logistic_seminar.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "350f7400",
   "metadata": {},
   "source": [
    "# Log-Reg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cda4d2c5",
   "metadata": {},
   "source": [
    "### 1D классификация"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec649897",
   "metadata": {},
   "source": [
    "Рассмотрим одномерный пример. У нас есть данные по массе мышей. Часть из них определена как мыши с нормальной массой тела, а часть — как мыши с ожирением. Чтобы их отделить друг от друга, нам достаточно одного критерия. Мы можем посмотреть на график и визуально определить предельную массу, после которой мышки будут жирненькими."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2fc4e932",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.metrics import accuracy_score "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7ec11555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_data(total_len=40):\n",
    "    x = np.hstack(\n",
    "        [\n",
    "            np.random.uniform(14, 21, total_len // 2),\n",
    "            np.random.uniform(24, 33, total_len // 2),\n",
    "        ]\n",
    "    )\n",
    "    y = np.hstack([np.zeros(total_len // 2), np.ones(total_len // 2)])\n",
    "    return x, y\n",
    "\n",
    "\n",
    "def plot_data(x, y, total_len=40, s=50, threshold=None, margin=None):\n",
    "    ax = sns.scatterplot(x=x, y=np.zeros(len(x)), hue=y, s=s)\n",
    "    if threshold:\n",
    "        ax.axvline(threshold, color=\"red\", ls=\"dashed\")\n",
    "    if margin:\n",
    "        for line in margin:\n",
    "            ax.axvline(line, color=\"pink\", ls=\"dashed\")\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    ax.legend(handles, [\"Normal\", \"Obese\"])\n",
    "    ax.set(xlabel=\"Mass, g\")\n",
    "    return ax\n",
    "\n",
    "\n",
    "total_len = 40\n",
    "x, y = generate_data(total_len=total_len)\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(x, y, threshold=21.5, total_len=total_len)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aef114a5",
   "metadata": {},
   "source": [
    "Теперь, пользуясь нашим простым критерием, попробуем классифицировать каких-то новых мышей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "59851254",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = np.random.uniform(14, 30, 5)\n",
    "\n",
    "\n",
    "def classify(x, threshold=21.5):\n",
    "    y = np.zeros_like(x)\n",
    "    y[x > threshold] = 1\n",
    "    return y\n",
    "\n",
    "\n",
    "total_len = 40\n",
    "threshold = 21.5\n",
    "x, y = generate_data(total_len=total_len)\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(x, y, threshold=threshold, total_len=total_len)\n",
    "ax = plot_data(x_test, classify(x_test, threshold), total_len=total_len, s=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c39acd21",
   "metadata": {},
   "source": [
    "Но что если наши мыши находятся тут?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8cf7027a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = np.array([21.45, 22.5])\n",
    "\n",
    "total_len = 40\n",
    "x, y = generate_data(total_len=total_len)\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(x, y, total_len=total_len)\n",
    "ax = plot_data(x_test, classify(x_test), threshold=21.5, total_len=total_len, s=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1b844b1",
   "metadata": {},
   "source": [
    "С точки зрения нашего классификатора, все просто: больше порогового значения — толстые мыши, меньше — нормальные. Но, с точки зрения здравого смысла, логичнее было бы классифицировать обоих мышей как нормальных, так как они значительно ближе к нормальным, чем к ожиревшим."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e70da9a",
   "metadata": {},
   "source": [
    "Вооружившись этим новым знанием, попробуем классифицировать наших отъевшихся мышек по-умному. Возьмем крайние точки в каждом кластере. И в качестве порогового значения будем использовать среднее между ними."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "41d8b77c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = generate_data(total_len=total_len)\n",
    "normal_limit = x[y == 0].max()  # extreme point for 'normal'\n",
    "obese_limit = x[y == 1].min()  # extreme point for 'obese'\n",
    "\n",
    "threshold = np.mean([normal_limit, obese_limit])  # separated with mean value\n",
    "\n",
    "x_test = np.array([21.5, 23])\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(\n",
    "    x, y, total_len=total_len, threshold=threshold, margin=[normal_limit, obese_limit]\n",
    ")\n",
    "ax = plot_data(\n",
    "    x_test,\n",
    "    classify(x_test, threshold=threshold),\n",
    "    total_len=total_len,\n",
    "    s=300,\n",
    "    threshold=threshold,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "addb262b",
   "metadata": {},
   "source": [
    "Мы можем посчитать, насколько наша мышь близка к тому, чтобы оказаться в другом классе. Такое расстояние называется **margin**. И оно считается как $\\mathrm{margin} = |\\mathrm{threshold} - \\mathrm{observation}|$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "343069cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.03599309 0.46400691]\n"
     ]
    }
   ],
   "source": [
    "margins = np.abs(x_test - threshold)\n",
    "print(margins)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a446811",
   "metadata": {},
   "source": [
    "Соответственно, если мы посчитаем margins для наших крайних точек `normal_limit` и `obese_limit`, мы найдем самое большое возможное значение margin для нашего классификатора"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4325bb16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5357142670956065 2.535714267095603\n"
     ]
    }
   ],
   "source": [
    "margin_0 = np.abs(normal_limit - threshold)\n",
    "margin_1 = np.abs(obese_limit - threshold)\n",
    "print(margin_0, margin_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "800bd259",
   "metadata": {},
   "source": [
    "Такой классификатор мы называем **Maximum Margin Classifier**. Он хорошо работает в случае, когда все данные размечены аккуратно. Теперь рассмотрим более реалистичный пример, где что-то пошло не так."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0a1a43bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g9KjtyuokhiURkbtSetT47SF0e3galoiISAbDkoiISAbDkojIRergzQZuqSb+DgxLIqIa5uEhDcIxGAy1XAkBQElJCQBApVLddh8c4ENEVMM8PT3h6+uLK1euQKVSQankcUltEEKgpKQEubm5CAoKsnyJuR0MSyKiGqZQKBAZGYmsrCycO3eutsup84KCghAREXFHfTAsiYhcwMvLC02bNuWp2FqmUqnu6IiyAsOSiMhFlErlXf+RYnINnkgnIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKSwbAkIiKS4fKwXLRoEeLj4+Ht7Y0OHTrg559/dtp++/bt6NChA7y9vdGoUSMsWbLEav7SpUvRrVs3BAcHIzg4GL169cKePXtcuQpERFTHuTQs16xZg3HjxuGNN97AgQMH0K1bN/Tt2xfZ2dl222dlZeGRRx5Bt27dcODAAbz++usYO3Ys1q5da2mTlpaGJ554Atu2bUNGRgZiYmKQlJSEixcvunJViIioDlMIIYSrOu/cuTPat2+PxYsXW6a1bNkSjz32GGbMmGHTfuLEidi4cSOOHTtmmTZmzBgcPHgQGRkZdt/DZDIhODgYCxcuxNNPP12lugoKCqDRaKDT6RAYGFjNtSIioj+LquaBy44sDQYD9u/fj6SkJKvpSUlJSE9Pt7tMRkaGTfvk5GTs27cPRqPR7jIlJSUwGo2oV6+ew1r0ej0KCgqsXkRERFXlsrC8evUqTCYTwsPDraaHh4dDq9XaXUar1dptX15ejqtXr9pdZtKkSWjQoAF69erlsJYZM2ZAo9FYXtHR0dVcGyIiqstcPsBHoVBY/VsIYTNNrr296QAwe/ZsrFq1CuvWrYO3t7fDPidPngydTmd5nT9/vjqrQEREdZynqzoODQ2Fh4eHzVFkbm6uzdFjhYiICLvtPT09ERISYjX9/fffx/Tp0/Hjjz+iTZs2TmtRq9VQq9W3sRZEREQuPLL08vJChw4dsGXLFqvpW7ZsQZcuXewuk5iYaNN+8+bN6NixI1QqlWXanDlzMG3aNKSmpqJjx441XzwREdEtXHoadsKECfj000/x2Wef4dixYxg/fjyys7MxZswYANLp0VtHsI4ZMwbnzp3DhAkTcOzYMXz22WdYtmwZXn31VUub2bNn480338Rnn32GuLg4aLVaaLVaFBUVuXJViIioDnPZaVgAGDp0KPLy8vDuu+8iJycHrVq1wqZNmxAbGwsAyMnJsbrnMj4+Hps2bcL48ePx0UcfISoqCgsWLMCgQYMsbRYtWgSDwYDBgwdbvdeUKVMwdepUV64OERHVUS69z9Jd8T5LIiIC3OA+SyIioj8LhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMhiUREZEMz9ougIgIAEoM5SgxmFBmNOHs1WIU6cvh5aFEbIgfAn1UUHkoEOTrVdtlUh3FsCSiWlVQasS1YgM+2XEGGzIvosRgsmmjVABdGodi7MNN0CQsAPX8GJp0dzEsiahWCCGQV2zA3M0n8e892U7bmgXwy+9X8cvvV9GmoQYLU9ojLMAL3ip+hNHdwWuWRHTXmc0C5/NL0f/DX2SDsrJDF3To9cF2pJ++hmJ9uYsqJLLGsCSiu05bUIZBi9JxSVd2W8sbTGaMWrEXe89eg6HcXMPVEdliWBLRXZVfbMALX+7HlSL9HfVjFsDfvvoVV++wH6KqYFgS0V1jLDfju0OXcPiirkb6KzWaMOHrTOQXG2qkPyJHeHX8NpQZTSjSlyOvyACFAqjn54VAbxW8PO1/99AbTSjUl+NasQEQQJCvCgaTGSUGE+r5eSFA7Qm1ysNmOSEErhUbYDSbYTJJ76svN6N+gBq+Xh5QeyqhKzXCaDIjr8gAtUoJjY8KwX5e8FRa15JXpEeJQaq7np8XvFUe0Piobmv9jSYzivTlKNaXwyyAwjIj6vl5wUflYTW0v8RQjhK9CVeL9VAplQj08YRZAFeL9FB5KBHko0KwrxdUdrbb9RIDSgwmXCs2QOMjbVuVUgF9uQlQKHCt2GBZh2AfFTw8qv+9r9RQjuIb9XkqlQjyVUHjo4LKQV/XivUwlJthKDdDrfJAXpEePl6eCPD2RLCvFzyUimrXUNfoyoyYt+Vkjfa568w1FJcZEQwdoC8CDEWAXxig8gG8A+U7KLkGlJdK/+sTDHj6AH4hN+cbywB9IVByVfq3b6jUr6caMJYCZTqg+CqgUAJ+oYDpRnAX5wE+QYCHF+AfDihdfGxiKAH0BUBpPmAyAv5hgMoP8A6QX7bkOmAqBQovA16+gFcAoIDUj8pXWi9njCWAvhgovgIoPQCfejfW/ZbPGGMZUHZd2lYQgF99aVv7aGz7M5uBkjzAUCitl/+Nv6c6ADCbpL+VvkDa/rfOcyGXh+WiRYswZ84c5OTk4J577sH8+fPRrVs3h+23b9+OCRMm4MiRI4iKisJrr72GMWPGWLVZu3Yt3nrrLZw+fRqNGzfGe++9h4EDB7p6VQAA+SUGLN95Fst+yULRjcEFQb4qvPRgEwzu0NDmPrDrJQas3J2Nj3ecRkGp1D7Q2xNPd4lDx9hgPLE0A8890AgpnWJsgubopQKcvlIEpUKBeVtOWq7vqD2V+GJkJ0QGeWNJ2hms/fUC9Deu24QHqjGxTwv0ahmOQB8VSo0mnNAW4rVvD+Lk5SIAgEIBPNg8DNMHtkaExrta668rMeLX7GvwU3viX98fw6ELN48QEhuFYPbgNmgQ5ANdqRELt/6Of+/JhodSgWUjOuKr3eewZu95y60BIX5eGN+rGR69N9Ky7iazwIX8Erz27SHszrpm6btns1DMGNQGH2w5hY2Zl2AwSesbpfHGW48moGuTUARWI/zziw1YuO13/Ht3NkqNUj2h/l54Nak5+raOgMbn5t/CaDLhXF4pZv5wDGMfboplv2Rh0+EcGE0CANAw2Afv9m+F++KDEeB9e19A6orfLuqQX2Ks0T7Hd49Cvby9wP8mAHmnpYlKD6DFo8Aj70sfpvaYTIDuHLDhRSA74+b0Bh2Ax5YA9eKlkNy7FEhfKH04A1Kgdn8NaD0Y2LUI2LNUCujYLkDydGDL20DWjpv9RbUH+s0HguLsB0NNKMoFTv4P2PYeUJgjTfP0BtqmAD0nO94GAFCoBf73OnD0P4D5xoCp4Hgg6V9AUCzw9TNS/aHNpFCqrOQa8Ms8YN8ywFAsTfMLBR58A7jncSk0i68Ce5cBuz6SvlwAgHcQcP/fgI7PSl8mKugLgexdwKZXgfyz0jQPFZAwEEj+F5B7HNj4MnD93M159zwOJL8nBbCLKIQQwlWdr1mzBsOHD8eiRYvQtWtXfPzxx/j0009x9OhRxMTE2LTPyspCq1atMHr0aLzwwgvYuXMnXnzxRaxatQqDBg0CAGRkZKBbt26YNm0aBg4ciPXr1+Ptt9/GL7/8gs6dO1eproKCAmg0Guh0OgQGVuGb5w26EgNmpZ5wOHpv7MNN8Xz3ePirpQ/MwjIjFvz0O5b+fMZu+6fuj0WDIG/MSj2B57s1wssPN7F82B66cB0fbz+NHs3D8Nq3h6yWS+kUgyfvj8HMH47j51NX7fY9c1BrPN6uIU5fKUL/hb9YPthv1TDYB//5e1eE+KurtP6lBhM2ZF5Ay0gNnvhklyVkbhXi54Xvx3bD9E1HsfGg9B/t7MFtsO14Ln74TWu339cfaYHh98fBx8sDlwvK0Pf/fpaOwm/x+Yj78NG237HvXL7dPj5KaY/kVuE2R9T2XC8xYPK6ww7rmdIvAcM6xcDnxtH+hfwSJM/bgU+e7ohZqcetviDc6rNn7kPP5vWh5BGmXfpyEyavO4x1v16ssT47xdfDJz2MCFozABB2BvrUbwGM+N7+kVFBDrA4UToSq0wdAIzZCfz6BfDz+7bzh3wBnPgBOLhK+reXHzAyFfjycenoqjKVL/DCdilwalpJPvDbWmDTK/bnN3oQGPSp/W1QlAusHAzkHLSdp1AAQ1dKR2//eRF44WegfvNK731NCrXf1tp/76T3gHYpwLZZwJ4l9tt0fgHo9ooUmGYzcHorsHKQ/baRbYGkacCKfrbzotoDT34jfxRcSVXzwKXnBebOnYvnnnsOo0aNQsuWLTF//nxER0dj8eLFdtsvWbIEMTExmD9/Plq2bIlRo0Zh5MiReP/9mzvr/Pnz0bt3b0yePBktWrTA5MmT8fDDD2P+/PmuXBUAQJHBhFV7HQ9zX5J2GqW33FBdYjDhs51ZDtv/e/c5dG9WH2pPJZbtzLIccV0rNmDKf47gqfvjMHez7SmrJ++PQX6x0WFQAsDMH47jeokB73x3xG5QAsCF/FL88JsWZnPVvi8V68txvcSIpTvO2A1KAMgrNuCLXWctXxjq+XmhUaifw2ACgHlbTqFIXw690YTPfsmyCcrG9f1hEsJhUALAu/89gutVPGLJKzY4reeDzScttyQU68sxb8tJxIX6Ib/Y4DAoAWDqd0dwrYTXzhwpLCvHwfM1c62ywoQuIQjaNtl+UALAlePA2Z22041lQPqH9oMSkI5udsySTkVW5h0EhLW8GZQA0HoIcHCN/aAEpNOUW9+TwqmmlZcAae85nn9mG1Dg4AvKpQP2gxIAhJCOkht2AqAA/vcGUHrduk1pvuOgBIC06UC5Xjo6d2Tvp1IgA0BpHvDDPx23zckEii4DUe3srMuvwOUjjpe9Qy4LS4PBgP379yMpKclqelJSEtLT0+0uk5GRYdM+OTkZ+/btg9FodNrGUZ8AoNfrUVBQYPW6HZuPaOHsONxgMmPP2Zv/8f186gpMToLILID003loHxMMk1ng55PSf2iGcjNO5RZBoZCG2N+qYbAPhFngh99ynNZ6vcSIi9dLkXW12Gm7VXuykV/FD/jj2kIkNgrB5qOOgwYA1u2/iAdbSKd9ujQOwY/HLjttX2o04eglHQrKyrHugO1/1D2b18f3h5yv7+UCvU3IOvLtvgtO5xfpy3HqxinrUqMJ/z2UgwdbhOG/h53XkH2thPf9ybiQX1Kj/TUJUQGXf3PeaN8y2w95fQFwaLXz5Q6vBZom2U6PewA49l/rac2SgCPrnfd3/L/S9baalndaOsJzZt/ntu+tLwT2fSbT9+/S9dzoTsDpHwFTpZHHh9Y4X95QDFw8AIQ0dtzGbAJObZbqMZQA1+yfibP4bZ39vwsghbLB+Wfe7XJZWF69ehUmkwnh4eFW08PDw6HV2v+w1Wq1dtuXl5fj6tWrTts46hMAZsyYAY1GY3lFR0ffziqhoFT+yKW47OaHZWGZ/Adnib4c6hsDXApvfNCazGaoPZV2H/ul9lRCbzKjWC//H12xvhxqT9uBQ1bvbzChigeW0jVahcLhkerNPm+uk9pTWaVaK67/ltgJG2lbyG/LUjvbqzIhBArKqvB3rKhDAPryG3+PKgRhmYMjbpI4+/J4ex1W4WyCoch+SMl9qJaXAUo7wzo81Tevu1mmecv3Zy53fAR8u8wmaVCTHEOh7TYwl1ctWIyl0mlkIaTTpLeq/CXEHn2htH2ctimStk15Fe67NRQ77s9QfPO6aw1z+a0jCoX1eQwhhM00ufaVp1e3z8mTJ0On01le58+fr3L9t+rcKES2TZuGNy/gd4gNlm3fqoEGZ24c/VW0V3t6QAggIlANz0rXv3J0ZQj29bJ6H3sUCiA+1F/2FGv7mCD4ejkP1AotIgJwuaAMjev7O23XpmGQZZ3OXCmWrRUAEqI0UHko0KZhkM28M1eL0bqB7fRbeSgViKzCYCWFQoEHmshf02gW4X+jvbTeZ64Uo7Wd2m7l5aFEPb+qXf+ti4TAbY/AdqRMoQa8nO+PiEm0baP0tH8q71YRrW8OMLlV3u9AbFfraVdPyfcX0kTaoWqS0kO6jijXb3wPwLPS83RV/kDM/c6X8/QGfEOk09mahrZfHhr1lK8xqi2gk/nMje4kvZdPsPRlxJkG7YG8U/bnxXaVrh+7gMvCMjQ0FB4eHjZHfLm5uTZHhhUiIiLstvf09ERISIjTNo76BAC1Wo3AwECr1+1oEuaPKCcfyC0iAlA/4OYfukGQD+JDHf/h4kJ8ofJQIvtaCeJD/dAgSBppFuijwvDEWGw/eQXJ90RYLVNiMGH3mWt4oGko/NWOBzP3aFofvl4eeCox1mEbhQL4W8/G8HPSz60CfVTYk5WHZ7o47hOQBjp9d/ASAODA+etoGuaPECcPvm4fEwyNjwpBvl4Y16upzfyfjl3GQy3qw1vleHftc084fKoY+vfF10OQr+MP7U7x9RBw45priL8aYx9uik2Hc/BI6wh4OblFZUDbqCp/8aiL1J5KJETd3n97jvw7Mx/6tk87bqD0ADo/D6gqfQD71pNGiTrT7VVpEE9lOQeBoBgg4Jb/Nvcvl97HmS4vS7dU1DQvP6BJLyfz/e2ftvRUAR2esb69o7I2Q6RT1vlngS7/kLbbraLvcz6gJrqTNFjKx8mBQ0gTafStp1q61aXNMMdtPVTAPQPtn/L28JJG/9o7G1ADXBaWXl5e6NChA7Zs2WI1fcuWLejSpYvdZRITE23ab968GR07doRKpXLaxlGfNamerxe+GtXZ7gd/lMYbnz7T0WpkaYi/GiuevQ9hAbbflOoHqDF/aFvM+d8JhAVI7SqW9fJUYkSXOBzXFmJMj8Zo1cD6A2bhtt/hqVRgyVMd4Gfnw7lZuD9mD26DYD8vDL0vGn1bRdi0USiAWY+3QXhg1W8dqefnhVHdGqFRqB/+2qGh3Tb/TGqGZuH+mDbgHgTcCOE5m09g0ZPtEehjuxPHhvhiYUo7y69ItIgMxPhKgWk0CXy84ww+Ht7Rcnr3VvdEBeKdAa2qfNtGkI8K/x51PwK9beuJD/XDgmHtEHzL37hL4xA80SkGK9LPYf6wtnYDs11MECb1bVHlLx51UaCPCl0aV2+kopwVe7S41OpvMMX3sJ2p9AD+ugLwdXA7QeS9QI/X7M/rPAZo1APo+br92y5+fh8YvuFmeOQele5R7O5gcErbJ4HmjwCq6t2qVSW+IcCj84GwBNt5Xn436nRwVswnRBrxai8wozsDPSYBm14DWg2WbpVRVvq88a4HPL1RGvRUWb1GwF+XAwGRwJPfWt8eUiEgAhi26uZ2VPsBD78tvXdlHl7AsNXA7z/eHBB067yUr52H8h26K7eOLFmyBImJifjkk0+wdOlSHDlyBLGxsZg8eTIuXryIL774AsDNW0deeOEFjB49GhkZGRgzZozVrSPp6eno3r073nvvPQwYMAD/+c9/8Oabb96VW0cA6ZpLfokBacdzsek3LZQKYGC7Bri/UYjdWzAqHizwy+9XsfHG0VbyPRFoFx2Eb/afxz1RGjzQJBT1/LxsTiVfKzZAW1AKsxm4mF+CDZmXUGo0IbFxCAa1bwilAig1mLHx4EXszroGtacHht0XjTYNNVa15BcbcOF6KT7fmYW8IgPuiQrEk51joPFRwf827gvMK9Ijr9iAwjIj1uw9j8sFejQK9cMzXeKkBzT4qGA0mXG9xIjU33Lw0/FctI0OwuAODZF2Ihc/HbsClYcCj7dvgI5x9RBaabsVlBqRV6THioxzyLpajAiNN57tEocAb+m+0R8O52B/dj58VB546v5YtIwMqPbpz4r6/ndEix+PXYaXhxJD7otG+5hguz//pCsxILdIj8xz13FvTBB+OJyDA9nX4af2xNOJsWgazp+NqopL10vRddZWpwPlqquenxd+HNMK9couALuXSDe+N+goHTV5a5yfliu9Lt38vnsJcO00oImV7v3zry998JrN0gjN338CjqwDoABa/1UKUu960oMKTvwAnPheCpxurwLqQGDPJ8C134HABsB9o6WgCHB89uuOmYzSIJ+L+6RRuuVlQHxPoPUgKRArn4K9laFEGtV64Cvgwh6p/vZPS7e5HN0gncINjLI9qrS8dzlQeg04/j1wYpO0Hdo+KQVexVGn2QyUXAFO/Qgc+w8AhXQfbNPe0vt5+Vr3WZwHXD0hbUd9oXQqve2T0n2qhlLptPDepdK82AeAtsOkwLZ3H6iMquaBS8MSkB5KMHv2bOTk5KBVq1aYN28eunfvDgAYMWIEzp49i7S0NEv77du3Y/z48ZaHEkycONHmoQTffvst3nzzTZw5c8byUILHH3+8yjXdSVhWEEJIg0AUsNwmIadIbwQE4O+tQlGZscrLlhlNMJnNEAAgFPDxUsLjlvsJS/XlKC03w8tD4TT8yowmGE1meKs8HD6lpjpK9OUwCQEhAB8v+32azQIlRhMUAPzUnigzmlBikH7UVy6oDeVmFBvK4aEAfLw8ofJQotRogslkhlkAKg8FfLzu7Eiucn1yDOXSU5RUHkoYTWZ4Ku+8hrpEV2rAuDWZ2HbcwS0WtyHQ2xNbX+0pfekylt586oxHNf4u5QYpYDzV9q+ZCSENFIICUPvbziu9DkBI71uul57mU15248kyMtdUa5LZJJ02FUL6olD5SNDpsuXSeihV0hcMY4l0xFbVo2GzGTAWA1BKR4iOlORLg3m8gwAPmfoMJVJdXr62p1edzasGtwlLd1QTYUlEt+difikenpuGMmPNjAxd9GR79E4Ir5EvgFT3uMVDCYiIKgsN8ML0ga1rpK9eLcPQpXEIg5JcjnsYEd1Vak8P9GoZjol9mss3duL+RvUwe3Abm+cxE7kCw5KI7rpAHxVSOsdi8ZPtnd4CZY9CAYx6IB6LnuzA+1rprmFYElGt0Pio8HDLcGyZ0B2D2jdweg9rhfvigvHdSw/gH72acvQx3VUc4MMBPkS1rlhfjhJDOXZnXcMvp67iyKUClBjK4alUIr6+H7o2DkHP5mHwV3ta3QNLdKeqmgcc805Etc5P7Qk/tScebROF5HsiUFhmtDyz2NfLA768PYdqGfdAInIrKj5jl9wQr1kSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJcGlY5ufnY/jw4dBoNNBoNBg+fDiuX7/udBkhBKZOnYqoqCj4+PigZ8+eOHLkiGX+tWvX8PLLL6N58+bw9fVFTEwMxo4dC51O58pVISKiOsylYZmSkoLMzEykpqYiNTUVmZmZGD58uNNlZs+ejblz52LhwoXYu3cvIiIi0Lt3bxQWFgIALl26hEuXLuH999/H4cOHsXz5cqSmpuK5555z5aoQEVEdphBCCFd0fOzYMSQkJGDXrl3o3LkzAGDXrl1ITEzE8ePH0bx5c5tlhBCIiorCuHHjMHHiRACAXq9HeHg4Zs2ahRdeeMHue33zzTd46qmnUFxcDE9PT9naCgoKoNFooNPpEBgYeAdrSUREf2RVzQOXHVlmZGRAo9FYghIA7r//fmg0GqSnp9tdJisrC1qtFklJSZZparUaPXr0cLgMAMtKOgpKvV6PgoICqxcREVFVuSwstVotwsLCbKaHhYVBq9U6XAYAwsPDraaHh4c7XCYvLw/Tpk1zeNQJADNmzLBcN9VoNIiOjq7qahAREVU/LKdOnQqFQuH0tW/fPgCAQqGwWV4IYXf6rSrPd7RMQUEB/vKXvyAhIQFTpkxx2N/kyZOh0+ksr/Pnz1dlVYmIiAAA8hf4KnnppZcwbNgwp23i4uJw6NAhXL582WbelStXbI4cK0RERACQjjAjIyMt03Nzc22WKSwsRJ8+feDv74/169dDpVI5rEetVkOtVjutmYiIyJFqh2VoaChCQ0Nl2yUmJkKn02HPnj3o1KkTAGD37t3Q6XTo0qWL3WXi4+MRERGBLVu2oF27dgAAg8GA7du3Y9asWZZ2BQUFSE5OhlqtxsaNG+Ht7V3d1SAiIqoyl12zbNmyJfr06YPRo0dj165d2LVrF0aPHo1HH33UaiRsixYtsH79egDS6ddx48Zh+vTpWL9+PX777TeMGDECvr6+SElJASAdUSYlJaG4uBjLli1DQUEBtFottFotTCaTq1aHiIjqsGofWVbHypUrMXbsWMvo1v79+2PhwoVWbU6cOGH1QIHXXnsNpaWlePHFF5Gfn4/OnTtj8+bNCAgIAADs378fu3fvBgA0adLEqq+srCzExcW5cI2IiKguctl9lu6M91kSERHgBvdZEhER/VkwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGQwLImIiGS4NCzz8/MxfPhwaDQaaDQaDB8+HNevX3e6jBACU6dORVRUFHx8fNCzZ08cOXLEYdu+fftCoVBgw4YNNb8CREREcHFYpqSkIDMzE6mpqUhNTUVmZiaGDx/udJnZs2dj7ty5WLhwIfbu3YuIiAj07t0bhYWFNm3nz58PhULhqvKJiIgkwkWOHj0qAIhdu3ZZpmVkZAgA4vjx43aXMZvNIiIiQsycOdMyraysTGg0GrFkyRKrtpmZmaJhw4YiJydHABDr16+vcm06nU4AEDqdrnorRUREfypVzQOXHVlmZGRAo9Ggc+fOlmn3338/NBoN0tPT7S6TlZUFrVaLpKQkyzS1Wo0ePXpYLVNSUoInnngCCxcuREREhGwter0eBQUFVi8iIqKqcllYarVahIWF2UwPCwuDVqt1uAwAhIeHW00PDw+3Wmb8+PHo0qULBgwYUKVaZsyYYbluqtFoEB0dXdXVICIiqn5YTp06FQqFwulr3759AGD3eqIQQvY6Y+X5ty6zceNGbN26FfPnz69yzZMnT4ZOp7O8zp8/X+VliYiIPKu7wEsvvYRhw4Y5bRMXF4dDhw7h8uXLNvOuXLlic+RYoeKUqlarRWRkpGV6bm6uZZmtW7fi9OnTCAoKslp20KBB6NatG9LS0mz6VavVUKvVTmsmIiJypNphGRoaitDQUNl2iYmJ0Ol02LNnDzp16gQA2L17N3Q6Hbp06WJ3mfj4eERERGDLli1o164dAMBgMGD79u2YNWsWAGDSpEkYNWqU1XKtW7fGvHnz0K9fv+quDhERkaxqh2VVtWzZEn369MHo0aPx8ccfAwCef/55PProo2jevLmlXYsWLTBjxgwMHDgQCoUC48aNw/Tp09G0aVM0bdoU06dPh6+vL1JSUgBIR5/2BvXExMQgPj7eVatDRER1mMvCEgBWrlyJsWPHWka39u/fHwsXLrRqc+LECeh0Osu/X3vtNZSWluLFF19Efn4+OnfujM2bNyMgIMCVpRIRETmkEEKI2i7ibisoKIBGo4FOp0NgYGBtl0NERLWkqnnAZ8MSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJYFgSERHJ8KztAmqDEAIAUFBQUMuVEBFRbarIgYpccKROhmVhYSEAIDo6upYrISIid1BYWAiNRuNwvkLIxemfkNlsxqVLlxAQEACFQlHb5aCgoADR0dE4f/48AgMDa7ucKvuj1g2w9trwR60bYO214W7VLYRAYWEhoqKioFQ6vjJZJ48slUolGjZsWNtl2AgMDPxD7cwV/qh1A6y9NvxR6wZYe224G3U7O6KswAE+REREMhiWREREMhiWbkCtVmPKlClQq9W1XUq1/FHrBlh7bfij1g2w9trgbnXXyQE+RERE1cEjSyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMyxq2Y8cO9OvXD1FRUVAoFNiwYYPV/BEjRkChUFi97r//ftl+165di4SEBKjVaiQkJGD9+vV3te7KNVe85syZ47DP5cuX212mrKysxuqeMWMG7rvvPgQEBCAsLAyPPfYYTpw4YdVGCIGpU6ciKioKPj4+6NmzJ44cOSLbt6u3uVztRqMREydOROvWreHn54eoqCg8/fTTuHTpktN+3WW7u+O+XpW63XVfX7x4Mdq0aWO5ST8xMRE//PCDZb677udytbvzfn4rhmUNKy4uxr333ouFCxc6bNOnTx/k5ORYXps2bXLaZ0ZGBoYOHYrhw4fj4MGDGD58OIYMGYLdu3fftbpvrTcnJwefffYZFAoFBg0a5LTfwMBAm2W9vb1rrO7t27fj73//O3bt2oUtW7agvLwcSUlJKC4utrSZPXs25s6di4ULF2Lv3r2IiIhA7969Lc8ItudubHO52ktKSvDrr7/irbfewq+//op169bh5MmT6N+/v2zf7rDdAffb16tSt7vu6w0bNsTMmTOxb98+7Nu3Dw899BAGDBhgCUR33c/lanfn/dyKIJcBINavX2817ZlnnhEDBgyoVj9DhgwRffr0sZqWnJwshg0bdocV2mev7soGDBggHnroIadtPv/8c6HRaGqusCrIzc0VAMT27duFEEKYzWYREREhZs6caWlTVlYmNBqNWLJkicN+7vY2F8K2dnv27NkjAIhz5845bOMO212IP8a+XpVt7q77uhBCBAcHi08//fQPtZ9XqKjdHnfcz3lkWQvS0tIQFhaGZs2aYfTo0cjNzXXaPiMjA0lJSVbTkpOTkZ6e7soyHbp8+TK+//57PPfcc7Jti4qKEBsbi4YNG+LRRx/FgQMHXFqbTqcDANSrVw8AkJWVBa1Wa7X91Go1evTo4XT71cY2r1y7ozYKhQJBQUFO+6rt7V7B3fd1uW3urvu6yWTC6tWrUVxcjMTExD/Ufl65dnvccT9nWN5lffv2xcqVK7F161Z88MEH2Lt3Lx566CHo9XqHy2i1WoSHh1tNCw8Ph1ardXW5dq1YsQIBAQF4/PHHnbZr0aIFli9fjo0bN2LVqlXw9vZG165dcerUKZfUJYTAhAkT8MADD6BVq1YAYNlG1d1+d3ub26u9srKyMkyaNAkpKSlOHyztDtsdcP99vSrb3N329cOHD8Pf3x9qtRpjxozB+vXrkZCQ8IfYzx3VXpm77uc8DetCqMLpzEuXLgmVSiXWrl3rsI1KpRL//ve/raZ99dVXQq1W10SZNuTqbt68uXjppZeq3a/JZBL33nuvePnll++gOsdefPFFERsbK86fP2+ZtnPnTgFAXLp0yartqFGjRHJyssO+7vY2t1f7rQwGgxgwYIBo166d0Ol01eq7Nra7Pe62r1elbnfb1/V6vTh16pTYu3evmDRpkggNDRVHjhz5Q+znjmq/lTvv53XyJ7rcSWRkJGJjY51+G4qIiLD5ppebm2vzjfBu+Pnnn3HixAmsWbOm2ssqlUrcd999Lvnm9/LLL2Pjxo3YsWOH1c+vRUREAJC+QUdGRlqmy22/u7nNHdVewWg0YsiQIcjKysLWrVur/XNFtbHd7XGnfb0qdbvjvu7l5YUmTZoAADp27Ii9e/fi//7v/zBx4kQA7r2fO6r9448/BuDe+znA07C1Li8vD+fPn7fawStLTEzEli1brKZt3rwZXbp0cXV5NpYtW4YOHTrg3nvvrfayQghkZmY6Xdfb6fOll17CunXrsHXrVsTHx1vNj4+PR0REhNX2MxgM2L59u9Ptdze2uVztwM0PkFOnTuHHH39ESEjIbb3P3d7u9rjDvl6dut1tX3f0Pnq93q33c0cqagfcdz+v/AZUgwoLC8WBAwfEgQMHBAAxd+5cceDAAXHu3DlRWFgoXnnlFZGeni6ysrLEtm3bRGJiomjQoIEoKCiw9DF8+HAxadIky7937twpPDw8xMyZM8WxY8fEzJkzhaenp9i1a9ddqbuCTqcTvr6+YvHixXb7qFz31KlTRWpqqjh9+rQ4cOCAePbZZ4Wnp6fYvXt3jdX9t7/9TWg0GpGWliZycnIsr5KSEkubmTNnCo1GI9atWycOHz4snnjiCREZGVnr21yudqPRKPr37y8aNmwoMjMzrdro9XqHtbvDdnfXfb0q+4sQ7rmvT548WezYsUNkZWWJQ4cOiddff10olUqxefNmIYT77udytbvzfn4rhmUN27ZtmwBg83rmmWdESUmJSEpKEvXr1xcqlUrExMSIZ555RmRnZ1v10aNHD/HMM89YTfvmm29E8+bNhUqlEi1atHB63aem667w8ccfCx8fH3H9+nW7fVSue9y4cSImJkZ4eXmJ+vXri6SkJJGenl6jddurGYD4/PPPLW3MZrOYMmWKiIiIEGq1WnTv3l0cPnzYae1CuH6by9WelZXlsM22bdsc1u4O291d9/Wq7C9CuOe+PnLkSBEbG2t5j4cfftgSlEK4734uV7s77+e34k90ERERyeA1SyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMSyIiIhkMSyI3NWLECCgUCowZM8Zm3osvvgiFQoERI0bc/cKI6iCGJZEbi46OxurVq1FaWmqZVlZWhlWrViEmJqYWKyOqWxiWRG6sffv2iImJwbp16yzT1q1bh+joaLRr186qbWpqKh544AEEBQUhJCQEjz76KE6fPm2ZbzAY8NJLLyEyMhLe3t6Ii4vDjBkzLPOnTp2KmJgYqNVqREVFYezYsdWqNT09HW3btoW3tzc6duyIDRs2QKFQIDMz8/ZWnsiNMCyJ3Nyzzz6Lzz//3PLvzz77DCNHjrRpV1xcjAkTJmDv3r346aefoFQqMXDgQJjNZgDAggULsHHjRnz99dc4ceIEvvrqK8TFxQEAvv32W8ybNw8ff/wxTp06hQ0bNqB169ZVrrGwsBD9+vVD69at8euvv2LatGmW31gk+jPgjz8Tubnhw4dj8uTJOHv2LBQKBXbu3InVq1cjLS3Nqt2gQYOs/r1s2TKEhYXh6NGjaNWqFbKzs9G0aVM88MADUCgUiI2NtbTNzs5GREQEevXqBZVKhZiYGHTq1KnKNa5cuRIKhQJLly6Ft7c3EhIScPHiRYwePfqO1p3IXfDIksjNhYaG4i9/+QtWrFiBzz//HH/5y18QGhpq0+706dNISUlBo0aNEBgYaPlh4+zsbADSgKHMzEw0b94cY8eOxebNmy3L/vWvf0VpaSkaNWqE0aNHY/369SgvL69yjSdOnECbNm3g7e1tmVadsCVydwxLoj+AkSNHYvny5VixYoXdU7AA0K9fP+Tl5WHp0qXYvXs3du/eDUC6VglI1z+zsrIwbdo0lJaWYsiQIRg8eDAAaSDRiRMn8NFHH8HHxwcvvvgiunfvDqPRWKX6hBBQKBQ204j+LBiWRH8Affr0gcFggMFgQHJyss38vLw8HDt2DG+++SYefvhhtGzZEvn5+TbtAgMDMXToUCxduhRr1qzB2rVrce3aNQCAj48P+vfvjwULFiAtLQ0ZGRk4fPhwlepr0aIFDh06BL1eb5m2b9++21xbIvfDa5ZEfwAeHh44duyY5f9XFhwcjJCQEHzyySeIjIxEdnY2Jk2aZNVm3rx5iIyMRNu2baFUKvHNN98gIiICQUFBWL58OUwmEzp37gxfX198+eWX8PHxsbqu6UxKSgreeOMNPP/885g0aRKys7Px/vvvA4DNESfRHxGPLIn+IAIDAxEYGGh3nlKpxOrVq7F//360atUK48ePx5w5c6za+Pv7Y9asWejYsSPuu+8+nD17Fps2bYJSqURQUBCWLl2Krl27ok2bNvjpp5/w3XffISQkBIB0W0nFyFlHtX333XfIzMxE27Zt8cYbb+Dtt98GAKvrmER/VArBCwtEJKPiSUHLly+v8jIrV67Es88+C51OBx8fH9cURnSX8DQsEcnavn07duzY4bTNF198gUaNGqFBgwY4ePAgJk6ciCFDhjAo6U+BYUlEsrKysmTbaLVavP3229BqtYiMjMRf//pXvPfee3ehOiLX42lYIiIiGRzgQ0REJINhSUREJINhSUREJINhSUREJINhSUREJINhSUREJINhSUREJINhSUREJINhSUREJOP/AYTsY5Pzk2brAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_realistic_data(total_len=40):\n",
    "    x = np.hstack(\n",
    "        [\n",
    "            np.random.uniform(14, 21, total_len // 2),\n",
    "            np.random.uniform(24, 33, total_len // 2),\n",
    "        ]\n",
    "    )\n",
    "    y = np.hstack([np.zeros(total_len // 2), np.ones(total_len // 2)])\n",
    "    indx = np.where(x == x[y == 1].min())[0]\n",
    "    y[indx] = 0\n",
    "    s = np.ones_like(x) * 50\n",
    "    s[indx] = 300\n",
    "    return x, y, s\n",
    "\n",
    "\n",
    "total_len = 40\n",
    "x, y, s = generate_realistic_data(total_len=total_len)\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(x, y, total_len=total_len, s=s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf1fe3d",
   "metadata": {},
   "source": [
    "В таком случае наш **Maximum Margin Classifier** работать не будет. Исходя из этого, мы можем прийти к выводу, что наш классификатор очень чувствителен к выбросам. Решение этой проблемы будет рассмотрено в следующем разделе."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5237fee7",
   "metadata": {},
   "source": [
    "### 2D классификация"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db619987",
   "metadata": {},
   "source": [
    "Теперь рассмотрим пример, где мы измерили не только вес мышей, но и их длину от хвоста до носа. Мы можем применить метод Support Vector Classifier, и теперь классы разделяет не одно пороговое значение (по сути, точка), а линия."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "43f0fe46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import svm\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "\n",
    "def generate_2d_data(total_len=40):\n",
    "    x, y = make_blobs(n_samples=total_len, centers=2, random_state=42)\n",
    "    x[:, 0] += 10\n",
    "    x[:, 1] += 20\n",
    "    return x, y\n",
    "\n",
    "\n",
    "def plot_data(x, y, total_len=40, s=50, threshold=21.5):\n",
    "    ax = sns.scatterplot(x=x[:, 0], y=x[:, 1], hue=y, s=s)\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    ax.legend(handles, [\"Normal\", \"Obese\"])\n",
    "    ax.set(xlabel=\"Mass, g\", ylabel=\"Length, cm\")\n",
    "    return ax\n",
    "\n",
    "\n",
    "total_len = 40\n",
    "x, y = generate_2d_data(total_len=total_len)\n",
    "plt.figure(figsize=(5, 3))\n",
    "ax = plot_data(x, y, total_len=total_len)\n",
    "\n",
    "# Code for illustration, later we will understand how it works\n",
    "# fit the model, don't regularize for illustration purposes\n",
    "clf = svm.SVC(kernel=\"linear\", C=1000)\n",
    "clf.fit(x, y)\n",
    "\n",
    "# plot the decision function\n",
    "ax = plt.gca()\n",
    "xlim = ax.get_xlim()\n",
    "ylim = ax.get_ylim()\n",
    "\n",
    "# create grid to evaluate model\n",
    "xx = np.linspace(xlim[0], xlim[1], 30)\n",
    "yy = np.linspace(ylim[0], ylim[1], 30)\n",
    "YY, XX = np.meshgrid(yy, xx)\n",
    "xy = np.vstack([XX.ravel(), YY.ravel()]).T\n",
    "Z = clf.decision_function(xy).reshape(XX.shape)\n",
    "\n",
    "# plot decision boundary and margins\n",
    "ax.contour(\n",
    "    XX, YY, Z, colors=\"k\", levels=[-1, 0, 1], alpha=0.5, linestyles=[\"--\", \"-\", \"--\"]\n",
    ")\n",
    "# plot support vectors\n",
    "ax.scatter(\n",
    "    clf.support_vectors_[:, 0],\n",
    "    clf.support_vectors_[:, 1],\n",
    "    s=100,\n",
    "    linewidth=1,\n",
    "    facecolors=\"none\",\n",
    "    edgecolors=\"k\",\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "068d7cfc",
   "metadata": {},
   "source": [
    "### 3D классификация"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0349bb49",
   "metadata": {},
   "source": [
    "Если мы добавим еще одно измерение — возраст, мы обнаружим, что наши данные стали трехмерными, а разделяет их теперь не линия, а плоскость."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce073bdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_3d_data(total_len=40):\n",
    "    x, y = make_blobs(n_samples=total_len, centers=2, random_state=42, n_features=3)\n",
    "    x[:, 0] += 10\n",
    "    x[:, 1] += 20\n",
    "    x[:, 2] += 10\n",
    "    return x, y\n",
    "\n",
    "\n",
    "def plot_data(x, y, total_len=40, s=50, threshold=21.5):\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection=\"3d\")\n",
    "    ax.scatter(xs=x[:, 0], ys=x[:, 1], zs=x[:, 2], c=y, s=s, cmap=\"Set1\")\n",
    "    # plot the decision function\n",
    "    ax = plt.gca()\n",
    "    xlim = ax.get_xlim()\n",
    "    ylim = ax.get_ylim()\n",
    "\n",
    "    # create grid to evaluate model\n",
    "    xx = np.linspace(xlim[0], xlim[1], 30)\n",
    "    yy = np.linspace(ylim[0], ylim[1], 30)\n",
    "    YY, XX = np.meshgrid(yy, xx)\n",
    "    ax.plot_surface(XX, YY, XX * YY * 0.2, alpha=0.2)\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    ax.legend(handles, [\"Normal\", \"Obese\"])\n",
    "    ax.set(xlabel=\"Mass, g\", ylabel=\"Length, cm\", zlabel=\"Age, days\")\n",
    "    return ax\n",
    "\n",
    "\n",
    "total_len = 40\n",
    "x, y = generate_3d_data(total_len=total_len)\n",
    "ax = plot_data(x, y, total_len=total_len)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77c24f13",
   "metadata": {},
   "source": [
    "Соответственно, если бы у нас было 4 измерения и больше (например: вес, длина, возраст, кровяное давление), то многомерная плоскость, которая бы разделяла наши классы, называлась бы **гиперплоскость** (рисовать мы ее, конечно же, не будем). Чисто технически, и точка, и линия — тоже гиперплоскости. Но все же гиперплоскостью принято называть то, что нельзя нарисовать на бумаге."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a1ef558",
   "metadata": {},
   "source": [
    "### Геометрическая интерпретация"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b0696e9",
   "metadata": {},
   "source": [
    "Теперь, когда мы разобрались с тем, что такое регрессия, вернемся к задаче классификации изображений из датасета CIFAR-10. Как можно применить регрессию для классификации?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90d5f286",
   "metadata": {},
   "source": [
    "Предположим, у нас есть только 2 класса. Как можно использовать регрессию для того, чтобы определить относится ли изображение к классу 0 или к классу 1? В упрощенном варианте задача будет состоять в том, чтобы провести разделяющую плоскость (прямую) между 2-мя классами. Например, мы можем провести прямую через 0.\n",
    "\n",
    "Такая прямая будет задана направляющим вектором $\\vec W$, число компонентов которого будет равно размерности пространства признаков. Уравнение гиперплоскоскости в этом случае имеет вид\n",
    "\n",
    "$$\\large \\sum_i W_i \\cdot x_i = 0$$\n",
    "или, что эквивалентно:\n",
    "$$\\large ( \\vec W , \\vec x) = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fab6c873",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/regression_for_classification_imgs.png\" width=\"270\">\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9924284f",
   "metadata": {},
   "source": [
    "Рассмотрим другую ситуацию. В этом случае мы не можем просто провести прямую через 0, но можем отступить от 0 на какое-то расстояние и провести ее там. Вспомним, что уравнение прямой это $y=wx+b$, где $b$ — это смещение (*bias*). Соответственно, если b != 0, то прямая через 0 проходить не будет, а будет проходить через значение b."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "335fc923",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/regression_for_classification_add_bias.png\" width=\"270\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "361f2d52",
   "metadata": {},
   "source": [
    "Таким образом, для классификации объектов на два класса нам нужно подобрать значение вектора $W$ и величину смещения $B$. Вместе они зададут гиперплоскость вида:\n",
    "$$\\large ( \\vec W , \\vec x) - B = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2011b94",
   "metadata": {},
   "source": [
    "[Linear Classification Loss Visualization\n",
    "](http://vision.stanford.edu/teaching/cs231n-demos/linear-classify/)\n",
    "\n",
    "\n",
    "Если у нас есть несколько классов, мы можем для каждого из них посчитать уравнение $y_{i} = w_{i}x_{i}+b_{i}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c54fe44",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/regression_for_classification_add_bias_add_multiclasses.jpg\" width=\"400\">\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9adfb103",
   "metadata": {},
   "source": [
    "На картинке нас интересуют 3 класса. Соответственно, мы можем записать систему линейных уравнений:\n",
    "\n",
    "\\begin{cases}\n",
    "y_{0} = w_{0}x_{0} + b_{0} \\\\\n",
    "y_{1} = w_{1}x_{1} + b_{1} \\\\\n",
    "y_{2} = w_{2}x_{2} + b_{2} \\\\\n",
    "\\end{cases}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed815632",
   "metadata": {},
   "source": [
    "### Единообразный подход к учету смещения"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78c1b066",
   "metadata": {},
   "source": [
    "Мы их можем собрать в матрицу, тогда получится следующее:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21804846",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/scalar_product_add_bias.png\" width=\"750\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f8b4522",
   "metadata": {},
   "source": [
    "У нас есть матрица коэффициентов, которые мы каким-то образом подобрали, пока ещё непонятно как. Есть вектор $x$, соответствующий изображению.\n",
    "\n",
    "Мы умножаем вектор на матрицу, получаем нашу гиперплоскость для четырехмерного пространства в данном случае. Чтобы оно не лежало в 0, мы должны добавить смещение. И мы можем сделать это после, но можно взять и этот вектор смещения (вектор **b**) просто приписать к матрице **W**.\n",
    "\n",
    "Что будет выходом такой конструкции? Мы умножили матрицу весов на наш вектор, соответствующий изображению, получили некоторый отклик. По этому отклику мы так же, как и при реализации метода ближайшего соседа можем судить: если он больше остальных, то мы предполагаем, что это кошка.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ae4fccdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image  [ 56 231  24   2]\n",
      "Weights  [ 0.2 -0.5  0.1  2. ]\n",
      "img * w_cat  [  11.2 -115.5    2.4    4. ]\n",
      "sum  -97.89999999999999\n",
      "Add bias  -96.8\n"
     ]
    }
   ],
   "source": [
    "img = np.array([56, 231, 24, 2])\n",
    "w_cat = np.array([0.2, -0.5, 0.1, 2.0])\n",
    "print(\"Image \", img)\n",
    "print(\"Weights \", w_cat)\n",
    "print(\"img * w_cat \", img * w_cat)\n",
    "print(\"sum \", (img * w_cat).sum())\n",
    "print(\"Add bias \", (img * w_cat).sum() + 1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f06ca1e",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/img_to_function_get_scores.png\" width=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78910c5a",
   "metadata": {},
   "source": [
    "Обозначим входное изображение как $x$, а шаблон для первого из классов как $w_0$.\n",
    "\n",
    "Элементы пронумеруем подряд 1,2,3 … $n$. То есть развернем матрицу пикселей изображения в вектор.\n",
    "\n",
    "Тогда результат сравнения изображения с этим шаблоном будет вычисляться по формуле: $x[0]*w_0[0] + x[1]*w_0[1] + … x[n-1]*w_0[n-1]$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87f89e19",
   "metadata": {},
   "source": [
    "**Предварительная обработка**\n",
    "\n",
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/img_to_vector_to_compute_scalar_product.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35cc8574",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/scalar_product_ways_to_use.png\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d94b9e0f",
   "metadata": {},
   "source": [
    "Эта простая модель лежит в основе практически всех сложных моделей, которые мы будем рассматривать дальше. Внутри будем также пользоваться скалярным произведением.\n",
    "\n",
    "В дальнейшем мы будем проходить сверточные сети, они работают очень похоже:\n",
    "мы тоже накладываем шаблон на некоторую матрицу и перемножаем элементы, затем складываем. Единственное отличие — обычно ядро свертки меньше, чем размер самого изображения.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6a1eaca",
   "metadata": {},
   "source": [
    "Собирая все вместе, получаем какое-то компактное представление, что у нас есть некоторая функция, на вход которой мы подаем изображение, и у нее есть параметры (веса). Пока происходит просто умножение вектора на матрицу, в дальнейшем это может быть что-то более сложное, функция будет представлять какую-то более сложную модель. А на выходе (для классификатора) мы получаем числа, которые интерпретируют уверенность модели в том, что изображение принадлежит к определенному классу.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bc67d57",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/input_img_scalar_product_add_bias_get_scores.png\" width=\"450\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72306831",
   "metadata": {},
   "source": [
    "Соответственно, эти коэффициенты, которые являются весами модели, надо каким-то образом подбирать. Но прежде чем подбирать коэффициенты, давайте определимся со следующим: как мы будем понимать, что модель работает хорошо или плохо? Вывод модели представляет собой просто некоторый набор чисел. Но как эти числа следует правильно интерпретировать? Рассмотрим этот вопрос в следующем разделе."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "896e6748",
   "metadata": {},
   "source": [
    "## Линейный классификатор с пороговой функций принятия решения. Hard Margin Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a997df0",
   "metadata": {},
   "source": [
    "Рассмотрим пример задачи классификации на два класса. У нас имеется:\n",
    "1. Набор данных из $N$ наблюдений.\n",
    "2. Для каждого из наблюдений нам известно признаковое описание объекта в виде набора вещественных чисел. То есть объекту под номером $i$ соответствует вектор $\\vec x_i$.\n",
    "3. Также для каждого наблюдения нам известна истинная метка класса. Мы знаем что объекту с признаковым описанием $\\vec x_i$ соответствует метка класса $y_i$. Будем считать, что метки классов принимают значения $y_i \\in \\pm 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6671826",
   "metadata": {},
   "source": [
    "Мы хотим подобрать такие $\\vec W$ и $B$, чтобы можно было провести такие гиперплоскости:\n",
    "\n",
    "$$\\large (\\vec W \\vec x) - B  = 1$$\n",
    "**\"Лежащие на этой плоскости и выше объекты относятся к классу $+1$\"**\n",
    "\n",
    "$$\\large (\\vec W \\vec x) - B  = -1$$\n",
    "**\"Лежащие на этой плоскости и ниже объекты относятся к классу $-1$\"**\n",
    "\n",
    "Расстояние между двумя этими **жесткими** границами задаётся просто длиной вектора $\\vec W$ и равно $\\frac{2}{||\\vec W||}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a4b62fd",
   "metadata": {},
   "source": [
    "Условие того, что объекты лежат $(\\vec x_i, y_i)$ лежат по правильную сторону от разделяющих поверхностей можно записать в совместно:\n",
    "\n",
    "$$\\large y_i ((\\vec W, \\vec x_i) - B )\\ge 1,$$ которое должно выполняться для всех объектов $1 \\le i \\le N$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b613fff0",
   "metadata": {},
   "source": [
    "Среди всех решений $\\vec W$ и $B$, которые удовлетворяют условию выше, мы хотим подобрать такое, при котором пороговые разделяющие поверхности будут находится дальше всего. Так как расстояние между ними равно $\\frac{2}{||\\vec W||}$, мы приходим к следующей задаче на условный экстремум:\n",
    "\n",
    "$$\\large ||\\vec W|| \\rightarrow \\min, \\; y_i ((\\vec W, \\vec x_i) - B )\\ge 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "138383d3",
   "metadata": {},
   "source": [
    "Подобная задача на условный экстремум может быть решена при помощи [метода множителей Лагранжа](https://en.wikipedia.org/wiki/Lagrange_multiplier):\n",
    "\n",
    "Найти $\\alpha_i$, $\\vec W$ и $B$, которые реализуют минимум функции потерь:\n",
    "\n",
    "$$\\large L =  (\\vec W, \\vec W) + \\sum_i \\alpha_i (y_i ((\\vec W, \\vec x_i) - B )$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5858252f",
   "metadata": {},
   "source": [
    "## Линейный классификатор с Hinge loss. Soft Margin Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e77c1a7c",
   "metadata": {},
   "source": [
    "Мы можем модифицировать функцию потерь на одном примере, разрешив классификатору ошибаться и упорядочивать некоторые объекты по \"неправильную\" сторону от разделяющих поверхностей.\n",
    "Данная модификация называется [Hinge_loss](https://en.wikipedia.org/wiki/Hinge_loss):\n",
    "$$\\large L_i = \\max(0, 1 - y_i ((\\vec W, \\vec x_i) - B ))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5256901f",
   "metadata": {},
   "source": [
    "Давайте рассмотрим, как линейная модель классификации с Hinge loss работает на практике. Мы можем применить линейный классификатор в том числе и к изображениям — достаточно просто вытянуть изображение из тензора формата $(\\text{C}, \\text{H}, \\text{W})$ в $(\\text{C} \\cdot \\text{H} \\cdot \\text{W})$-мерный вектор. Применим линейный классификатор к нескольким изображениям из датасета CIFAR-10:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a7047ef",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/model_predicted_scores_for_10_classes.png\" width=\"550\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56e51c91",
   "metadata": {},
   "source": [
    "По аналогии с тем, что мы уже делали, мы можем сравнивать отклик на ключевой класс  (про который нам известно, что он на изображении, так как у нас есть метка этого класса) с остальными. Соответственно, мы подали изображение кошки и получили на выход вектор. Чем больше значение, тем больше вероятность того, что, по мнению модели, на изображении этот класс. Для кошки в данном случае это значение 2.9. Хорошо это или плохо? Нельзя сказать, пока мы не проанализировали остальную часть вектора. Если бы мы могли посмотреть на все значения в векторе, мы бы увидели, что есть значения больше, то есть в данном случае модель считает, что это собака, а не кошка, потому что для собаки значение максимально."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4fe27a6",
   "metadata": {},
   "source": [
    "На основании этого можно построить некоторую оценку. Давайте смотреть на разницу правильного класса с неправильными. Насколько уверенность в кошке будет больше остальных, настолько хорошо работает наша модель.\n",
    "\n",
    "Но поскольку нам важна не работа модели на конкретном изображении, а важно оценить ее работу в целом, то эту операцию нужно проделать либо для всего датасета, либо для некоторой выборки, которую мы подаем на вход и подсчитываем средний показатель. Этот показатель (насколько хорошо работает модель), называется функцией потерь, или **loss function**. Называется она так потому, что она показывает не то, насколько хорошо работает модель, а то, насколько плохо.\n",
    "\n",
    "Дальше будет понятно, почему так удобнее (разница только в знаке). Как это посчитать для всего датасета?\n",
    "\n",
    "Мы каким-то образом считаем loss для конкретного изображения, потом усредняем по всем изображениям."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ecbca7",
   "metadata": {},
   "source": [
    "Дано: 3 учебных примера, 3 класса. При некотором W баллы f (a, W) = Wx равны:\n",
    "\n",
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/model_predicted_scores_for_3_classes.png\" width=\"450\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e86e450a",
   "metadata": {},
   "source": [
    "Функция потерь показывает, насколько хорош наш текущий классификатор.\n",
    "\n",
    "Дан датасет примеров:\n",
    "\n",
    "$\\begin{Bmatrix} (x_i,y_i)  \\end{Bmatrix}_{i=1}^N \t$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8788500",
   "metadata": {},
   "source": [
    "Где **$x_i$** — изображение, **$y_i$** — метка (число).\n",
    "\n",
    "Потери по набору данных — это среднее значение потерь для примеров:\n",
    "\n",
    "$ L = {1 \\over N}\\sum_iL_i(f(x_i,W),y_i)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d5eb239",
   "metadata": {},
   "source": [
    "Построим функцию потерь для одного примера $L_i(f(x_i,W),y_i)$:\n",
    "\n",
    "1. Вычислим вектор значений прогнозов классификатора $s = f(x_i, W)$.\n",
    "1. Для всех примеров рассмотрим разницу между оценкой на истинной категории и всеми оценками классификатора для неправильных категорий: $s_{y_i} - s_j$ для $j \\neq y_i$.\n",
    "1. Если получившаяся разница положительная и превышает некоторое пороговое значение («зазор»), которое мы установим равным $1$, то будем считать, что категория $j$ не мешает модели верно классифицировать входной объект, припишем категории $j$ нулевой вклад в $L_i(f(x_i,W),y_i)$.\n",
    "1. Если получившаяся разница не превосходит установленного нами единичного «зазора», то мы будем считать что ответ классификатора $s_j$ в категории $j$ мешает верной классификации входного объекта. В этом случае припишем для категории $j$ аддитивный вклад в $L_i(f(x_i,W),y_i)$ равный $s_j-s_{y_i}+1$.\n",
    "\n",
    "Описанную процедуру гораздо проще записать в виде формулы:\n",
    "\n",
    "\n",
    "$L_i = \\sum_{j\\neq y_i}\\begin{cases}\n",
    "  0,  & \\mbox{если } s_{y_i}\\geq s_j+1\\mbox{} \\\\\n",
    "  s_j-s_{y_i}+1, & \\mbox{если наоборот, то} \\mbox{}\n",
    "\\end{cases}$\n",
    "\n",
    "$=\\sum_{j\\neq y_i}max(0,s_j-s_{y_i}+1)$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05211d2b",
   "metadata": {},
   "source": [
    "Логика такая: если у нас уверенность модели в правильном классе большая, то модель работает хорошо и loss для данного конкретного примера должен быть равен нулю. Если есть класс, в котором модель уверена больше, чем в правильном, то loss должен быть не равен нулю, а отображать какую-то разницу, поскольку модель сильно ошиблась. При этом есть ещё одно соображение: что будет, если на выходе у правильного и ошибочного класса будут примерно равные веса? То есть, например, у кошки было бы 3.2, а у машины не 5.2, а 3.1. В этом случае ошибки нет, но понятно, что при небольшом изменении в данных (просто шум) скорее всего она появится.\n",
    "\n",
    "То есть модель плохо отличает эти классы. Поэтому мы и вводили некоторый зазор, который должен быть между правильным и неправильным ответом.\n",
    "\n",
    "Посмотрим на изображение снизу. У нас есть два класса: фиолетовые треугольники и синие квадраты, разделенные зазором. Также можем увидеть желтые треугольники и квадраты — это ошибочно распознанные классы.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8309bf1",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/svm_decision_boundary.png\" width=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77ea28dd",
   "metadata": {},
   "source": [
    "И тоже учитывать его в loss function: сравнивать его результат для правильного класса не с чистым выходом для другого, а добавить к нему некоторую дельту (в данном случае — 1(единица)). Смотрим: если разница больше 0, то модель работает хорошо и $L_i = 0$. Если нет, то мы возвращаем эту разницу, и loss будет складываться из этих индивидуальных разниц.\n",
    "\n",
    "$L_i = \\sum_{j\\neq y_i}\\begin{cases}\n",
    "  0,  & \\mbox{если } s_{y_i}\\geq s_j+1\\mbox{} \\\\\n",
    "  s_j-s_{y_i}+1, & \\mbox{если наоборот, то} \\mbox{}\n",
    "\\end{cases}$\n",
    "\n",
    "$=\\sum_{j\\neq y_i}max(0,s_j-s_{y_i}+1)$\n",
    "\n",
    "Ниже пример того, как считается loss."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59dc751b",
   "metadata": {},
   "source": [
    "Считаем функцию потерь для 1-ого изображения:\n",
    "\n",
    "$$\\large L_i = \\sum_{j \\neq y_i} \\max(0, s_j-s_{y_i} +1)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28de5d0a",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/compute_loss_use_model_scores_for_1_example.png\" width=\"300\">\n",
    "\n",
    "$L_i = \\max(0, 5.1-3.2+1) + \\max(0, -1.7-3.2+1) = \\max(0, 2.9) + \\max(0, -3.9) = 2.9+0 = 2.9$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b16b4397",
   "metadata": {},
   "source": [
    "Также считаем потери для второго и третьего изображений:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a894e72",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/compute_loss_use_model_scores_for_2.png\" width=\"300\">\n",
    "\n",
    "$L_i = \\max(0, 1.3-4.9+1) + \\max(0, 2.0-4.9+1) = \\max(0, -2.6) + \\max(0, -1.9) = 0+0 = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "098753d5",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/compute_loss_use_model_scores_for_3.png\" width=\"300\">\n",
    "\n",
    "$L_i = \\max(0, 2.2-(-3.1)+1) + \\max(0, 2.5-(-3.1)+1) = \\max(0, 6.3) + \\max(0, 6.6) = 6.3+6.6 = 12.9$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ebf578d",
   "metadata": {},
   "source": [
    "Значения потерь получились следующие:\n",
    "\n",
    "<font color=2BA8E0 size=6><pre>Потери: 2.9   0   12.9</pre></font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b854084",
   "metadata": {},
   "source": [
    "Считаем среднее значение loss для всего датасета:\n",
    "\n",
    "$ L = {1 \\over N}\\sum_{i=1}^N L_i$\n",
    "\n",
    "$L={2.9 + 0 + 12.9 \\over 3} = 5.27$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1edf361",
   "metadata": {},
   "source": [
    "SVM loss\n",
    "\n",
    "$L_i=\\sum_{j\\neq y_i}\\max(0,s_j-s_{y_i}+1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "710ff607",
   "metadata": {},
   "source": [
    "### MSE-loss\n",
    "$$MSE = \\frac 1 N \\sum_i(y_i - \\hat{y_i})^2 $$\n",
    "\n",
    "$y_i$, $\\hat{y_i}$ — константы, не являются функциями друг от друга\n",
    "$$\\hat{y} = wx_i + b $$\n",
    "\n",
    "$$\\frac {\\delta MSE} {\\delta w} = \\frac 1 N \\sum \\frac {\\delta (y_i - \\hat{y_i}) ^2} {\\delta \\hat{y_i}} \\frac {\\delta \\hat{y_i}} {\\delta w}$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ac74d7e",
   "metadata": {},
   "source": [
    "## Кросс-энтропия как общая функция потерь для задач классификации"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f066c0f6",
   "metadata": {},
   "source": [
    "### Переход к вероятностям\n",
    "\n",
    "**Softmax**\n",
    "\n",
    "[Видео от StatQuest, которое объясняет Softmax](https://www.youtube.com/watch?v=KpKog-L9veg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ac4cf97",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/scores_to_probability.png\" width=\"750\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0797063b",
   "metadata": {},
   "source": [
    "Перейти к вероятностям мы сможем, проведя с весами некоторые не очень сложные математические преобразования.\n",
    "\n",
    "На слайде выше показано, почему выходы модели часто называют [logit’ами](https://en.wikipedia.org/wiki/Logit). Если предположить, что у нас есть некая вероятность, от которой мы берем такую функцию (logit), то результат может принимать значение в любых вещественных числах. Мы можем считать, что выходы модели — это logit’ы."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c88c4801",
   "metadata": {},
   "source": [
    "Например, мы могли бы просто взять индекс массива, в котором значение (logit) максимально. Предположим, что наша модель выдала следующие значения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d1ad860",
   "metadata": {},
   "outputs": [],
   "source": [
    "logits = [\n",
    "    5.1,  # cat\n",
    "    3.2,  # car\n",
    "    -1.7,  # frog\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93bbecf5",
   "metadata": {},
   "source": [
    "Тогда, чтобы узнать какой класс наша сеть предсказала, мы могли бы просто взять `argmax` от наших `logits`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a25ad5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "print(\"Predicted class = %i (Cat)\" % (np.argmax(logits)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30070f3d",
   "metadata": {},
   "source": [
    "Но от argmax нельзя посчитать градиент, так как производная от константы равна 0. Соответственно, если бы мы вставили производную от argmax в градиентный спуск, мы бы получили везде нули, и соответственно, наша модель бы вообще ничему не научилась"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9410549e",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(5, 3))\n",
    "plt.scatter(np.arange(3), [1, 0, 0], color=\"red\", s=50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24bbea4e",
   "metadata": {},
   "source": [
    "А мы бы хотели получить не logit’ы, а настоящую вероятность на выходе модели. Да еще и таким образом, чтобы от наших вероятностей можно было посчитать градиент. Для этого мы можем применить к нашим логитам функцию **Softmax**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dcf85db",
   "metadata": {},
   "source": [
    "<img src =\"https://edunet.kea.su/repo/EduNet-content/L02/out/linear_classifier_softmax.png\" width=\"600\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acec4eb8",
   "metadata": {},
   "source": [
    "Функция SoftMax:\n",
    "\n",
    "$s=f(x_i; W);$\n",
    "\n",
    "$ \\displaystyle P(Y=k|X=x_i) = \\frac{e^{s_k}}{\\sum_je^{s_j}}.$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1928095a",
   "metadata": {},
   "source": [
    "1. Отобразим наши logit’ы на значения $[0, +∞)$.\n",
    "\n",
    "Для этого возведем экспоненту (число Эйлера 2.71828) в **степень логита**. В результате, мы получим вектор гарантированно неотрицательных чисел (положительное число, возведенное в степень, даже отрицательную, даст положительное значение).\n",
    "\n",
    "2. Нормализуем.\n",
    "\n",
    "Чтобы  интерпретировать числа как вероятности, их сумма должна быть равна единице. Мы должны их нормализовать, то есть **поделить на сумму**.\n",
    "\n",
    "Это преобразование называется **Softmax функцией**. **Получаются вероятности**, то есть числа, которые можно интерпретировать, как вероятности."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54b286c2",
   "metadata": {},
   "source": [
    "$\\large \\displaystyle \\text{Softmax}_\\text{кошка} = \\frac{e^{5.1}}{e^{5.1} + e^{3.2} + e^{-1.7}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7f4aefa7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[8.98018392e-01 1.83640088e-03 9.95698183e-02]\n",
      " [3.59044959e-05 9.17867738e-05 4.47697980e-04]]\n",
      "Sum = 1.00\n"
     ]
    }
   ],
   "source": [
    "def softmax(logits):\n",
    "    return np.exp(logits) / np.sum(np.exp(logits))\n",
    "\n",
    "\n",
    "print(softmax(logits))\n",
    "print(\"Sum = %.2f\" % np.sum(softmax(logits)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5cbe1a4",
   "metadata": {},
   "source": [
    "Можно обратить внимание, что Softmax никоим образом не поменял порядок значений. Самому большому logit'у соответствует самая большая вероятность, а самому маленькому, соответственно, самая маленькая."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c92fb17",
   "metadata": {},
   "source": [
    "Посмотрим на графиках. Возьмем массив случайных логитов и применим к ним softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "571972bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand_logits = np.linspace(-1, 1, 50)\n",
    "fig, ax = plt.subplots(ncols=2, figsize=(6, 3))\n",
    "\n",
    "ax[0].plot(np.arange(50), rand_logits)\n",
    "ax[0].set_title(\"Logits\")\n",
    "ax[1].plot(np.arange(50), softmax(rand_logits))\n",
    "ax[1].set_title(\"Softmax\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13a8ee03",
   "metadata": {},
   "source": [
    "#### Практическое вычисление SoftMax\n",
    "\n",
    "При вычислении экспоненты от выходов модели могут получиться очень большие числа в силу очень высокой скорости роста экспоненты. Этот факт необходимо учитывать, чтобы вычисления SoftMax были численно стабильны:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a42821a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[123 456 789] [ 0.  0. nan]\n"
     ]
    }
   ],
   "source": [
    "from warnings import simplefilter\n",
    "\n",
    "simplefilter(\"ignore\", category=RuntimeWarning)\n",
    "\n",
    "f = np.array([123, 456, 789])\n",
    "p = np.exp(f) / np.sum(np.exp(f))\n",
    "print(f, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d894e7f",
   "metadata": {},
   "source": [
    "Чтобы регуляризовать вычисление, нам следует предварительно упростить возникающую в вычислении дробь. Для этого мы можем вычесть из каждого $s_i$ положительную константу, чтобы уменьшить значения экспонент. В качестве константы можно выбрать максимальный элемент этого вектора, тогда у нас гарантированно не будет очень больших чисел, и такой способ будет работать более стабильно.\n",
    "\n",
    "$$M = \\max_j s_{y_{j}}$$\n",
    "$$s^{new}_{y_{i}}  = s_{y_{i}} - M $$\n",
    "\n",
    "$$ \\dfrac {e^{s^{new}_{y_{i}}}} {\\sum_j e^{s^{new}_{y_{j}}}}  = \\dfrac {e^{s_{y_{i}} - M }} {\\sum_j e^{s_{y_{j}} - M }} = \\dfrac {e^{s_{y_{i}}}e ^ {-M}} {\\sum_j e^{s_{y_{j}}} e ^ {-M}} = \\dfrac {e ^ {-M} e^{s_{y_{i}}}} {e ^ {-M} \\sum_j e^{s_{y_{j}}} } = \\dfrac { e^{s_{y_{i}}}} { \\sum_j e^{s_{y_{j}}} }$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "277a56c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-666 -333    0] [5.75274406e-290 2.39848787e-145 1.00000000e+000]\n"
     ]
    }
   ],
   "source": [
    "f = np.array([123, 456, 789])\n",
    "f -= f.max()\n",
    "p = np.exp(f) / np.sum(np.exp(f))\n",
    "print(f, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "100b47e6",
   "metadata": {},
   "source": [
    "### Градиент функции потерь. Кросс-энтропия\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdb4ccf2",
   "metadata": {},
   "source": [
    "[Cross Entropy Loss](https://wandb.ai/wandb_fc/russian/reports/---VmlldzoxNDI4NjAw#:~:text=%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F%20%D0%BF%D0%BE%D1%82%D0%B5%D1%80%D1%8C%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BA%D1%80%D0%B5%D1%81%D1%82%D0%BD%D0%BE%D0%B9%20%D1%8D%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D0%B8%20%E2%80%93%20%D1%8D%D1%82%D0%BE,%2C%20%D0%B3%D0%B4%D0%B5%200%20%E2%80%93%20%D0%B8%D0%B4%D0%B5%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "674a1636",
   "metadata": {},
   "source": [
    "$$ -L = \\sum_i y_i \\log p_i = \\sum_i y_i \\log(\\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}})$$\n",
    "\n",
    "$$s_{y_i} = w_i x$$\n",
    "\n",
    "$$ \\dfrac {\\partial L} {\\partial w_i} = \\dfrac {\\partial L} {\\partial s_{y_i}} \\dfrac {\\partial s_{y_i}} {\\partial w_i} $$\n",
    "\n",
    "$$\\dfrac {\\partial s_{y_i}} {\\partial w_i} = x$$\n",
    "\n",
    "Только один $y_k = 1$\n",
    "\n",
    "\n",
    "$$ -L = y_k \\log p_i = \\log(\\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}})$$\n",
    "\n",
    "i = k\n",
    "\n",
    "$$ -L = \\log(\\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}}) = \\log e^{s_{y_i}} - \\log  \\sum_j e^{s_{y_j}}  = s_{y_i} - \\log  \\sum_j e^{s_{y_j}}$$\n",
    "\n",
    "$$\\dfrac {\\partial -L} {\\partial s_{y_i}} = 1 - \\dfrac 1 {\\sum_j e^{s_{y_j}}} \\cdot \\dfrac {\\partial {\\sum_j e^{s_{y_j}}}} {\\partial s_{y_i}} = 1 - \\dfrac 1 {\\sum_j e^{s_{y_i}}} \\cdot \\dfrac {\\partial e^{s_{y_i}}} {\\partial s_{y_i}} = 1 - \\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}} = 1 - p_i$$\n",
    "\n",
    "$$\\dfrac {\\partial L} {\\partial s_{y_j}} = p_i - 1 $$\n",
    "\n",
    "$$ \\dfrac {\\partial L_i} {\\partial w_i}  = \\dfrac {\\partial L} {\\partial s_{y_i}} \\dfrac {\\partial s_{y_i}} {\\partial w_i} = (p_i - 1) x $$\n",
    "\n",
    "i != k\n",
    "\n",
    "$$ -L = \\log(\\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}}) = \\log e^{s_{y_k}} - \\log  \\sum_j e^{s_{y_j}}  = s_{y_k} - \\log  \\sum_j e^{s_{y_j}}$$\n",
    "\n",
    "$$\\dfrac {\\partial -L} {\\partial s_{y_i}} = - \\dfrac 1 {\\sum_j e^{s_{y_j}}} \\cdot \\dfrac {\\partial {\\sum_j e^{s_{y_j}}}} {\\partial s_{y_i}} =  \\dfrac 1 {\\sum_j e^{s_{y_i}}} \\cdot \\dfrac {\\partial e^{s_{y_i}}} {\\partial s_{y_i}} = \\dfrac {e^{s_{y_i}}} {\\sum_j e^{s_{y_j}}} = - p_i$$\n",
    "\n",
    "$$\\dfrac {\\partial L} {\\partial s_{y_j}} = p_i $$\n",
    "$$ \\dfrac {\\partial L_i} {\\partial w_i}  = \\dfrac {\\partial L} {\\partial s_{y_i}} \\dfrac {\\partial s_{y_i}} {\\partial w_i} = p_i x $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7c7d4db",
   "metadata": {},
   "source": [
    "В коде это будет выглядеть вот так:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "56c515ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scores(Logits) \n",
      " [[-7.1993243   6.41313488 -0.04889715]\n",
      " [ 0.07235065  1.04705308  0.81849337]] \n",
      "\n",
      "Probs \n",
      " [[1.21094807e-06 9.88419774e-01 1.54353533e-03]\n",
      " [1.74250416e-03 4.61829545e-03 3.67467972e-03]] \n",
      "\n",
      "Grads dL/dW \n",
      " [[-0.9982575  -0.01158023  0.00521822]\n",
      " [-2.00348501  3.97683955 -0.00426229]\n",
      " [-3.          2.96525932  0.00463061]\n",
      " [-4.          3.9536791   0.00617414]]\n"
     ]
    }
   ],
   "source": [
    "# Input batch of 2 vector with 4 elements\n",
    "x = np.array([[1, 2, 3, 4], [1, -2, 0, 0]])\n",
    "# Weights\n",
    "W = np.random.randn(3, 4)  # 3 class\n",
    "\n",
    "# model output\n",
    "logits = x.dot(W.T)\n",
    "print(\"Scores(Logits) \\n\", logits, \"\\n\")\n",
    "\n",
    "# Probabilities\n",
    "probs = softmax(logits)  # defined before\n",
    "print(\"Probs \\n\", probs, \"\\n\")\n",
    "\n",
    "# Ground true classes\n",
    "y = [0, 1]\n",
    "\n",
    "# Derivative\n",
    "probs[np.arange(2), y] = -1  # substract one from true class prob\n",
    "dW = x.T.dot(probs)  # dot product with input\n",
    "\n",
    "print(\"Grads dL/dW \\n\", dW)  # have same shape as W"
   ]
  }
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