc+ZMAMCoUaNw/PhxnDx5Ena7HR999BEmTpyIvn37QqvVYs+ePQCcR3D0xu/Bpk2b8NFHH+HDDz/E4sWLccMNN+Dvf/97QLd5ypQp+Prrr1FXVwe73Y4dO3Zg2rRpAd3mYcOGoaioCE1NTRBFEYWFhQH/u93G03aq1Wpcf/31+OSTTwAAH3zwgcftl1UPITY2FllZWcjIyIDVasWcOXOQmJjo77Iu2T/+8Q9YLBasXr1aWpeeno7Vq1fjD3/4AywWCyZNmoRp06YBANasWYOnnnoKDQ0NGD58ODIyMvxVerfSarUB3eZRo0bhgQcewN133w2r1Yrx48fjrrvuwqBBgwK2zRMmTMChQ4cwe/ZsqNVqjBw5En/4wx8wfvz4gG1zm678Pi9btgxLly7Fq6++ivj4eLz44osefSbvmEZERABkNmREREQXxkAgIiIADAQiImrFQCAiIgAMBCIiasVAIDpHVVUVrrjiCgDAtm3bpKuKdkV9fb3Hhz7u378fzzzzTJc/k6irZHUeApGnbrzxRtx4441dfn1tbS0OHDjg0WuOHTvWq67BQ4GDgUC93oYNG/Duu+8iODgY119/PbZt24bCwkIsXboUNTU1KC4uxuTJkzFnzhxkZ2ejsbERJpMJw4YNw0svvQStVouCggLp6qEjRoyQ3js3NxefffYZXn/9ddTX12PlypU4cuQIrFYrkpKS8Oijj0KlUmHkyJGYP38+du7cifLycukEsscffxzNzc2YNWsWcnNzXS65sHv3bqxevRoOhwMA8OCDDyIxMRF//etfUV9fj8cffxzPPvssCgsL8eqrr8JqtUKn0+Gxxx7DNddcg3Xr1uHkyZM4c+aM1J6VK1ciJCQEb731FjZv3gy1Wg2tVovs7GwkJCT4/GdDvcylXL+byN+++uorMSUlRaytrRUdDof4+OOPi1OmTBFFURQfe+wx8d5775X2Xb16tfjBBx+IoiiKLS0tYmpqqpifny+aTCbxuuuuk+6N8dprr4lDhw4VRVEU33vvPXH+/PmiKIri0qVLxTfffFMURVG02Wziww8/LG7YsEEURVEcOnSo+L//+7+iKIrigQMHxBEjRojNzc1icXGxePXVV3dYe0ZGhnTt+p9++klcvnz5eZ95/PhxMTU1VayqqhJFURSPHDkijh8/XmxsbBT/+te/ihMnThRNJpNot9vFJUuWiKtXrxZtNps4fPhwsaysTBRFUXz//ffFzZs3X+q3mmSAPQTq1b788ktMmzYNYWFhAIB77rkH33zzjbT9uuuuk54/8sgj2LlzJzZu3IgTJ06gvLwcTU1N2LNnD4YOHSr9Bz137twOT/nfvn07Dhw4gHfffRcA0Nzc7LK9bWhp+PDhaGlpQVNT00Vrnz59OrKzs1FYWIjk5GQsWbLkvH3aehzz5s2T1gmCgFOnTgEApk2bhpiYGADAnDlzsGrVKjz22GOYNm0a0tPTMXnyZEyYMAGTJk26aC1EAIeMqJdTqVQQ2119pf2QDADo9Xrp+ZIlS2C32zF9+nRMnjwZpaWl0mvbv0fb9eTP5XA48PLLL2Pw4MEAgLq6OpfLC2u1WgBnLzksurkqTHp6OqZMmYKdO3dix44dWL9+/Xk3NHE4HEhKSsJLL70krSstLYXRaMTnn3/u0l6HwwGFwnmcyJo1a3DkyBEUFRVhw4YN+PDDD/Hyyy9ftB4iHmVEvdqkSZNQUFCA+vp6AJD+e+/I119/jYceeggzZswAAOzbtw92ux2jR4/GsWPHcPjwYQDOeYOOTJgwAW+88QZEUURLSwsWLlyIf/7znxetT6VSwW63dxgO6enp0r1xV6xYgbq6OphMJiiVSukeuUlJSdi5cyd++eUXAM4e0S233CL1TrZt24b6+no4HA5s2bIFU6ZMQVVVFSZNmoSIiAjMmzcP//3f/+3xxDbJE3sI1KslJSXhzjvvxNy5c6HT6TBkyBAEBQV1uG9WVhYeeugh6PV6hISEYPTo0Th16hSioqKwZs0aPPzww1Cr1Rg9enSHr3/yySexcuVKpKWlwWq1Ijk5GQ888MBF6zMYDEhMTMTMmTORk5ODyMhIadvDDz+MVatW4aWXXoIgCFi0aBH69esHu92OV155BYsWLcL69euRnZ2NJUuWQBRFqFQqvPrqqwgODgbgvEdCZmYmqqurMXr0aCxYsAA6nQ4LFy7EvHnzoNPpoFQqL+nQWZIPXu2UerUDBw5g79690rH+mzZtwr59+1yGWALVunXrUF1dzXMWqNuwh0C92sCBA7Fx40Zs2bIFgiAgPj4eK1as8HdZRL0SewhERASAk8pERNSKgUBERAAYCERE1IqBQEREABgIRETUioFAREQAgP8P5ZFmxu6BaL8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ylabel('loss function')\n",
    "plt.xlabel('gradient steps')\n",
    "plt.plot(model.loss_history)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0FhSCAv_DvZJ"
   },
   "source": [
    "## PART 2: Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lYyGsSxEDvZJ"
   },
   "source": [
    "#### 6. [1 point] Using the same dataset, train SVM Classifier from Sklearn.\n",
    "Investigate how different parameters influence the quality of the solution:\n",
    "+ Try several kernels: Linear, Polynomial, RBF (and others if you wish). Some Kernels have hypermeters: don't forget to try different.\n",
    "+ Regularization coefficient \n",
    "\n",
    "Show how these parameters affect accuracy, roc_auc and f1 score. \n",
    "Make plots for the dependencies between metrics and parameters. \n",
    "Try to formulate conclusions from the observations. How sensitive are kernels to hyperparameters? How sensitive is a solution to the regularization? Which kernel is prone to overfitting?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "Nicu_O3IDvZK"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score, roc_auc_score, f1_score\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "rom = {\n",
    "  \"linear\": {\"arguments\": dict(kernel='linear'), \"color\": 'C0'},\n",
    "  # \"poly deg=2\": {\"arguments\": dict(kernel='poly', degree=2), \"color\": 'C5'},\n",
    "  \"poly deg=3\": {\"arguments\": dict(kernel='poly', degree=3), \"color\": 'C2'},\n",
    "  \"poly deg=4\": {\"arguments\": dict(kernel='poly', degree=4), \"color\": 'C3'},\n",
    "  \"rbf ɣ=0.25\": {\"arguments\": dict(kernel='rbf', gamma=0.25), \"color\": 'C4'},\n",
    "  \"rbf ɣ=0.5\": {\"arguments\": dict(kernel='rbf', gamma=0.5), \"color\": 'C1'},\n",
    "  \"sigmoid\": {\"arguments\": dict(kernel='sigmoid'), \"color\": 'C6'},\n",
    "}\n",
    "\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, test_size=0.2, random_state=122)\n",
    "\n",
    "def calc_scores(dest, clf, X, y):\n",
    "  ypred = clf.predict(X)\n",
    "  dest[\"accurancy\"].append(accuracy_score(y, ypred))\n",
    "  dest[\"roc_auc\"].append(roc_auc_score(y, ypred))\n",
    "  dest[\"f1\"].append(f1_score(y, ypred))\n",
    "\n",
    "reg_coeff = np.logspace(-2, 2, num=10)\n",
    "for ker in rom.values():\n",
    "  ker[\"test\"] = {\"accurancy\": [], \"roc_auc\": [], \"f1\": [], \"linestyle\": '-'}\n",
    "  ker[\"train\"] = {\"accurancy\": [], \"roc_auc\": [], \"f1\": [], \"linestyle\": '--'}\n",
    "  for reg in reg_coeff:\n",
    "    clf = SVC(**ker[\"arguments\"], C=reg)\n",
    "    clf.fit(Xtrain, ytrain)\n",
    "    calc_scores(ker[\"test\"], clf, Xtest, ytest)\n",
    "    calc_scores(ker[\"train\"], clf, Xtrain, ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 856.8x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.axes\n",
    "%config InlineBackend.figure_formats = ['svg']\n",
    "\n",
    "def plot(ax: matplotlib.axes.Axes, ker=\"linear\", set=None, score=\"accurancy\"):\n",
    "  ax.set_xscale(\"log\")\n",
    "  ax.set_ylabel(score)\n",
    "  ax.set_xlabel(\"regularization coefficient\")\n",
    "  ax.set_ylim(0.45, 1.05)\n",
    "\n",
    "  label = ker\n",
    "  if set:\n",
    "    label = ker + \" \" + set\n",
    "  else:\n",
    "    set = \"test\"\n",
    "\n",
    "  ax.plot(reg_coeff, rom[ker][set][score], rom[ker][set][\"linestyle\"], label=label, c=rom[ker][\"color\"])\n",
    "  pass\n",
    "\n",
    "fig, axs = plt.subplots(1,3, figsize=(11.9, 3))\n",
    "fig.subplots_adjust(left=0.04, right=0.99)\n",
    "fig.suptitle(\"Performance metrics comparison\", fontsize=20)\n",
    "for ax, score in zip(axs, [\"accurancy\", \"roc_auc\", \"f1\"]):\n",
    "  for k in rom:\n",
    "    plot(ax, k, score=score)\n",
    "  ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 856.8x504 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def flatten(t):\n",
    "  return [item for sublist in t for item in sublist]\n",
    "\n",
    "fig, axs = plt.subplots(2,3, figsize=(11.9, 7))\n",
    "fig.subplots_adjust(left=0.04, right=0.99)\n",
    "fig.suptitle(\"Overfitting demonstration\", fontsize=20)\n",
    "for ax, k in zip(flatten(axs), rom.keys()):\n",
    "  plot(ax, k, set=\"train\")\n",
    "  plot(ax, k, set=\"test\")\n",
    "  ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На коэффициент регуляризации больше всех реагирует полиномный кёрнел четвёртого порядка, а все остальные доситигают 100%ной точности на почти всех значениях $C$, кроме сигмойда, которой вообще ведёт себя очень плохо и $C$ ему совсем не помогает.\n",
    "Что насчёт оверфитинга, он есть в сигмойде и в томже `poly deg=4`. (на графике пунктирная линия выше обычной)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sY8q6JdCDvZK"
   },
   "source": [
    "## PART 3: Natural Language Processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eD4xKhYfDvZK"
   },
   "source": [
    "#### 7. [2 point] Form the dataset\n",
    "\n",
    "We are going to form a dataset that we will use in the following tasks for binary and multiclass classification\n",
    "\n",
    "0. Choose **six** authors that you like (specify who you've chosen) and download the <a href=\"https://www.kaggle.com/d0rj3228/russian-literature?select=prose\">relevant data</a> from **prose** section\n",
    "1. Build your own dataset for these authors: [0.5 point]\n",
    "    * divide each text into sentences such that we will have two columns: *sentence* and *target author*, each row will contain one sentence and one target\n",
    "    * drop sentences where N symbols in a sentence < 15\n",
    "    * fix random state and randomly choose sentences in the folowing proportion \"30k : 15k : 7k : 20k: 40k : 3k\" for the authors respectively\n",
    "    \n",
    "    sample data may look like:\n",
    "    \n",
    "    <center> \n",
    "    <table>\n",
    "        <tr>\n",
    "            <th> sentence </th>\n",
    "            <th> author </th>\n",
    "        </tr> \n",
    "        <tr><td> Несколько лет тому назад в одном из своих поместий жил старинный русской барин, Кирила Петрович Троекуров. </td><td> Пушкин </td><td> \n",
    "        <tr><td> Уже более недели приезжий господин жил в городе, разъезжая по вечеринкам и обедам и таким образом проводя, как говорится, очень приятно время. </td><td> Гоголь </td><td> \n",
    "        <tr><td> ... </td><td> ... </td><td> \n",
    "        <tr><td> Я жил недорослем, гоняя голубей и играя в чехарду с дворовыми мальчишками. </td><td> Пушкин </td><td>         \n",
    "    </table>\n",
    "</center>\n",
    "     \n",
    "2. Preprocess (tokenize and clean) the dataset  [1.5 point]\n",
    "    * tokenize, remove all stop words (nltk.corpus.stopwords), punctuation (string.punctuation) and numbers\n",
    "    * convert to lower case and lemmatize the words\n",
    "    * vectorize words using both **bag of words** and **tf-idf** (use sklearn)\n",
    "    * observe and describe the difference between vectorized output (what do numbers look like after transformations and what do they represent?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "from glob import glob\n",
    "\n",
    "# awk $'length>=15 && /[.,?!…–\\-:;()«»\"—]/ {gsub(/\\u00a0/, \" \"); $1=$1; print}'\n",
    "def load_text(dir):\n",
    "  res = []\n",
    "  for file in glob(f\"prose/{dir}/*.txt\"):\n",
    "    for line in open(file):\n",
    "      line = line.strip()\n",
    "      if len(line) < 15:\n",
    "        continue\n",
    "      if not re.search('[.,?!…–\\-:;()«»\"—]', line):\n",
    "        continue\n",
    "      res.append(line)\n",
    "  return re.sub(r'\\s+', ' ', ' '.join(res))\n",
    "\n",
    "def sentences(text):\n",
    "  # code \"inspired\" by https://github.com/mediacloud/sentence-splitter\n",
    "  text = re.sub(r'([.?!…])(?: [-–—]| --)? («?[A-ZА-ЯЁÀ-Ý][a-zа-яёà-ÿ]*)', '\\\\1\\n\\\\2', text)\n",
    "  text = text.replace('…', '...')\n",
    "  return [e for e in text.split('\\n') if len(e) >= 15]\n",
    "\n",
    "romen = [\"Dostoevsky\", \"Chekhov\", \"Pushkin\", \"Turgenev\", \"Gorky\", \"Herzen\"]\n",
    "romru = [\"Достоевский\", \"Чехов\", \"Пушкин\", \"Тургенев\", \"Горький\", \"Герцен\"]\n",
    "romsize = [30_000, 15_000, 7_000, 20_000, 40_000, 3_000]\n",
    "\n",
    "np.random.seed(122)\n",
    "col1 = []\n",
    "col2 = []\n",
    "for en, ru, l in zip(romen, romru, romsize):\n",
    "  col1 += list(np.random.choice(sentences(load_text(en)), l, replace=False))\n",
    "  col2 += [ru]*l\n",
    "\n",
    "df = pd.DataFrame(data={\"sentence\": col1, \"author\": col2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sentence</th>\n",
       "      <th>author</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Весь город назвали, а меня нет!</td>\n",
       "      <td>Достоевский</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Я только махнул рукой.</td>\n",
       "      <td>Достоевский</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Тут надо плакать, а не куражиться\".</td>\n",
       "      <td>Достоевский</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Да, ты, может быть, это знаешь», – прибавил он...</td>\n",
       "      <td>Достоевский</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Совсем, совсем, я тебе скажу, исчез прежний до...</td>\n",
       "      <td>Достоевский</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114995</th>\n",
       "      <td>Что тебе? - отвечала Глафира.</td>\n",
       "      <td>Герцен</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114996</th>\n",
       "      <td>Сельский священник, ходивший поздравить Бельто...</td>\n",
       "      <td>Герцен</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114997</th>\n",
       "      <td>Тут-то я вас и ждал.</td>\n",
       "      <td>Герцен</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114998</th>\n",
       "      <td>Вот отчего люди, провозглашавшие республику, с...</td>\n",
       "      <td>Герцен</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114999</th>\n",
       "      <td>Погодите здесв, - сказал князь Ивану Сергеевич...</td>\n",
       "      <td>Герцен</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>115000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 sentence       author\n",
       "0                         Весь город назвали, а меня нет!  Достоевский\n",
       "1                                  Я только махнул рукой.  Достоевский\n",
       "2                     Тут надо плакать, а не куражиться\".  Достоевский\n",
       "3       Да, ты, может быть, это знаешь», – прибавил он...  Достоевский\n",
       "4       Совсем, совсем, я тебе скажу, исчез прежний до...  Достоевский\n",
       "...                                                   ...          ...\n",
       "114995                      Что тебе? - отвечала Глафира.       Герцен\n",
       "114996  Сельский священник, ходивший поздравить Бельто...       Герцен\n",
       "114997                               Тут-то я вас и ждал.       Герцен\n",
       "114998  Вот отчего люди, провозглашавшие республику, с...       Герцен\n",
       "114999  Погодите здесв, - сказал князь Ивану Сергеевич...       Герцен\n",
       "\n",
       "[115000 rows x 2 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[nltk_data] Downloading package punkt to\n",
      "[nltk_data]     C:\\Users\\user\\AppData\\Roaming\\nltk_data...\n",
      "[nltk_data]   Package punkt is already up-to-date!\n",
      "[nltk_data] Downloading package stopwords to\n",
      "[nltk_data]     C:\\Users\\user\\AppData\\Roaming\\nltk_data...\n",
      "[nltk_data]   Package stopwords is already up-to-date!\n"
     ]
    }
   ],
   "source": [
    "import nltk\n",
    "from nltk.corpus import stopwords\n",
    "from nltk.tokenize import word_tokenize\n",
    "import pymorphy2\n",
    "\n",
    "nltk.download('punkt')\n",
    "nltk.download('stopwords')\n",
    "\n",
    "lemmatizer = pymorphy2.MorphAnalyzer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import string \n",
    "\n",
    "stop_words = set(stopwords.words('russian'))\n",
    "stop_words |= set(string.punctuation)\n",
    "stop_words |= set(string.digits)\n",
    "stop_words |= {'…', '...', '..'}\n",
    "\n",
    "def lemma(word):\n",
    "  return lemmatizer.parse(word)[0].normal_form.lower()\n",
    "\n",
    "def lemma_sent(s):\n",
    "  return [lemma(t.lower()) for t in word_tokenize(s) if t.lower() not in stop_words and t.isalpha()]\n",
    "\n",
    "def lemma_sents(data):\n",
    "  return [lemma_sent(sent) for sent in data]\n",
    "\n",
    "df[\"lemma\"] = lemma_sents(df[\"sentence\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import CountVectorizer, TfidfVectorizer\n",
    "\n",
    "joined_lemma = [' '.join(e) for e in df[\"lemma\"]]\n",
    "\n",
    "def columnify(sparsematrix):\n",
    "  t = np.asarray(sparsematrix.todense())\n",
    "  return [t[i] for i in range(t.shape[0])]\n",
    "\n",
    "df[\"bag\"] = columnify(CountVectorizer(max_features=1000).fit_transform(joined_lemma))\n",
    "df[\"tfidf\"] = columnify(TfidfVectorizer(max_features=1000).fit_transform(joined_lemma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sentence</th>\n",
       "      <th>author</th>\n",
       "      <th>lemma</th>\n",
       "      <th>bag</th>\n",
       "      <th>tfidf</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Весь город назвали, а меня нет!</td>\n",
       "      <td>Достоевский</td>\n",
       "      <td>[весь, город, назвать]</td>\n",
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       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Я только махнул рукой.</td>\n",
       "      <td>Достоевский</td>\n",
       "      <td>[махнуть, рука]</td>\n",
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       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Тут надо плакать, а не куражиться\".</td>\n",
       "      <td>Достоевский</td>\n",
       "      <td>[плакать, куражиться]</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Да, ты, может быть, это знаешь», – прибавил он...</td>\n",
       "      <td>Достоевский</td>\n",
       "      <td>[это, знать, прибавить, проникновенный, раздум...</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Совсем, совсем, я тебе скажу, исчез прежний до...</td>\n",
       "      <td>Достоевский</td>\n",
       "      <td>[ты, сказать, исчезнуть, прежний, доктор, кото...</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114995</th>\n",
       "      <td>Что тебе? - отвечала Глафира.</td>\n",
       "      <td>Герцен</td>\n",
       "      <td>[ты, отвечать, глафира]</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114996</th>\n",
       "      <td>Сельский священник, ходивший поздравить Бельто...</td>\n",
       "      <td>Герцен</td>\n",
       "      <td>[сельский, священник, ходить, поздравить, бель...</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114997</th>\n",
       "      <td>Тут-то я вас и ждал.</td>\n",
       "      <td>Герцен</td>\n",
       "      <td>[ждать]</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114998</th>\n",
       "      <td>Вот отчего люди, провозглашавшие республику, с...</td>\n",
       "      <td>Герцен</td>\n",
       "      <td>[отчий, человек, провозглашать, республика, сд...</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...</td>\n",
       "      <td>[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114999</th>\n",
       "      <td>Погодите здесв, - сказал князь Ивану Сергеевич...</td>\n",
       "      <td>Герцен</td>\n",
       "      <td>[погодить, здесв, сказать, князь, иван, сергее...</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>115000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 sentence       author  \\\n",
       "0                         Весь город назвали, а меня нет!  Достоевский   \n",
       "1                                  Я только махнул рукой.  Достоевский   \n",
       "2                     Тут надо плакать, а не куражиться\".  Достоевский   \n",
       "3       Да, ты, может быть, это знаешь», – прибавил он...  Достоевский   \n",
       "4       Совсем, совсем, я тебе скажу, исчез прежний до...  Достоевский   \n",
       "...                                                   ...          ...   \n",
       "114995                      Что тебе? - отвечала Глафира.       Герцен   \n",
       "114996  Сельский священник, ходивший поздравить Бельто...       Герцен   \n",
       "114997                               Тут-то я вас и ждал.       Герцен   \n",
       "114998  Вот отчего люди, провозглашавшие республику, с...       Герцен   \n",
       "114999  Погодите здесв, - сказал князь Ивану Сергеевич...       Герцен   \n",
       "\n",
       "                                                    lemma  \\\n",
       "0                                  [весь, город, назвать]   \n",
       "1                                         [махнуть, рука]   \n",
       "2                                   [плакать, куражиться]   \n",
       "3       [это, знать, прибавить, проникновенный, раздум...   \n",
       "4       [ты, сказать, исчезнуть, прежний, доктор, кото...   \n",
       "...                                                   ...   \n",
       "114995                            [ты, отвечать, глафира]   \n",
       "114996  [сельский, священник, ходить, поздравить, бель...   \n",
       "114997                                            [ждать]   \n",
       "114998  [отчий, человек, провозглашать, республика, сд...   \n",
       "114999  [погодить, здесв, сказать, князь, иван, сергее...   \n",
       "\n",
       "                                                      bag  \\\n",
       "0       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "1       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "2       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "3       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "4       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "...                                                   ...   \n",
       "114995  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "114996  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "114997  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "114998  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "114999  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...   \n",
       "\n",
       "                                                    tfidf  \n",
       "0       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "1       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "2       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "3       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "4       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "...                                                   ...  \n",
       "114995  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "114996  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "114997  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "114998  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "114999  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...  \n",
       "\n",
       "[115000 rows x 5 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`bag of words` просто считает количество слов, а `tfidf` ещё их нормирует на частоту этого слова во всём датасете.\n",
    "Тоесть получается что, когда у нас в `bag of words` $0$ в `tfidf` тоже будет $0$, а когда в `bag of words` $1$ в `tfidf` будет какое-то дробное число."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7019 нулевых предложений\n"
     ]
    }
   ],
   "source": [
    "print(sum(np.sum(np.vstack(df[\"bag\"]), axis=1) == 0), \"нулевых предложений\")\n",
    "df = df.loc[np.sum(np.vstack(df[\"bag\"]), axis=1) != 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "У нас после векторизации получилось очень много предложений, в которых нет не одного слова из самых популярных 1000, и поэтому в их векторной репрезентации одни нули. Такие предложения невозможно склацифицировать к какому либо автору, и им нечего делать в датасете. Их придётся удалить. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LuTi3rvnDvZL"
   },
   "source": [
    "###  Binary classification\n",
    "\n",
    "#### 8. [2 point] Train model using Logistic Regression (your own) and SVC (SVM can be taken from sklearn) \n",
    "\n",
    "##### 1. [1 point]\n",
    "* choose *two* authors from the dataset that you have formed in the previous task\n",
    "* check the balance of the classes\n",
    "* divide the data into train and test samples with 3/4 split rate (don't forget to fix the random state)\n",
    "* train the models using cross validation\n",
    "* plot confusion matrix for train and test samples\n",
    "* compute all possible and relevant metrics for test sample (useful to check the seminars 5 and 6, use sklearn) \n",
    "* make conclusions about the performance of your models\n",
    "\n",
    "##### 2. [1 point]\n",
    "* using GridSearchCV - find the best parameters for the models (by ROC_AUC score)\n",
    "* make several plots to address the dependence between ROC_AUC score and parameters\n",
    "* make conclusions about the models\n",
    "\n",
    "**HINT:** In the task 8.2 you should analyze models for binary classification task. How do you think the AUC_ROC should be high? Is the 0.6 enough for us?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "XZUP1HqFDvZL"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "У Достоевскийа 28314 предложений, а у Горькийа – 37429\n",
      "Баланс неочень… один класс в 1.32 раза больше другого\n"
     ]
    }
   ],
   "source": [
    "authorpair = (\"Достоевский\", \"Горький\")\n",
    "df2 = df[(df[\"author\"] == authorpair[0]) | (df[\"author\"] == authorpair[1])]\n",
    "count1 = sum(df2[\"author\"] == authorpair[0])\n",
    "count2 = sum(df2[\"author\"] == authorpair[1])\n",
    "factor = max(count1, count2)/min(count1, count2)\n",
    "print(f\"У {authorpair[0]}а {count1} предложений, а у {authorpair[1]}а – {count2}\")\n",
    "print(f\"Баланс неочень… один класс в {factor:.2f} раза больше другого\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# я выбрал tfidf, потому что это более sophisticated алгоритм, и зачемто же мы его считали🙃 \n",
    "y = np.array([-1, 1])[(df2[\"author\"] == authorpair[0]) + 0]\n",
    "X = np.vstack(df2[\"tfidf\"])\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, test_size=0.25, random_state=69)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_score, recall_score, confusion_matrix\n",
    "\n",
    "# код из семенара\n",
    "def show_results(test_y, pred, name=\"SVC\", labels=authorpair[::-1]):\n",
    "    print(f\"{name} Precision:  {precision_score(test_y, pred, average='macro', zero_division=0):.2f}\")\n",
    "    print(f\"{name} Recall:     {recall_score(test_y, pred, average='macro'):.2f}\")\n",
    "    print(f\"{name} F1-measure: {f1_score(test_y, pred, average='macro'):.2f}\")\n",
    "    print(f\"{name} Accuracy:   {accuracy_score(test_y, pred):.2f}\")\n",
    "    # print(\"ROC-AUC  =  {0:6.2f}\".format(roc_auc_score(test_y, proba[:,1]),))\n",
    "\n",
    "    #classification_report\n",
    "    sns.heatmap(data=confusion_matrix(test_y, pred), annot=True, fmt=\"d\", cbar=False, xticklabels=labels, yticklabels=labels)\n",
    "    plt.ylabel(\"True\")\n",
    "    plt.xlabel(\"Predicted\")\n",
    "    plt.title(f\"Confusion matrix for {name}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Сначала прогоняем SVC из sklearn-а"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC Precision:  0.77\n",
      "SVC Recall:     0.76\n",
      "SVC F1-measure: 0.76\n",
      "SVC Accuracy:   0.77\n"
     ]
    },
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clfsvc = SVC(kernel='linear', C=1, random_state=420)\n",
    "clfsvc.fit(Xtrain, ytrain)\n",
    "ypred = clfsvc.predict(Xtest)\n",
    "show_results(ytest, ypred, \"SVC\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC on training data Precision:  0.78\n",
      "SVC on training data Recall:     0.77\n",
      "SVC on training data F1-measure: 0.77\n",
      "SVC on training data Accuracy:   0.78\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_results(ytrain, clfsvc.predict(Xtrain), \"SVC on training data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'fit_time': array([1052.08774757, 1052.06847811, 1058.21385455, 1053.52146435,\n",
       "        1055.27611804]),\n",
       " 'score_time': array([207.26501155, 205.84223866, 206.81292343, 206.81111312,\n",
       "        207.48642182]),\n",
       " 'test_score': array([0.84988123, 0.84109511, 0.84864892, 0.84628326, 0.85400778])}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_validate\n",
    "\n",
    "cvclf = SVC(kernel='linear', C=1, random_state=420)\n",
    "scores = cross_validate(cvclf, Xtrain, ytrain, cv=5, scoring='roc_auc')\n",
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### А потом наш Logistic Regression, тоесть Logit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logit Precision:  0.65\n",
      "Logit Recall:     0.63\n",
      "Logit F1-measure: 0.63\n",
      "Logit Accuracy:   0.65\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = Logit(0, 0, lr=.7)\n",
    "clf.fit(Xtrain, ytrain)\n",
    "ypred = clf.predict(Xtest)\n",
    "show_results(ytest, ypred, \"Logit\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logit on training data Precision:  0.65\n",
      "Logit on training data Recall:     0.63\n",
      "Logit on training data F1-measure: 0.63\n",
      "Logit on training data Accuracy:   0.65\n"
     ]
    },
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_results(ytrain, clf.predict(Xtrain), \"Logit on training data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'fit_time': array([38.74202132, 38.64661908, 38.43767357, 38.63636303, 38.63344264]),\n",
       " 'score_time': array([0.00792837, 0.00786281, 0.00782347, 0.00782895, 0.00779581]),\n",
       " 'test_score': array([0.680916  , 0.67970975, 0.68829647, 0.68445313, 0.69501054])}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cvclf = Logit(0, 0, lr=.7)\n",
    "scores = cross_validate(cvclf, Xtrain, ytrain, cv=5, scoring='roc_auc')\n",
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Результаты классификаторов, мягко говоря, получились плохие.\n",
    "Матрицы путаницы (конфьюжена), в хороших сличиях, когда путаницы (конфьюжена) относительно мало, должны выглядить диагонально.\n",
    "То есть оба значения на диагонали должны быть больше обоих значений на на диагонали (плучается что на обратной диагонали, тк матрица 2х2).\n",
    "Это означает что ошибочных результатов всегда меньше чем верных.\n",
    "Хотя, в случиях когда у нас сильно несбалансированны классы, например при диагностики редких заболеваний, допустимо что вероятность false positive-а больше чем true positive-а, но к нам это не относится, тк классы у нас относительно сбалансированны. \n",
    "Хорошая матрица путаницы (конфьюжена) выглядит так:\n",
    "\n",
    "<center><code style=\"white-space: pre-wrap; font-family: consolas, monospace;\"\n",
    ">┌───┬───┐\n",
    "│ 9 > 1 │\n",
    "├─v─┼─^─┤\n",
    "│ 1 < 9 │\n",
    "└───┴───┘</code></center>\n",
    "\n",
    "А у нас матрицы путаницы (конфьюжена) не хорошие. 🙁\n",
    "В них всегда false Горького больше чем true Достоевского.\n",
    "И все метрики поулчаются гдето между $0.6$ и $0.7$.\n",
    "To put this in perspective, рандомный классификатор будет довать метрики $0.5$, и наша модель получается только на $20\\%$ лучше полного рандома…\n",
    "\n",
    "Библиотечный Support Vector Classifier дал нам лучшие резальтаты и красивые матрицы путаницы (конфьюжена) а также метрики по $0.8$. Он молодец.\n",
    "\n",
    "Спойлер: сделав GridSeaech мы выясним, что надо было брать `Logit(1, 0)` а не `Logit(0, 0)`, и тогда он станет сравним с SVC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Теперь начинается больно от GridSearch-а"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C': 1, 'kernel': 'linear'}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "# если тут не поставить max_iter и n_jobs=-1 он будет считать 10 часов 😨\n",
    "params = {'C': [0.1, 1, 10], 'kernel': [\"linear\", \"poly\", \"rbf\"]}\n",
    "gscv = GridSearchCV(SVC(max_iter=10000), params, scoring='roc_auc', cv=3, n_jobs=-1)\n",
    "gscv.fit(Xtrain, ytrain)\n",
    "gscv.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "def destringify_array(arr):\n",
    "  if type(arr[0]) == str:\n",
    "    return np.arange(len(arr))\n",
    "  else:\n",
    "    return arr\n",
    "\n",
    "def plot3d(gscv, title=None):\n",
    "  keys = list(gscv.best_params_.keys())\n",
    "  xarr = destringify_array(gscv.param_grid[keys[0]])\n",
    "  yarr = destringify_array(gscv.param_grid[keys[1]])\n",
    "  xshape = len(xarr)\n",
    "  yshape = len(yarr)\n",
    "  \n",
    "  z = np.reshape(gscv.cv_results_[\"mean_test_score\"], (xshape,yshape)).T\n",
    "  mesh = np.meshgrid(xarr, yarr)\n",
    "\n",
    "  ax = plt.axes(projection=\"3d\")\n",
    "\n",
    "  ax.set_xlabel(keys[0])\n",
    "  ax.set_xticks(xarr)\n",
    "  ax.set_xticklabels(gscv.param_grid[keys[0]])\n",
    "  ax.set_ylabel(keys[1])\n",
    "  ax.set_yticks(yarr)\n",
    "  ax.set_yticklabels(gscv.param_grid[keys[1]])\n",
    "  ax.set_zlabel(\"Score\")\n",
    "  ax.set_title(title)\n",
    "\n",
    "  ax.scatter3D(*mesh, z, c=\"green\")\n",
    "  ax.plot_surface(*mesh, z, alpha=0.3)\n",
    "  plt.show()\n",
    "\n",
    "def plot4d(gscv, title=None):\n",
    "  keys = list(gscv.best_params_.keys())\n",
    "  xarr = destringify_array(gscv.param_grid[keys[0]])\n",
    "  yarr = destringify_array(gscv.param_grid[keys[1]])\n",
    "  warr = destringify_array(gscv.param_grid[keys[2]])\n",
    "  xshape = len(xarr)\n",
    "  yshape = len(yarr)\n",
    "  wshape = len(warr)\n",
    "  \n",
    "  z = np.reshape(gscv.cv_results_[\"mean_test_score\"], (xshape,yshape,wshape))\n",
    "  mesh = np.meshgrid(yarr, xarr)\n",
    "\n",
    "  ax = plt.axes(projection=\"3d\")\n",
    "\n",
    "  ax.set_xlabel(keys[0])\n",
    "  ax.set_xticks(xarr)\n",
    "  ax.set_xticklabels(gscv.param_grid[keys[0]])\n",
    "  ax.set_ylabel(keys[1])\n",
    "  ax.set_yticks(yarr)\n",
    "  ax.set_yticklabels(gscv.param_grid[keys[1]])\n",
    "  ax.set_zlabel(\"Score\")\n",
    "  ax.set_title(title)\n",
    "\n",
    "  ax.scatter3D(*mesh[::-1], z[:,:,0], c=\"green\")\n",
    "  ax.plot_surface(*mesh[::-1], z[:,:,0], alpha=0.3)\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3d(gscv, \"Support Vector Classifier\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'beta': 1, 'gamma': 0, 'lr': 0.01}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prams = {'lr': [0.01, 0.1, 0.7], 'beta': [0, 0.1, 1, 2], 'gamma': [0, 0.1, 1, 2]}\n",
    "gscv2 = GridSearchCV(Logit(), prams, scoring='roc_auc', cv=3, n_jobs=-1)\n",
    "gscv2.fit(Xtrain, ytrain)\n",
    "gscv2.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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   "source": [
    "plot4d(gscv2, \"Logistic Regression\")"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Параметр `learning_rate`, по какой-то неведомой причине, совсем не влияет на метрику ROC_AUC.\n",
    "Ко всем остальным параметрам модели чуствительны, но хаотично: даже потратив пять часов на гридсёрч, у нас неполусчилось найти такие параметры, чтобы ROC_AUC был больше того, с которого мы начинали. Получилось найти только самые плохие комбинации параметров, а самый лучший мало чем отличается от того, который мы получили тыкнув здравым смыслом в пространство всех параметров. \n",
    "\n",
    "Хотя, если внимательно посмотреть на график, что easier said then done, потому что 3d графики вообще сложны к восприятию, особенно если их нельзя вращять и они рендерятся на cpu (у меня уже от них глаза болят), можно заметить, что для Logistic Regression в точках $\\beta \\ge 1,\\, \\gamma=0$ и $\\beta = 0.1$ результаты получаются сильно лучше (на $20\\%$) изначальных. "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "5G1kt0qbDvZL"
   },
   "source": [
    "#### 9. [1 point] Analysing ROC_AUC\n",
    "\n",
    "It is possible to control the proportion of statistical errors of different types using different thresholds for choosing a class. Plot ROC curves for Logistic Regression and SVC, show the threshold on ROC curve plots. Choose such a threshold that your models have no more than 30% of false positive errors rate "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "id": "BZ2GZ8-uDvZL"
   },
   "outputs": [],
   "source": [
    "logit_proba = clf.decision_function(Xtest)\n",
    "svc_proba = clfsvc.decision_function(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_threshold(proba, name=\"Logistic Regression\", desiredFPR=0.3):\n",
    "  fpr, tpr, threshold = roc_curve(ytest, proba)\n",
    "\n",
    "  plt.title(f\"ROC curve plot for {name}\")\n",
    "  plt.xlabel(\"False Positive Rate\")\n",
    "  plt.ylabel(\"True Positive Rate\")\n",
    "  plt.plot(fpr, tpr, zorder=10)\n",
    "  plt.plot([desiredFPR, desiredFPR], [0, 1], zorder=10) # нам в условие написали что false positive rate нужен 30%\n",
    "\n",
    "  idx = np.argmin(np.abs(fpr - desiredFPR)) - 1 # вычитаем 1 чтобы ТОЧНО было меньше 30%\n",
    "  plt.scatter([fpr[idx]], [tpr[idx]], c='red', zorder=11)\n",
    "  return threshold[idx]\n",
    "\n",
    "def predict_with_threshold(proba, threshold):\n",
    "  return np.where(proba < threshold, -1, 1)\n",
    "\n",
    "def check_false_positive_rate(test_y, pred):\n",
    "  mat = confusion_matrix(test_y, pred, labels=[1, -1])\n",
    "  return mat[1,0]/sum(mat[1])\n",
    "\n",
    "def check_threshold(proba, name=\"Logistic Regression\"):\n",
    "  threshold = find_threshold(proba, name)\n",
    "  pred = predict_with_threshold(proba, threshold)\n",
    "  fpr = check_false_positive_rate(ytest, pred)\n",
    "  print(f\"Got {fpr*100:.2f}% false positive rate for {name}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Got 29.99% false positive rate for Logistic Regression\n"
     ]
    },
    {
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92.879861 170.744511 \nL 92.944488 170.575488 \nL 93.332254 170.350123 \nL 93.429195 169.843053 \nL 93.461509 169.843053 \nL 93.526137 169.617689 \nL 93.687706 169.617689 \nL 93.784647 169.364154 \nL 93.913902 169.364154 \nL 93.97853 169.223301 \nL 94.140099 169.13879 \nL 94.23704 169.026107 \nL 94.301668 168.941596 \nL 94.398609 168.63172 \nL 94.49555 168.547208 \nL 94.592492 168.293673 \nL 94.754061 168.209162 \nL 94.851002 167.871115 \nL 94.947944 167.786603 \nL 95.012571 167.673921 \nL 95.303395 167.58941 \nL 95.400337 167.392216 \nL 95.464964 167.307704 \nL 95.561906 166.969658 \nL 95.723475 166.885146 \nL 95.788102 166.800634 \nL 95.981985 166.772464 \nL 96.046613 166.631611 \nL 96.305123 166.57527 \nL 96.402064 166.434417 \nL 96.466692 166.349905 \nL 96.563633 166.152712 \nL 96.757516 166.0682 \nL 96.854458 165.899177 \nL 96.983713 165.871006 \nL 97.016027 165.701983 \nL 97.306851 165.673812 \nL 97.403792 165.363936 \nL 97.597675 165.279425 \nL 97.629989 165.166743 \nL 97.72693 165.166743 \nL 97.823871 164.941378 \nL 97.888499 164.913208 \nL 97.98544 164.659673 \nL 98.243951 164.575161 \nL 98.340892 164.490649 \nL 98.437833 164.406138 \nL 98.534775 164.265285 \nL 98.631716 164.180773 \nL 98.696344 164.01175 \nL 98.890227 163.955409 \nL 98.92254 163.814556 \nL 99.213365 163.730045 \nL 99.310306 163.617362 \nL 99.439561 163.532851 \nL 99.536503 163.391998 \nL 99.568816 163.391998 \nL 99.60113 163.222975 \nL 99.827327 163.138463 \nL 99.924268 162.96944 \nL 100.150465 162.941269 \nL 100.215092 162.744075 \nL 100.344347 162.687734 \nL 100.441289 162.575052 \nL 100.635172 162.490541 \nL 100.699799 162.349688 \nL 100.861368 162.265176 \nL 100.95831 162.011641 \nL 101.119878 161.9553 \nL 101.152192 161.786277 \nL 101.281447 161.758106 \nL 101.313761 161.617254 \nL 101.507644 161.532742 \nL 101.604585 161.251037 \nL 101.636899 161.251037 \nL 101.636899 161.138354 \nL 101.733841 161.138354 \nL 101.830782 161.053843 \nL 101.89541 160.94116 \nL 102.056979 160.856649 \nL 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115.079438 148.03905 \nL 115.176379 147.954538 \nL 115.273321 147.813686 \nL 115.402576 147.729174 \nL 115.467204 147.672833 \nL 115.596459 147.644662 \nL 115.6934 147.53198 \nL 115.854969 147.50381 \nL 115.919597 147.306616 \nL 116.210421 147.222104 \nL 116.307362 147.053081 \nL 116.6305 146.968569 \nL 116.695128 146.912228 \nL 116.921324 146.827717 \nL 116.985952 146.743205 \nL 117.147521 146.686864 \nL 117.179835 146.574182 \nL 117.470659 146.51784 \nL 117.5676 146.179794 \nL 117.761483 146.095282 \nL 117.858424 145.898088 \nL 118.019993 145.813577 \nL 118.116935 145.729065 \nL 118.343131 145.644554 \nL 118.375445 145.391019 \nL 118.698583 145.306507 \nL 118.795524 145.137484 \nL 119.18329 145.052972 \nL 119.280231 144.855778 \nL 119.344859 144.827608 \nL 119.409487 144.574073 \nL 119.538742 144.545902 \nL 119.635683 144.264197 \nL 119.700311 144.264197 \nL 119.700311 144.151515 \nL 120.023449 144.067003 \nL 120.12039 143.89798 \nL 120.249645 143.869809 \nL 120.346587 143.700786 \nL 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135.587668 \nL 130.783942 135.503157 \nL 130.880884 135.390474 \nL 131.010139 135.305963 \nL 131.10708 134.967916 \nL 131.397905 134.883405 \nL 131.462532 134.798893 \nL 131.753356 134.714381 \nL 131.850298 134.601699 \nL 132.04418 134.573529 \nL 132.108808 134.348164 \nL 132.270377 134.348164 \nL 132.335005 134.179141 \nL 132.72277 134.094629 \nL 132.819712 134.010118 \nL 133.175163 133.925606 \nL 133.272105 133.841094 \nL 133.433674 133.812924 \nL 133.530615 133.61573 \nL 133.886067 133.531218 \nL 133.983008 133.474877 \nL 134.209205 133.390366 \nL 134.306146 133.305854 \nL 134.467715 133.221342 \nL 134.564656 133.08049 \nL 134.855481 133.024149 \nL 134.952422 132.883296 \nL 135.049363 132.826955 \nL 135.146305 132.629761 \nL 135.404815 132.60159 \nL 135.469443 132.291714 \nL 135.695639 132.235373 \nL 135.792581 132.150862 \nL 135.921836 132.122691 \nL 135.921836 132.038179 \nL 136.277288 131.981838 \nL 136.341915 131.840986 \nL 136.568112 131.756474 \nL 136.665053 131.615621 \nL 137.020505 131.53111 \nL 137.020505 131.474768 \nL 137.311329 131.390257 \nL 137.40827 131.305745 \nL 137.537526 131.277575 \nL 137.634467 131.136722 \nL 137.892977 131.05221 \nL 137.989919 130.995869 \nL 138.08686 130.911358 \nL 138.183802 130.798675 \nL 138.280743 130.798675 \nL 138.313057 130.601482 \nL 138.539253 130.51697 \nL 138.636195 130.432458 \nL 138.733136 130.432458 \nL 138.797764 130.263435 \nL 138.959333 130.178923 \nL 138.959333 130.150753 \nL 139.314784 130.066241 \nL 139.411726 129.869047 \nL 139.70255 129.840877 \nL 139.799491 129.559171 \nL 139.96106 129.47466 \nL 140.058002 129.390148 \nL 140.478081 129.333807 \nL 140.542709 129.108443 \nL 140.89816 129.023931 \nL 140.995102 128.883078 \nL 141.415181 128.798567 \nL 141.447495 128.685884 \nL 141.609064 128.601373 \nL 141.706005 128.488691 \nL 141.932202 128.404179 \nL 142.029143 128.291497 \nL 142.319967 128.291497 \nL 142.416909 128.150644 \nL 142.643105 128.150644 \nL 142.707733 127.897109 \nL 143.030871 127.840768 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123.84055 \nL 148.685785 123.699698 \nL 148.782726 123.671527 \nL 148.879668 123.474333 \nL 149.041237 123.389822 \nL 149.105864 123.33348 \nL 149.170492 123.33348 \nL 149.235119 123.192628 \nL 149.49363 123.108116 \nL 149.525944 123.023604 \nL 149.849082 122.995434 \nL 149.913709 122.854581 \nL 150.236847 122.770069 \nL 150.333788 122.657387 \nL 150.592299 122.601046 \nL 150.592299 122.544705 \nL 151.012378 122.460193 \nL 151.012378 122.432023 \nL 151.400144 122.375682 \nL 151.497085 122.037635 \nL 151.561713 121.953124 \nL 151.561713 121.812271 \nL 151.820223 121.727759 \nL 151.820223 121.643248 \nL 151.949478 121.643248 \nL 152.014106 121.417883 \nL 152.30493 121.333372 \nL 152.401871 121.192519 \nL 152.466499 121.164348 \nL 152.56344 120.967154 \nL 152.692696 120.910813 \nL 152.789637 120.629108 \nL 152.886578 120.600937 \nL 152.951206 120.460085 \nL 153.177402 120.431914 \nL 153.209716 120.319232 \nL 153.403599 120.291061 \nL 153.50054 119.981185 \nL 153.565168 119.953015 \nL 153.629796 119.72765 \nL 153.823678 119.69948 \nL 153.888306 119.530457 \nL 154.017561 119.502286 \nL 154.082189 119.305092 \nL 154.340699 119.220581 \nL 154.43764 119.136069 \nL 154.728465 119.079728 \nL 154.825406 118.910705 \nL 155.277799 118.826193 \nL 155.277799 118.798022 \nL 155.600937 118.741681 \nL 155.633251 118.600829 \nL 155.762506 118.516317 \nL 155.827134 118.403635 \nL 156.085644 118.319123 \nL 156.117958 118.234611 \nL 156.182585 118.234611 \nL 156.247213 118.234611 \nL 156.344154 117.952906 \nL 156.538037 117.868394 \nL 156.602665 117.783883 \nL 156.861175 117.699371 \nL 156.958116 117.64303 \nL 157.41051 117.558518 \nL 157.442823 117.445836 \nL 157.507451 117.445836 \nL 158.476865 116.713402 \nL 158.735375 116.657061 \nL 158.800003 116.544379 \nL 158.929258 116.459867 \nL 159.026199 116.375355 \nL 159.252396 116.290844 \nL 159.317024 116.178162 \nL 159.54322 116.12182 \nL 159.575534 115.980968 \nL 159.866358 115.896456 \nL 159.963299 115.783774 \nL 160.027927 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187.397711 101.642159 \nL 187.656222 101.557648 \nL 187.656222 101.501307 \nL 187.882418 101.416795 \nL 187.947046 101.304113 \nL 188.108615 101.275942 \nL 188.205556 101.13509 \nL 188.399439 101.050578 \nL 188.431753 100.966066 \nL 188.496381 100.966066 \nL 188.593322 100.881555 \nL 188.657949 100.825213 \nL 189.013401 100.740702 \nL 189.013401 100.712531 \nL 189.110343 100.712531 \nL 189.239598 100.712531 \nL 189.239598 100.65619 \nL 191.113798 99.10681 \nL 191.824701 99.022299 \nL 191.824701 98.937787 \nL 192.083212 98.853275 \nL 192.083212 98.684252 \nL 192.470977 98.627911 \nL 192.567919 98.543399 \nL 192.600233 98.543399 \nL 192.66486 98.346205 \nL 192.794115 98.261694 \nL 192.891057 98.0645 \nL 193.117253 97.979988 \nL 193.117253 97.923647 \nL 193.375764 97.839136 \nL 193.440391 97.726453 \nL 193.795843 97.641942 \nL 193.892784 97.55743 \nL 193.957412 97.55743 \nL 194.571374 96.937678 \nL 195.120709 96.881337 \nL 195.185336 96.796825 \nL 195.346905 96.712314 \nL 195.443846 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88.768219 \nL 211.277606 88.683708 \nL 211.374547 88.571026 \nL 211.600744 88.514685 \nL 211.600744 88.402002 \nL 212.440903 88.345661 \nL 212.473217 88.148467 \nL 212.990237 88.063956 \nL 212.990237 88.035785 \nL 213.18412 88.007615 \nL 213.18412 87.894932 \nL 213.248748 87.894932 \nL 213.507258 87.810421 \nL 213.571886 87.75408 \nL 214.024279 87.669568 \nL 214.088906 87.585056 \nL 214.218161 87.500545 \nL 214.282789 87.444204 \nL 214.670555 87.359692 \nL 214.670555 87.331522 \nL 215.026006 87.331522 \nL 215.122948 87.190669 \nL 215.801537 87.106157 \nL 215.866165 86.965304 \nL 215.898479 86.965304 \nL 216.156989 86.880793 \nL 216.156989 86.852622 \nL 216.577068 86.768111 \nL 216.641696 86.71177 \nL 216.706324 86.71177 \nL 216.706324 86.599087 \nL 216.835579 86.599087 \nL 216.867893 86.458235 \nL 216.964834 86.458235 \nL 216.964834 86.430064 \nL 217.061775 86.23287 \nL 217.191031 86.2047 \nL 217.191031 86.120188 \nL 217.449541 86.035676 \nL 217.546482 85.979335 \nL 217.772679 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244.011481 73.471613 \nL 244.108422 73.33076 \nL 244.463874 73.246248 \nL 244.528501 73.189907 \nL 244.754698 73.161736 \nL 244.754698 73.077225 \nL 245.174777 73.049054 \nL 245.174777 72.964543 \nL 245.271719 72.964543 \nL 245.62717 72.880031 \nL 245.62717 72.85186 \nL 245.724112 72.85186 \nL 245.853367 72.82369 \nL 245.950308 72.682837 \nL 246.338074 72.598326 \nL 246.435015 72.485643 \nL 247.339801 72.401132 \nL 247.436743 72.260279 \nL 248.115333 72.175767 \nL 248.212274 72.091256 \nL 248.503098 72.006744 \nL 248.567726 71.837721 \nL 249.020119 71.753209 \nL 249.052433 71.668698 \nL 249.181688 71.612356 \nL 249.181688 71.584186 \nL 249.440198 71.358821 \nL 249.666395 71.27431 \nL 249.763336 71.189798 \nL 249.892591 71.133457 \nL 249.989533 70.992604 \nL 250.862005 70.908093 \nL 250.926633 70.823581 \nL 251.185143 70.739069 \nL 251.249771 70.626387 \nL 251.766791 70.541876 \nL 251.766791 70.513705 \nL 252.251498 70.457364 \nL 252.283812 70.344682 \nL 252.34844 70.344682 \nL 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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   ],
   "source": [
    "check_threshold(logit_proba, \"Logistic Regression\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Got 29.99% false positive rate for SVC\n"
     ]
    },
    {
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130.714164 \nL 85.770826 130.54514 \nL 85.80314 130.54514 \nL 85.900081 130.207094 \nL 85.932395 130.207094 \nL 87.289574 128.573202 \nL 87.386516 128.206985 \nL 87.451143 128.122473 \nL 87.548085 127.95345 \nL 87.67734 127.868938 \nL 87.774281 127.615404 \nL 87.903536 127.530892 \nL 88.000478 127.333698 \nL 88.065105 127.249186 \nL 88.162047 127.164675 \nL 88.226674 127.080163 \nL 88.323616 126.882969 \nL 88.388243 126.798458 \nL 88.485185 126.432241 \nL 88.743695 126.347729 \nL 88.840636 126.037853 \nL 88.969892 126.037853 \nL 89.066833 125.784318 \nL 89.163774 125.699806 \nL 89.260716 125.220907 \nL 89.325343 125.220907 \nL 89.55154 124.85469 \nL 89.713109 124.798349 \nL 89.81005 124.206767 \nL 90.197816 123.868721 \nL 90.294757 123.389822 \nL 90.682523 122.910922 \nL 91.070288 122.544705 \nL 91.16723 122.488364 \nL 91.264171 121.981294 \nL 91.393426 121.981294 \nL 91.458054 121.840441 \nL 91.554995 121.7841 \nL 91.619623 121.558736 \nL 91.68425 121.558736 \nL 91.68425 121.502395 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102.515446 \nL 106.160831 102.346423 \nL 106.548596 102.261911 \nL 106.645537 102.092888 \nL 106.807106 102.008376 \nL 106.904048 101.839353 \nL 107.000989 101.754842 \nL 107.000989 101.67033 \nL 107.227186 101.416795 \nL 107.2595 101.332283 \nL 107.808834 100.909725 \nL 107.905775 100.740702 \nL 108.067344 100.684361 \nL 108.164286 100.599849 \nL 108.261227 100.515337 \nL 108.325855 100.402655 \nL 108.358169 100.402655 \nL 108.519738 100.318144 \nL 108.519738 100.261803 \nL 109.489151 99.839244 \nL 109.553779 99.61388 \nL 109.586093 99.61388 \nL 110.264683 99.163151 \nL 110.296996 99.022299 \nL 110.490879 98.994128 \nL 110.684762 98.712422 \nL 110.749389 98.515229 \nL 110.814017 98.515229 \nL 110.910958 98.205353 \nL 111.26641 98.149012 \nL 111.26641 98.0645 \nL 111.363352 98.0645 \nL 111.492607 97.979988 \nL 111.557234 97.839136 \nL 111.912686 97.754624 \nL 112.009627 97.501089 \nL 112.397393 97.416577 \nL 112.494334 97.247554 \nL 112.752845 97.191213 \nL 112.849786 97.078531 \nL 113.043669 96.994019 \nL 113.108296 96.881337 \nL 113.334493 96.627802 \nL 113.334493 96.51512 \nL 113.722259 96.430608 \nL 113.8192 96.289755 \nL 113.980769 96.233414 \nL 114.07771 96.00805 \nL 114.239279 96.00805 \nL 114.239279 95.895368 \nL 114.530103 95.810856 \nL 114.627045 95.698174 \nL 114.691672 95.670003 \nL 114.723986 95.529151 \nL 115.176379 95.106592 \nL 115.402576 95.050251 \nL 115.467204 94.740375 \nL 115.887283 94.655864 \nL 116.145793 94.45867 \nL 116.178107 94.317817 \nL 116.436617 94.092453 \nL 116.6305 94.064282 \nL 116.727442 93.92343 \nL 116.759755 93.92343 \nL 116.759755 93.838918 \nL 116.856697 93.41636 \nL 117.050579 93.331848 \nL 117.050579 93.275507 \nL 117.212148 93.219166 \nL 117.30909 93.078313 \nL 117.373717 93.078313 \nL 117.438345 92.852949 \nL 117.599914 92.796608 \nL 117.696855 92.627584 \nL 117.761483 92.543073 \nL 117.793797 92.430391 \nL 118.052307 92.345879 \nL 118.278504 92.007832 \nL 118.569328 91.923321 \nL 118.569328 91.89515 \nL 118.92478 91.810639 \nL 118.989407 91.754297 \nL 119.150976 91.669786 \nL 119.247918 91.585274 \nL 119.474114 91.528933 \nL 119.474114 91.35991 \nL 119.829566 91.275398 \nL 120.249645 91.134545 \nL 120.281959 90.909181 \nL 120.3789 90.909181 \nL 120.960549 90.514793 \nL 121.089804 90.430282 \nL 121.186745 90.34577 \nL 121.380628 90.261258 \nL 121.542197 90.148576 \nL 121.73608 90.120406 \nL 121.929963 89.8387 \nL 122.026904 89.782359 \nL 122.123845 89.556995 \nL 122.220787 89.387971 \nL 122.317728 89.247119 \nL 122.446983 89.162607 \nL 122.511611 89.049925 \nL 122.899376 88.965413 \nL 122.899376 88.937243 \nL 123.222514 88.740049 \nL 123.254828 88.430173 \nL 123.448711 88.345661 \nL 123.481025 88.26115 \nL 123.513339 88.26115 \nL 123.61028 88.26115 \nL 123.707221 87.979444 \nL 124.030359 87.894932 \nL 124.062673 87.838591 \nL 124.224242 87.838591 \nL 124.224242 87.75408 \nL 124.708949 87.387863 \nL 124.902832 87.359692 \nL 124.967459 87.134328 \nL 125.129028 87.077987 \nL 125.129028 87.021646 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
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     "metadata": {},
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   ],
   "source": [
    "check_threshold(svc_proba, \"SVC\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "У SVC получилась более выпуклая кривая, потому что чем лучше класификатор, тем выпуклеее его ROC кривая."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C-qubaK4DvZM"
   },
   "source": [
    "### Multiclass logit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yJQone-LDvZM"
   },
   "source": [
    "#### 10. [1 point] Take the One-VS-Rest classifier (use sklearn) and apply to Logit model (one you've made in the 4th task) in order to get multiclass linear classifier\n",
    "\n",
    "<a href=\"https://scikit-learn.org/stable/modules/generated/sklearn.multiclass.OneVsRestClassifier.html\">OneVsRestClassifier</a>\n",
    "\n",
    "* use the whole dataset with 6 authors\n",
    "* divide the data into train and test samples with 3/4 split rate\n",
    "* train the model using cross validation\n",
    "* plot confusion matrix for train and test samples\n",
    "* compute all possible and relevant metrics for test sample (use sklearn)\n",
    "* using GridSearchCV - find the best parameters for the models (by averaged ROC_AUC score). **HINT:** Do not forget about set jobs=-1 in the GridSearchCV init to speed up calculations.\n",
    "* make conclusions about the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "M4lR8qJ7DvZM"
   },
   "outputs": [],
   "source": [
    "from sklearn.multiclass import OneVsRestClassifier\n",
    "\n",
    "# баланнсируем классы, тк у нас теперь они соовсем разных размеров\n",
    "dfs = [df[df[\"author\"] == k] for k in romru]\n",
    "minlen = min(len(df) for df in dfs)\n",
    "df2 = pd.concat([df[:minlen] for df in dfs])\n",
    "\n",
    "X1train, X1test, y1train, y1test = train_test_split(np.vstack(df2[\"tfidf\"]), df2[\"author\"], test_size=0.25, random_state=69)\n",
    "\n",
    "ovr = OneVsRestClassifier(Logit(0, 0, lr=15, max_iter=1000, tolerance=1e-6), n_jobs=-1)\n",
    "ovr.fit(X1train, y1train)\n",
    "y1pred = ovr.predict(X1test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiclass Logit Precision:  0.41\n",
      "Multiclass Logit Recall:     0.41\n",
      "Multiclass Logit F1-measure: 0.41\n",
      "Multiclass Logit Accuracy:   0.41\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_results(y1test, y1pred, \"Multiclass Logit\", sorted(romru))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'fit_time': array([52.1108017 , 52.13429713, 52.10834193, 52.13136148, 52.15676975]),\n",
       " 'score_time': array([0.02975917, 0.03819323, 0.03610659, 0.03845501, 0.03348207]),\n",
       " 'test_score': array([0.73908462, 0.74327128, 0.73144474, 0.73996203, 0.74481453])}"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = cross_validate(ovr, X1train, y1train, cv=5, scoring='roc_auc_ovr')\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'estimator__beta': 0.1, 'estimator__gamma': 0}"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prams = {'estimator__beta': [0, 0.1, 1], 'estimator__gamma': [0, 0.1, 1]}\n",
    "ovr1 = OneVsRestClassifier(Logit(0, 0, lr=0.7, max_iter=1000, tolerance=1e-6), n_jobs=-1)\n",
    "gscvovr = GridSearchCV(ovr1, prams, scoring='roc_auc_ovr', cv=3, n_jobs=-1)\n",
    "gscvovr.fit(Xtrain, ytrain)\n",
    "gscvovr.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3d(gscvovr, \"Multiclass Logit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Модель выдаёт красивые диагональные матрицы путаницы (конфьюжена) и метрики в районе $0.75$ на кроссвалидации, не смотря на то что она обучается довольно быстро. Гридсёрч нам как всегда не дал никакой полезной информации."
   ]
  }
 ],
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