sem8/main.ipynb

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   },
   "source": [
    "# Критерии выбора моделей и методы отбора признаков"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "q70dGzWril_0",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s3qWY0M5LA6r",
    "slideshow": {
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    }
   },
   "source": [
    "## Библиотеки"
   ]
  },
  {
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   "execution_count": 2,
   "metadata": {
    "id": "opbX7Dx8LA6s",
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.image import imread\n",
    "from mpl_toolkits import mplot3d\n",
    "from matplotlib import gridspec\n",
    "from mlxtend.plotting import plot_decision_regions\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "from scipy.special import softmax\n",
    "from scipy.spatial.distance import cdist\n",
    "import numpy as np\n",
    "import torch\n",
    "import itertools\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC, SVR\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import classification_report, roc_auc_score, roc_curve\n",
    "from sklearn.metrics import auc\n",
    "from sklearn.model_selection import KFold, ParameterGrid\n",
    "from sklearn.datasets import make_classification, load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from torchvision import datasets\n",
    "from torchvision import transforms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9aXP0enLLA60",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Оценка качества моделей"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "yZ3fMARHLA62",
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   "source": [
    "При выборе модели машиного обучения\n",
    "$$\n",
    "f: \\mathbb{X} \\to \\mathbb{Y},\n",
    "$$\n",
    "модель выбирается согласно некоторого критерия $L$ (функции ошибки, минус логарифм правдоподобия и тд.). Обычно в качестве функции $L$ рассматривается некоторая функция ошибки модели $f$ на выборке $\\mathfrak{D}$:\n",
    "$$\n",
    "f = \\arg\\min_{f \\in \\mathfrak{F}} L\\bigr(f, \\mathfrak{D}\\bigr)\n",
    "$$\n",
    "\n",
    "В зависимости от вида функции $L$ разделяют два типа критериев:\n",
    "1. внутрений критерий качества;\n",
    "2. внешний критерий качества.\n",
    "\n",
    "Далее будем рассматривать два типа выборок:\n",
    "1. $\\mathfrak{D}$ это вся выборка, которая доступна для выбора модели;\n",
    "2. $\\mathfrak{D}'$ это выборка на которой проверяется качество уже выбраной модели.\n",
    "3. $\\mathfrak{D}^{l_k}_k$ это $k$-я подвыборка выборки $\\mathfrak{D}$ размера $l_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
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    "id": "BY0UPpMaLA62",
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   "outputs": [
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     "data": {
      "text/plain": [
       "((206, 13), (206,), (300, 13), (300,))"
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   ],
   "source": [
    "data = load_boston()\n",
    "\n",
    "D_all = data['data'], data['target']\n",
    "np.random.seed(0)\n",
    "X_train, X_test, y_train, y_test = train_test_split(D_all[0], D_all[1], \n",
    "                                                    test_size=300)\n",
    "\n",
    "X_train.shape, y_train.shape, X_test.shape, y_test.shape"
   ]
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   "source": [
    "### Внутрений критерий:\n",
    "Простой пример для регрессии:\n",
    "$$\n",
    "f = \\arg\\min_{f\\in \\mathfrak{F}} \\sum_{\\left(x, y\\right) \\in \\mathfrak{D}}\\left(f(x) - y\\right)^2\n",
    "$$"
   ]
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    "id": "R278LaE4LA68",
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   "source": [
    "class Perceptron(torch.nn.Module):\n",
    "    def __init__(self, input_dim=13, num_layers=0, \n",
    "                 hidden_dim=10, output_dim=1, p=0.0, device='cpu'):\n",
    "        super(Perceptron, self).__init__()\n",
    "        \n",
    "        self.layers = torch.nn.Sequential()\n",
    "        \n",
    "        prev_size = input_dim\n",
    "        for i in range(num_layers):\n",
    "            self.layers.add_module('layer{}'.format(i), \n",
    "                                  torch.nn.Linear(prev_size, hidden_dim))\n",
    "            self.layers.add_module('relu{}'.format(i), torch.nn.ReLU())\n",
    "            self.layers.add_module('dropout{}'.format(i), torch.nn.Dropout(p=p))\n",
    "            prev_size = hidden_dim\n",
    "        \n",
    "        self.layers.add_module('classifier', \n",
    "                               torch.nn.Linear(prev_size, output_dim))  \n",
    "\n",
    "        self.device = device      \n",
    "        self.to(device)\n",
    "        \n",
    "    def forward(self, input):\n",
    "        return self.layers(input)"
   ]
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      "text/plain": [
       "Perceptron(\n",
       "  (layers): Sequential(\n",
       "    (layer0): Linear(in_features=13, out_features=20, bias=True)\n",
       "    (relu0): ReLU()\n",
       "    (dropout0): Dropout(p=0.0, inplace=False)\n",
       "    (classifier): Linear(in_features=20, out_features=1, bias=True)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "model = Perceptron(num_layers=1, \n",
    "                   hidden_dim=20,\n",
    "                   device=device)\n",
    "model"
   ]
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   "source": [
    "X_train_pt = torch.from_numpy(X_train).float()\n",
    "X_test_pt = torch.from_numpy(X_test).float()\n",
    "\n",
    "y_train_pt = torch.from_numpy(y_train).float()\n",
    "y_test_pt = torch.from_numpy(y_test).float()\n",
    "\n",
    "train_dataset = torch.utils.data.TensorDataset(X_train_pt, y_train_pt)\n",
    "test_dataset = torch.utils.data.TensorDataset(X_test_pt, y_test_pt)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "K-YR_DdvL_tL",
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   "source": [
    "def testing(model, dataset):\n",
    "    model.eval()\n",
    "    generator = torch.utils.data.DataLoader(dataset, \n",
    "                                            batch_size=64, pin_memory=True)\n",
    "\n",
    "    pred = []\n",
    "    real = []\n",
    "    for x, y in generator:\n",
    "        with torch.no_grad():\n",
    "            pred.extend(model(x).cpu().numpy().tolist())\n",
    "            real.extend(y.cpu().numpy().tolist())\n",
    "\n",
    "    return np.sqrt(np.mean((np.array(real) - np.array(pred))**2))"
   ]
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   "source": [
    "epochs = 1000\n",
    "\n",
    "optim = torch.optim.Adam(model.parameters(), lr=0.0001,)\n",
    "loss_function = torch.nn.MSELoss()\n",
    "\n",
    "list_of_train_error = [testing(model, train_dataset)]\n",
    "list_of_test_error = [testing(model, test_dataset)]\n",
    "\n",
    "iterator = tqdm(range(epochs))\n",
    "for epoch in iterator:\n",
    "    generator = torch.utils.data.DataLoader(train_dataset, shuffle=True,\n",
    "                                            batch_size=16, pin_memory=True)\n",
    "    \n",
    "    for batch_x, batch_y in generator:\n",
    "        optim.zero_grad()\n",
    "\n",
    "        model.train()\n",
    "        output = model(batch_x)\n",
    "        loss = loss_function(output, batch_y.to(device))\n",
    "\n",
    "        loss.backward()\n",
    "        optim.step()\n",
    "\n",
    "    list_of_train_error.append(testing(model, train_dataset))\n",
    "    list_of_test_error.append(testing(model, test_dataset))\n",
    "\n",
    "    iterator.set_postfix({'train': round(list_of_train_error[-1], 2), \n",
    "                          'test':round(list_of_test_error[-1], 2)})"
   ]
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13133a438>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list_of_train_error[10:], label='train')\n",
    "plt.plot(list_of_test_error[10:], label='test')\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6DLtJ0zXgoEa",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "На самом деле выше должна была быть красивая картинка переобучения на реальных данных, но не вышло:( \n",
    "\n",
    "Поэтому вставлю синтетический пример с первого семинара."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "w0Pge0MigmOP",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "l = 6\n",
    "n = 1\n",
    "w = np.random.randn(n)\n",
    "X_tr = np.random.randn(l, n)\n",
    "y_tr = X_tr@w + np.random.randn(l)\n",
    "\n",
    "X_vl = np.random.randn(l, n)\n",
    "y_vl = X_vl@w + np.random.randn(l)\n",
    "\n",
    "X_ts = np.random.randn(l, n)\n",
    "y_ts = X_ts@w + np.random.randn(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "HOeu7eDqhB47",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "x_begin = -1.05\n",
    "x_end = 2.5\n",
    "X_polinom = np.hstack([X_tr**0, X_tr**1, X_tr**2, X_tr**3, X_tr**4, X_tr**5])\n",
    "w_polinom = np.linalg.inv(X_polinom.T@X_polinom)@X_polinom.T@y_tr\n",
    "y_polinom = list(map(lambda x: np.array([x**0, x**1, x**2, x**3, x**4, x**5])@w_polinom, \n",
    "                     np.linspace(x_begin, x_end)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "aIKnmBwIhCAa",
    "outputId": "9f30e9ab-75d9-45bc-aa68-2a9489e9e4ce",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13177a5c0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_tr, y_tr, 'o', label = 'points train')\n",
    "plt.plot(X_ts, y_ts, 'o', label = 'points test')\n",
    "plt.plot(np.linspace(x_begin, x_end), w*np.linspace(x_begin, x_end), \n",
    "         '-', label = 'real')\n",
    "plt.plot(np.linspace(x_begin, x_end), y_polinom, '-', label = 'polinom')\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eo3s39cMiJOf",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Теперь рассмотрим зависимость качества на контроле от числа использованых признаков. Воспользуемся PCA и построем качество от числа главных компонент."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 66,
     "referenced_widgets": [
      "5279a52e361e4b368950c0c28c510d5d",
      "d0e83bda2ad043fda1f5bf64447fd409",
      "788d62fa73f748a1931a07d2e2cefde5",
      "1d6dd7ed39d04bc8818d76ed4d694125",
      "66b88e0577e84f90bc82ff94d3b6841f",
      "7dc4b2ed941e4dddbb47fedc91087976",
      "380a5c3018ea4e8e8009612f055528a9",
      "f5552b43d6b24e3e99ac6735fe0b4163"
     ]
    },
    "id": "EmY6YqiViJEe",
    "outputId": "e417295c-47a7-4d1b-c35b-45011dcb58a2",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e69bdbc55cfc47bea6ba2e59da829d3f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=12.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "ns = list(range(1, X_train.shape[1]))\n",
    "\n",
    "scores_train = []\n",
    "scores_test = []\n",
    "for n in tqdm(ns):\n",
    "    pca = PCA(n)\n",
    "    X_train_low = pca.fit_transform(X_train)\n",
    "    X_test_low = pca.transform(X_test)\n",
    "\n",
    "    w = np.linalg.inv(X_train_low.T@X_train_low)@X_train_low.T@y_train\n",
    "\n",
    "    scores_train.append(np.mean((X_train_low@w - y_train)**2))\n",
    "    scores_test.append(np.mean((X_test_low@w - y_test)**2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "9q0f1cpqieSN",
    "outputId": "d76c16a1-b62f-4eb3-949c-c9438f9923f0",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x131796780>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns, scores_train, label='train')\n",
    "plt.plot(ns, scores_test, label='test')\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RCZp6nM0hMZK",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Внешний критерий:\n",
    "1. Разделить выборку $\\mathfrak{D}$ на две подвыборки\n",
    "2. Leave One Out\n",
    "3. Скользящий контроль\n",
    "4. Бутсреп\n",
    "5. Регуляризация\n",
    "6. Критерий Акаике\n",
    "7. BIC\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sId7hcg9mndR",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Отбор признаков"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6Pn6raB1mp54",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Используется два основных подхода\n",
    "1. Генерация признаков.\n",
    "2. Отбор существующих признаков."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nWK_Q_u8m63I",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Генерация признаков\n",
    "1. Построение статистик на основе уже существующих признаков и тд.\n",
    "2. Выше мы использовали PCA, что тоже генерит новые признаки.\n",
    "3. Нейросеть кроме последнего слоя, также можно рассматривать как метод генерации нового признаково пространства (к примеру прошлое домашнее задание)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cGaFftYTnaC0",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Отбор существующих признаков"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wSiv7A3FpNOo",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Полный перебор\n",
    "\n",
    "В данном случае берем множество всех подмножеств признакового описания."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 66,
     "referenced_widgets": [
      "e2f07fb705514fd29fada4f9c848273e",
      "4527585b3d3949e0bafa7d7101569ee3",
      "edadae79a1fc4a488a8fa06bf439180e",
      "7bf9498047004c198fa1c7bb73a939d8",
      "95f844bfd2be49c1a79e61c60eebc9cd",
      "5507a33e5fd94b87b39223e12c0bd513",
      "2f273853481c47a4a7a871dcf502396b",
      "c3600db62ee74bc5bb7897434a36fcaf"
     ]
    },
    "id": "g35iwCHtpww9",
    "outputId": "a1b9ce45-e905-4bf0-aab6-f4964c8173a4",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0bbce4e8839c4475a5230666e335b24a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=8192.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "indexes = list(itertools.product([0, 1], repeat=13))\n",
    "\n",
    "scores_train = dict()\n",
    "scores_test = dict()\n",
    "for i, ind in enumerate(tqdm(indexes)):\n",
    "    ind = np.array(ind, dtype=bool)\n",
    "\n",
    "    X_train_low = X_train[:, ind]\n",
    "    X_test_low = X_test[:, ind]\n",
    "\n",
    "    w = np.linalg.inv(X_train_low.T@X_train_low)@X_train_low.T@y_train\n",
    "\n",
    "    scores_train[i] = np.mean((X_train_low@w - y_train)**2)\n",
    "    scores_test[i] = np.mean((X_test_low@w - y_test)**2)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "tq-_Fi_UweoS",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "best_train = sorted(scores_train, key=lambda x: scores_train[x])[0]\n",
    "best_test = sorted(scores_test, key=lambda x: scores_test[x])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 119
    },
    "id": "bKhaYdS_rWkU",
    "outputId": "d1454a7d-73f9-47f9-f253-f269e3c27484",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best for train\n",
      "(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)\n",
      "['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT']\n",
      "best for test\n",
      "(0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1)\n",
      "['ZN', 'RM', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT']\n"
     ]
    }
   ],
   "source": [
    "print('best for train')\n",
    "print(indexes[best_train])\n",
    "print(data['feature_names'][np.array(indexes[best_train], dtype=bool)].tolist())\n",
    "\n",
    "print('best for test')\n",
    "print(indexes[best_test])\n",
    "print(data['feature_names'][np.array(indexes[best_test], dtype=bool)].tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 527
    },
    "id": "vSHy39nPrta3",
    "outputId": "ab25d1c8-41ea-4eec-e77e-22a5234b9ca3",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(data['DESCR'][49:1227])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "CwhwTuBN815I",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "scores = []\n",
    "\n",
    "for i, ind in enumerate(indexes):\n",
    "    scores.append((sum(ind), scores_train[i]))\n",
    "\n",
    "scores = np.array(scores)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 320
    },
    "id": "r0HXM3HF_TrO",
    "outputId": "dcf31f0a-ad58-4980-b5fd-5d06d79895f8",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13136f320>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15, 5))\n",
    "scores = np.zeros([len(indexes), 2])\n",
    "for i, ind in enumerate(indexes):\n",
    "    scores[i] = [sum(ind), scores_train[i]]\n",
    "plt.plot(scores[:, 0], scores[:, 1], 'ob')\n",
    "plt.axhline(y=np.min(scores[:, 1]), color='b', linestyle='-', label = 'train')\n",
    "\n",
    "for i, ind in enumerate(indexes):\n",
    "    scores[i] = [sum(ind), scores_test[i]]\n",
    "plt.plot(scores[:, 0], scores[:, 1], '.g')\n",
    "plt.axhline(y=np.min(scores[:, 1]), color='g', linestyle='-', label = 'test')\n",
    "\n",
    "plt.legend(loc='best'), plt.ylim((20, 150))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aea-di438yFf",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Жадный алгоритм: add\n",
    "\n",
    "Жадно добавляем один признак, который дает максимальный прирост качества."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "AtrLFwGCD7Se",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "X_val_train, X_val_test, y_val_train, y_val_test = train_test_split(\n",
    "    X_train, y_train, test_size=50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "ldRQTHsC7xpL",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "J_star, J, current, k_star, d = [], set(), 99999999999, 0, 1\n",
    "for k in range(X_val_train.shape[1]):\n",
    "    scores_val_test = dict()\n",
    "    for j in list(set(range(X_val_train.shape[1])) - J):\n",
    "        ind = [ i in (J | {j}) for i in range(X_val_train.shape[1])]\n",
    "        X_val_train_val = X_val_train[:, ind]\n",
    "        X_val_test_val = X_val_test[:, ind]\n",
    "        w = np.linalg.inv(\n",
    "            X_val_train_val.T@X_val_train_val)@X_val_train_val.T@y_val_train\n",
    "        scores_val_test[j] = np.mean((X_val_test_val@w - y_val_test)**2)\n",
    "\n",
    "    best = sorted(scores_val_test, key=lambda x: scores_val_test[x])[0]\n",
    "\n",
    "    J.add(best)\n",
    "    \n",
    "    if scores_val_test[best] < current:\n",
    "        current = scores_val_test[best]\n",
    "        k_star = k\n",
    "        J_star = set(J)\n",
    "    if k - k_star > d:\n",
    "        break\n",
    "ind = np.array([ i in J_star for i in range(X_val_train.shape[1])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 170
    },
    "id": "WkkyzhKLIBDR",
    "outputId": "9b020881-8334-46ec-d395-9d6c994349fd",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best for train\n",
      "[1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      "['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT']\n",
      "best for validation\n",
      "[1 0 1 1 0 1 1 1 0 1 1 0 0]\n",
      "['CRIM', 'INDUS', 'CHAS', 'RM', 'AGE', 'DIS', 'TAX', 'PTRATIO']\n",
      "best for test\n",
      "[0 1 0 0 0 1 0 1 1 1 1 1 1]\n",
      "['ZN', 'RM', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT']\n"
     ]
    }
   ],
   "source": [
    "print('best for train')\n",
    "print(np.array(indexes[best_train], dtype=int))\n",
    "print(data['feature_names'][np.array(indexes[best_train], dtype=bool)].tolist())\n",
    "\n",
    "print('best for validation')\n",
    "print(np.array(ind, dtype=int))\n",
    "print(data['feature_names'][np.array(ind, dtype=bool)].tolist())\n",
    "\n",
    "print('best for test')\n",
    "print(np.array(indexes[best_test], dtype=int))\n",
    "print(data['feature_names'][np.array(indexes[best_test], dtype=bool)].tolist())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9tRES5uHJTzc",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Жадный алгоритм: add-del\n",
    "\n",
    "Реализовать в качестве домашнего задания"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "macD4yLmJ0iu",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Оценка качества классификации"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jDsM4Zu3J5Yb",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Основные функции для оценки качества классификации:\n",
    "1. Accuracy (доля верных ответов)\n",
    "2. Precision (доля релевантных среди всех найденных)\n",
    "3. Recall (доля найденных среди релевантных)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Задача 1:\n",
    "Простая задача бинарной классификации. Прототип алгоритма:\n",
    "\n",
    "Вход: признаковое описание объекта.\n",
    "\n",
    "Выход: вероятность класса $1$. (и соответсвенно класс объекта на основе treshold)\n",
    "\n",
    "Метрики качества:\n",
    "$$\n",
    "ACC = \\frac{TP + TN}{TP + TN + FP + FN}\n",
    "$$\n",
    "\n",
    "$$\n",
    "PRECISION = \\frac{TP}{TP + FP}\n",
    "$$\n",
    "\n",
    "$$\n",
    "RECALL = \\frac{TP}{TP + FN}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "X, Y = make_classification(n_samples=400, n_features=2, \n",
    "                           n_informative=2, n_classes=2, \n",
    "                           n_redundant=0,\n",
    "                           n_clusters_per_class=1,\n",
    "                           random_state=0)\n",
    "\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, \n",
    "                                                    test_size=100, \n",
    "                                                    random_state=0)\n",
    "X_train_val, X_test_val, Y_train_val, Y_test_val = train_test_split(\n",
    "    X_train, Y_train, test_size=100, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "model = SVC(probability=True)\n",
    "_ = model.fit(X_train_val, Y_train_val)\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(\n",
    "    Y_test_val, model.predict_proba(X_test_val)[:,1], pos_label=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13133a668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         lw=2, label='ROC curve (area = {})'.format(round(auc(fpr, tpr), 2)))\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13185b898>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(thresholds, tpr, lw = 2, label = 'tpr')\n",
    "plt.plot(thresholds, 1-fpr, lw = 2, label = '1-fpr')\n",
    "\n",
    "threshold = thresholds[np.argmin((tpr - 1 + fpr)**2)]\n",
    "plt.axvline(x=threshold, \n",
    "            ls='--', c='black',\n",
    "            label='best threshold {}'.format(round(threshold, 2)))\n",
    "plt.xlabel('threshold')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.78      0.93      0.85        45\n",
      "           1       0.93      0.78      0.85        55\n",
      "\n",
      "    accuracy                           0.85       100\n",
      "   macro avg       0.86      0.86      0.85       100\n",
      "weighted avg       0.86      0.85      0.85       100\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    classification_report(\n",
    "        Y_test, model.predict_proba(X_test)[:, 1] > 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.77      0.91      0.84        45\n",
      "           1       0.91      0.78      0.84        55\n",
      "\n",
      "    accuracy                           0.84       100\n",
      "   macro avg       0.84      0.85      0.84       100\n",
      "weighted avg       0.85      0.84      0.84       100\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    classification_report(\n",
    "        Y_test, model.predict_proba(X_test)[:, 1] > threshold))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZgfbVnofLDYl",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Задача 2:\n",
    "Рассматрим задачу поиска ошибок в тексте. В качестве найденной ошибки выступает фрагмент, который состоит из пары чисел: начало и конец подстроки с ошибкой. Прототип алгоритма очень простой:\n",
    "\n",
    "Вход: текст.\n",
    "\n",
    "Выход: список фрагментов, в которых найдена ошибка.\n",
    "\n",
    "Требуется предложить внешний критерий качества для оценки качества алгоритма. Доступны документы с размеченными фрагментами, а также доступна разметка алгоритма."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XXkErAX4NA2A",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "В задаче поиска документов используют следующие метрики Precision и Recall:\n",
    "$$\n",
    "\\text{Precision} = \\frac{\\left|\\{\\text{релевантные документы}\\} \\cap \\{\\text{найденные документы}\\}\\right|}{\\left|\\{\\text{найденные документы}\\}\\right|}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{Recall} = \\frac{\\left|\\{\\text{релевантные документы}\\} \\cap \\{\\text{найденные документы}\\}\\right|}{\\left|\\{\\text{релевантные документы}\\}\\right|}\n",
    "$$\n",
    "\n",
    "\n",
    "Задания домой: на основе вышеуказаных метрик выписать как Вы би считали метрику для предыдущей задачи.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6n2KW5U6LA7G",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Как правильно составлять выборки"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VaiH2-luODm0",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Большая часть времени занимает построение выборки, которую уже потом требуется аппроксимировать. Правильное составление выборки позволяет решить много проблем в дальнейшем.\n",
    "\n",
    "Простые правила как правильно составить выборку:\n",
    "1. Сразу определиться с объектом исследования и целевой переменной.\n",
    "    * физичиский смысл признаков играет большую роль, так как именно они позволяют интерпретировать результаты модели, поэтому обязательно информацию о физическом смысле каждого признака требется сохранить.\n",
    "    * если рассматривается задача классификации, то требуется зафиксировать классы, описать эти классы, построить биекцию между классами и их названием физическим описанием.\n",
    "2. Выполнить разделение выборки на обучение и контроль заранее, убедившись, что они не пересекаются\n",
    "    * проверить что выборки статистически не различаються.\n",
    "    * для задачи классификации проверить, что баланс классов в обучении и контроле совпадает."
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