seminars/seminar4/seminar4.ipynb

{
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   "source": [
    "# Семинар 4\n",
    "\n",
    "## Линейная задача наименьших квадратов, решение линейных систем и QR разложение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Кластеризация и матричные разложения\n",
    "\n",
    "- Задача кластеризации относится к классу задач обучения без учителя, в которой требуется разбить наборы объектов на группы, в которых содержатся похожие объекты\n",
    "\n",
    "<img src=\"./clustering_demo.png\">\n",
    "\n",
    "Картинка из [этого](https://towardsdatascience.com/semantic-similarity-classifier-and-clustering-sentences-based-on-semantic-similarity-a5a564e22304) поста.\n",
    "\n",
    "- Отличие от классификации - меток объектов нет\n",
    "- Классический алгоритм решения такой задачи называется *k-means* или метод $k$-средних"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### $k$-means\n",
    "\n",
    "- Выбираем число кластеров $k$\n",
    "- Выбираем так называемые центры кластеров\n",
    "- Повторяем до сходимости\n",
    "    - Размечаем объекты на основании того, к какому центру они ближе\n",
    "    - Обновляем центр как среднее значение точек из каждого кластера\n",
    "\n",
    "- Подробности будут в курсе по машинному обучению"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Визуализация\n",
    "\n",
    "<img width=400 src=\"./K-means_convergence.gif\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Причём тут матричные разложения?\n",
    "\n",
    "- Пусть дано $N$ объектов, каждый из которых описывается $n$ числами.\n",
    "- Данные $N$ объектов уложены по столбцам в матрицу $X$\n",
    "- **Утверждение.** Алгоритм $k$-means решает следующую задачу оптимизации\n",
    "\n",
    "$$ \\| X - ZC\\|^2_F \\to \\min, $$\n",
    " \n",
    "где $X \\in \\mathbb{R}^{n \\times N}$, $Z \\in \\mathbb{R}^{n \\times k}$ и $C$ размера $k \\times N$\n",
    "- Матрица $C$ обладает следующим свойством\n",
    "\n",
    "$$ C_{ij} = \\begin{cases} 1, & x_j \\in \\mathcal{C}_i \\\\ 0, & \\text{иначе}, \\end{cases} $$\n",
    "\n",
    "где $\\mathcal{C}_i$ обозначает $i$-ый кластер, а $x_j$ – $j$-ый объект.\n",
    "\n",
    "- В каждом столбце матрицы $C$ ровно одна 1\n",
    "\n",
    "**Q:** что такое матрица $Z$?\n",
    "\n",
    "**Q:** какая интерпретация у столбцов матрицы $X - ZC$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Постановка линейной задачи наименьших квадратов: напоминание\n",
    "\n",
    "- Дана переопределённая система линейных уравнений с матрицей $A$, в которой строк больше, чем столбцов, и правой частью $b$\n",
    "- Задача решения такой системы в смысле наименьших квадратов записывается в виде\n",
    "\n",
    "\n",
    "$$\\Vert A x - b \\Vert_2 \\rightarrow \\min_{x}$$\n",
    "\n",
    "- Нормальное уравнение\n",
    "\n",
    "$$ A^* A x = A^* b $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Решение и метод вычисления\n",
    "\n",
    "- Псевдообратная матрица \n",
    "\n",
    "$$A^{\\dagger} = \\lim_{\\alpha \\rightarrow 0}(\\alpha I + A^* A)^{-1} A^*$$ \n",
    "\n",
    "- Решение записывается как \n",
    "\n",
    "$$ x = A^{\\dagger}b $$\n",
    "\n",
    "- Вычисление псевдообратной матрицы из SVD\n",
    "\n",
    "    Пусть $A = U \\Sigma V^*$ SVD матрицы $A$. Тогда,\n",
    "\n",
    "    $$A^{\\dagger} = V \\Sigma^{\\dagger} U^*,$$\n",
    "\n",
    "    где $\\Sigma^{\\dagger}$ состоит из обращённых ненулевых сингулярных чисел матрицы $A$.\n",
    "\n",
    "- Решение вычисляется с помощью QR разложения матрицы $A$\n",
    "\n",
    "$$\n",
    "Rx = Q^* b.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Сравнение методов решения нормального уравнения\n",
    "\n",
    "- Метод Гаусса\n",
    "- QR разложение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Сравниваем скорость"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as splin\n",
    "\n",
    "def lsqr_solver(A, b):\n",
    "    Q, R = np.linalg.qr(A)\n",
    "    return splin.solve_triangular(R, Q.T @ b, lower=False)\n",
    "#     return np.linalg.solve(R, Q.T @ b)\n",
    "\n",
    "def ls_gramm_solver(A, b):\n",
    "    gram_mat = A.T @ A\n",
    "    return np.linalg.solve(gram_mat, A.T @ b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09527491215630463 9.941874084144227e-06\n",
      "0.09527491215628506 9.941874084168457e-06\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "m = 10*n\n",
    "A = np.random.randn(m, n)\n",
    "x_true = np.random.randn(n)\n",
    "b = A @ x_true + 0.001 * np.random.randn(m)\n",
    "x = lsqr_solver(A, b)\n",
    "print(np.linalg.norm(A @ x - b), np.linalg.norm(x - x_true) / np.linalg.norm(x_true))\n",
    "x = ls_gramm_solver(A, b)\n",
    "print(np.linalg.norm(A @ x - b), np.linalg.norm(x - x_true) / np.linalg.norm(x_true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "dim_range = [10**i for i in range(1, 4)]\n",
    "time_qr_range = []\n",
    "time_gram_range = []\n",
    "for n in dim_range:\n",
    "    m = 10*n\n",
    "    A = np.random.randn(m, n)\n",
    "    x_true = np.random.randn(n)\n",
    "    b = A @ x_true + 0 * np.random.randn(m)\n",
    "    t = %timeit -o -q -r 1 lsqr_solver(A, b) \n",
    "    time_qr_range.append(t.best)\n",
    "    t = %timeit -o -q -r 1 ls_gramm_solver(A, b)\n",
    "    time_gram_range.append(t.best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(dim_range, time_qr_range, label=\"QR\")\n",
    "plt.plot(dim_range, time_gram_range, label=\"Gram matrix\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.xlabel(\"# columns\", fontsize=20)\n",
    "plt.ylabel(\"Time\", fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")\n",
    "plt.xticks(fontsize=18)\n",
    "_ = plt.yticks(fontsize=18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Сравниваем устойчивость\n",
    "- Оценка из лекции\n",
    "$$ \n",
    "\\frac{\\Vert \\widehat{x} - x \\Vert}{\\Vert x \\Vert} \\leq \\frac{\\mathrm{cond}(A)}{1 - \\mathrm{cond}(A)\\frac{\\|\\Delta A\\|}{\\|A\\|}} \\Big(\\frac{\\Vert\\Delta A\\Vert}{\\Vert A \\Vert} + \\frac{\\Vert \\Delta f \\Vert}{ \\Vert f \\Vert}\\Big) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "eps_range = [10**(-i) for i in range(1, 8)]\n",
    "m = 1000\n",
    "n = 100\n",
    "A = np.random.randn(m, n)\n",
    "accuracy_qr = np.zeros(len(eps_range))\n",
    "accuracy_gram = np.zeros(len(eps_range))\n",
    "cond_range = np.zeros(len(eps_range))\n",
    "for i, eps in enumerate(eps_range):\n",
    "    u, s, v = np.linalg.svd(A, full_matrices=False)\n",
    "    s_bad = s.copy()\n",
    "    s_bad[-1] = eps\n",
    "    cond_range[i] = s_bad[0] / s_bad[-1]\n",
    "    A_bad = (u * s_bad) @ v\n",
    "    x_true = np.random.randn(n)\n",
    "    b = A_bad @ x_true\n",
    "    x = lsqr_solver(A_bad, b)\n",
    "    accuracy_qr[i] = np.linalg.norm(x - x_true) / np.linalg.norm(x_true)\n",
    "    x = ls_gramm_solver(A_bad, b)\n",
    "    accuracy_gram[i] = np.linalg.norm(x - x_true) / np.linalg.norm(x_true)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(cond_range, accuracy_gram, label=\"Gram\")\n",
    "plt.plot(cond_range, accuracy_qr, label=\"QR\")\n",
    "plt.plot(cond_range, cond_range * np.finfo(np.float64).eps, label=\"$\\kappa \\cdot \\epsilon$\")\n",
    "plt.plot(cond_range, cond_range**2 * np.finfo(np.float64).eps, label=\"$\\kappa^2 \\cdot \\epsilon$\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")\n",
    "plt.legend(fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "plt.xlabel(\"Condition number of A, $\\kappa$\", fontsize=18)\n",
    "plt.ylabel(\"Relative error in solution\", fontsize=18)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Свойства псевдообратной матрицы\n",
    "\n",
    "- $A = AA^{\\dagger}A$\n",
    "- $A^{\\dagger} = A^{\\dagger}A A^{\\dagger}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Закон Мура\n",
    "\n",
    "- Количество транзизисторов на интегральной схеме удваивается каждые полтора-два года"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1971</th>\n",
       "      <th>1972</th>\n",
       "      <th>1974</th>\n",
       "      <th>1978</th>\n",
       "      <th>1982</th>\n",
       "      <th>1985</th>\n",
       "      <th>1989</th>\n",
       "      <th>1993</th>\n",
       "      <th>1997</th>\n",
       "      <th>1999</th>\n",
       "      <th>2000</th>\n",
       "      <th>2002</th>\n",
       "      <th>2003</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2250</td>\n",
       "      <td>2500</td>\n",
       "      <td>5000</td>\n",
       "      <td>29000</td>\n",
       "      <td>120000</td>\n",
       "      <td>275000</td>\n",
       "      <td>1180000</td>\n",
       "      <td>3100000</td>\n",
       "      <td>7500000</td>\n",
       "      <td>24000000</td>\n",
       "      <td>42000000</td>\n",
       "      <td>220000000</td>\n",
       "      <td>410000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   1971  1972  1974   1978    1982    1985     1989     1993     1997  \\\n",
       "0  2250  2500  5000  29000  120000  275000  1180000  3100000  7500000   \n",
       "\n",
       "       1999      2000       2002       2003  \n",
       "0  24000000  42000000  220000000  410000000  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "year_transistor = {\n",
    "1971: 2250,\n",
    "1972: 2500,\n",
    "1974: 5000,\n",
    "1978: 29000,\n",
    "1982: 120000,\n",
    "1985: 275000,\n",
    "1989: 1180000,\n",
    "1993: 3100000,\n",
    "1997: 7500000,\n",
    "1999: 24000000,\n",
    "2000: 42000000,\n",
    "2002: 220000000,\n",
    "2003: 410000000\n",
    "}\n",
    "\n",
    "data = pd.DataFrame([year_transistor])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1971</td>\n",
       "      <td>2250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1972</td>\n",
       "      <td>2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1974</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1978</td>\n",
       "      <td>29000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1982</td>\n",
       "      <td>120000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1985</td>\n",
       "      <td>275000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1989</td>\n",
       "      <td>1180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1993</td>\n",
       "      <td>3100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1997</td>\n",
       "      <td>7500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1999</td>\n",
       "      <td>24000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2000</td>\n",
       "      <td>42000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2002</td>\n",
       "      <td>220000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2003</td>\n",
       "      <td>410000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year          N\n",
       "0   1971       2250\n",
       "1   1972       2500\n",
       "2   1974       5000\n",
       "3   1978      29000\n",
       "4   1982     120000\n",
       "5   1985     275000\n",
       "6   1989    1180000\n",
       "7   1993    3100000\n",
       "8   1997    7500000\n",
       "9   1999   24000000\n",
       "10  2000   42000000\n",
       "11  2002  220000000\n",
       "12  2003  410000000"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(list(year_transistor.items()), columns=[\"Year\", \"N\"])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Модель\n",
    "\n",
    "$$ \\log_{2} N \\approx  w_1 + w_2 (t - 1970)$$\n",
    "\n",
    "- Логарифмирование – очень полезный приём преобразования данных, масштабы которых сильно отличаются "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.]\n",
      " [ 1.  2.]\n",
      " [ 1.  4.]\n",
      " [ 1.  8.]\n",
      " [ 1. 12.]\n",
      " [ 1. 15.]\n",
      " [ 1. 19.]\n",
      " [ 1. 23.]\n",
      " [ 1. 27.]\n",
      " [ 1. 29.]\n",
      " [ 1. 30.]\n",
      " [ 1. 32.]\n",
      " [ 1. 33.]]\n",
      "0     11.135709\n",
      "1     11.287712\n",
      "2     12.287712\n",
      "3     14.823765\n",
      "4     16.872675\n",
      "5     18.069072\n",
      "6     20.170355\n",
      "7     21.563837\n",
      "8     22.838459\n",
      "9     24.516531\n",
      "10    25.323886\n",
      "11    27.712928\n",
      "12    28.611049\n",
      "Name: N, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "y = np.log2(data[\"N\"])\n",
    "x = data[\"Year\"] - 1970\n",
    "X = np.ones((13, 2))\n",
    "X[:, 1] = x\n",
    "print(X)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4323270736375635\n",
      "[10.38299398  0.51163732]\n"
     ]
    }
   ],
   "source": [
    "w = np.linalg.lstsq(X, y, rcond=None)[0]\n",
    "print(np.linalg.norm(X @ w - y))\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '# transistors')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data[\"Year\"], y)\n",
    "plt.plot(data[\"Year\"], X @ w)\n",
    "plt.xlabel(\"Year\", fontsize=20)\n",
    "plt.ylabel(\"# transistors\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Предсказание на 2015 год\n",
    "\n",
    "- Микропроцессор IBM Z13 содержит $4 \\cdot 10^9$ транзисторов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33.40667332708807\n",
      "31.897352853986263\n"
     ]
    }
   ],
   "source": [
    "year = 2015\n",
    "pred_given_year = w[0] + w[1]* (year - 1970)\n",
    "print(pred_given_year)\n",
    "print(np.log2(4e9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Полиномиальная регрессия"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb524627f10>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_points = 10\n",
    "x = np.linspace(-2, 2, num=num_points)\n",
    "y = 5 - x - 10 * x**2 + x**3 + x**4\n",
    "y_noise = y + 0.01 * np.random.randn()\n",
    "plt.scatter(x, y_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 6)\n",
      "77.86934690287409\n"
     ]
    }
   ],
   "source": [
    "deg = 5\n",
    "V = np.vander(x, deg+1)\n",
    "print(V.shape)\n",
    "print(np.linalg.cond(V))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.01361564e-15  1.00000000e+00  1.00000000e+00 -1.00000000e+01\n",
      " -1.00000000e+00  5.00090497e+00]\n",
      "0.004047159273036428\n"
     ]
    }
   ],
   "source": [
    "w = np.linalg.lstsq(V, y_noise, rcond=None)[0]\n",
    "print(w)\n",
    "x_test = np.linspace(-3, 3, num=20)\n",
    "y_pred = np.vander(x_test, deg+1) @ w\n",
    "y_test_true = 5 - x_test - 10 * x_test**2 + x_test**3 + x_test**4\n",
    "print(np.linalg.norm(y_pred - y_test_true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb5245a2950>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_test, y_pred, label=\"Predicted\")\n",
    "plt.plot(x, y_noise, label=\"Train\")\n",
    "plt.plot(x_test, y_test_true, label=\"Test\")\n",
    "plt.legend(fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Моделирование миграции населения\n",
    "\n",
    "- Пусть $x_t \\in \\mathbb{R}^{100}$ распределение населения по возрастам в год $t$\n",
    "- Динамика этого распределения описывается во времени как \n",
    "\n",
    "$$ x_{t+1} = Ax_t + u $$\n",
    "\n",
    "- Что такое $u$?\n",
    "- Какой вид имеет матрица $A$ ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Определение миграционной политики\n",
    "\n",
    "- Дан вектор $x_1$, матрица $A$ и желаемое распределение $x_T = x_d$\n",
    "- Необходимо найти такой вектор $u$, чтобы желаемое распределение было достигнуто"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Резюме\n",
    "\n",
    "- Решение задачи кластеризации как вычисление матричного разложения\n",
    "- Приложения задачи наименьших квадратов"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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