{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorytm najszybszego spadku dla regresji wielomianowej. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Skład grupy:\n",
    "- Nowak Ania,\n",
    "- Łaźna Patrycja,\n",
    "- Bregier Damian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Podstawowe informacje o zbiorze danych"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ze względu na specyfikę wytycznych projektu zakładającego wykorzystanie jedynie dwóch cech: x i y oraz modelowanie zależności y od x za pomocą funkcji wielomianowej dobrany został przez nas odpowiedni dataset. Obejmuje on jedynie trzy kolumny, czyli: płeć, wzrost w calach oraz wagę w funtach, z czego ze względu na specyfikę projektu wykorzystywane są jedynie wzrost oraz waga. Każdy z parametrów zawiera po 10 tysięcy unikalnych wartości.\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Wczytywanie i preprocessing danych"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Stopień wielomianu\n",
    "degree = 4\n",
    "X_plot = np.linspace(0, 100, 1000)\n",
    "initial_theta = np.matrix([0] * (degree + 1)).reshape(degree + 1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wybór dwóch kolumn - dotyczących wzrostu i wagi\n",
    "data = pd.read_csv('weight-height.csv')[[\"Height\", \"Weight\"]]\n",
    "# Czyszczenie tabeli i wartości pustych\n",
    "data = data.dropna()\n",
    "data_matrix = np.matrix(data)\n",
    "\n",
    "m, n_plus_1 = data_matrix.shape\n",
    "n = n_plus_1 - 1\n",
    "X = (np.ones((m, 1)))\n",
    "\n",
    "for i in range(1, degree + 1):\n",
    "    Xn = np.power(data_matrix[:, 0:n], i)\n",
    "    Xn /= np.amax(Xn, axis=0)\n",
    "    X = np.concatenate((X, Xn), axis=1)\n",
    "\n",
    "X = np.matrix(X).reshape(m, degree * n + 1)\n",
    "Y = np.matrix(data_matrix[:, -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Metody do regresji wielomianowej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Implementacja wzrosu na regresję wielomianową\n",
    "def polynomial_regression(theta, x):\n",
    "    x = x/data[\"Height\"].max()\n",
    "    return sum(theta * np.power(x, i) for i, theta in enumerate(theta.tolist()))\n",
    "\n",
    "# Implementacja wzoru na RMSE, czyli pierwiastek z błędu średniokwadratowego\n",
    "def mean_squared_error(theta, X, Y):\n",
    "    J = 1.0 / (2.0 * m) * ((X * theta - Y).T * (X * theta - Y))\n",
    "    return J.item()\n",
    "\n",
    "# Wzór na gradient prosty\n",
    "def gradient(theta, X, Y):\n",
    "    return 1.0 / len(Y) * (X.T * (X * theta - Y)) \n",
    "\n",
    "# Batch gradient descent (BGD)\n",
    "def BGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, eps=10**-5, max_steps = 10000000000):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    \n",
    "    for i in range(max_steps):\n",
    "        theta = theta - alpha * gradient(theta, X, Y)\n",
    "        next_cost = cost_function(theta, X, Y)\n",
    "        logs.append([next_cost, theta])\n",
    "        if abs(cost - next_cost) <= eps:\n",
    "            break\n",
    "        cost = next_cost\n",
    "    return theta, logs\n",
    "\n",
    "# Batch gradient descent (BGD)\n",
    "def steepest_descent(X, Y, theta, cost_function = mean_squared_error, eps=10**-5, max_steps = 10000000000):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    \n",
    "    for i in range(max_steps):\n",
    "        theta = theta - alpha * gradient(theta, X, Y)\n",
    "        next_cost = cost_function(theta, X, Y)\n",
    "        logs.append([next_cost, theta])\n",
    "        if abs(cost - next_cost) <= eps:\n",
    "            break\n",
    "        cost = next_cost\n",
    "    return theta, logs\n",
    "\n",
    "# Mini-batch gradient descent (MBGD)\n",
    "def MBGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    start, end = 0, batch_size\n",
    "    \n",
    "    steps = m / batch_size\n",
    "    for i in range(epochs):\n",
    "        zipped_XY = list(zip(X, Y))\n",
    "        random.shuffle(zipped_XY)\n",
    "        X_shuffled, Y_shuffled = zip(*zipped_XY)\n",
    "        X_shuffled = np.concatenate(X_shuffled, axis=0) \n",
    "        Y_shuffled = np.concatenate(Y_shuffled, axis=0) \n",
    "        for j in range(int(steps)):\n",
    "            batch =  X_shuffled[start:end,:], Y_shuffled[start:end,:]\n",
    "            theta = theta - alpha * gradient(theta, batch[0], batch[1])\n",
    "            cost = cost_function(theta, X, Y)\n",
    "            logs.append([cost, theta])\n",
    "\n",
    "            if start + batch_size < batch_size:\n",
    "                start += batch_size\n",
    "            else:\n",
    "                start = 0\n",
    "            end = min(start + batch_size, m)\n",
    "    return theta, logs\n",
    "\n",
    "# Stochastic gradient descent (SGD)\n",
    "def SGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n",
    "    return MBGD(X, Y, theta, gradient, cost_function, alpha, epochs, 1)\n",
    "\n",
    "#print(mean_squared_error([1,2,1,1],[1,2,43,1]))\n",
    "#mean_squared_error(polynomial_regression(initial_theta, X), Y)\n",
    "#final_theta, logs_1 = BGD(X, Y, initial_theta)\n",
    "final_theta, logs_2 = MBGD(X, Y, initial_theta, epochs = 30, batch_size = 16)\n",
    "#final_theta, logs_2 = SGD(X, Y, initial_theta, epochs = 30)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metoda gradientu prostego\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Reprezentacja graficzna regresji wielomianowej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_polynomial_regression(theta):\n",
    "    fig = plt.figure(figsize=(10,5))\n",
    "    Y_plot = polynomial_regression(theta, X_plot).tolist()\n",
    "    chart = fig.add_subplot()\n",
    "    chart.plot(data[\"Height\"], Y ,\"go\")\n",
    "    chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {len(theta)}\")\n",
    "    plt.ylim([0,250])\n",
    "    plt.show()\n",
    "    \n",
    "#plot_polynomial_regression(initial_theta)\n",
    "plot_polynomial_regression(final_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-33.70007165990287x^0 + 36.22536357022561x^1 + 77.13438753083798x^2 + 97.31645980974973x^3 + 103.01308458334519x^4 + "
     ]
    }
   ],
   "source": [
    "for i,x in enumerate(final_theta.tolist()):\n",
    "    x = x[0]\n",
    "    print(f\"{x}x^{i}\", end=\" + \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Regresja wielomianowa z wykorzystaniem gotowej biblioteki"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.linear_model import Ridge, LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=4)),\n",
       "                ('linearregression', LinearRegression())])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = make_pipeline(PolynomialFeatures(degree=degree, include_bias=True), \n",
    "                       LinearRegression())\n",
    "model.fit(data[[\"Height\"]],Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y_plot_2 = model.predict([[x] for x in X_plot])\n",
    "\n",
    "fig = plt.figure(figsize=(10,5))\n",
    "chart = fig.add_subplot()\n",
    "chart.plot(data[\"Height\"], Y ,\"go\")\n",
    "chart.plot(X_plot, Y_plot_2, color=\"red\", lw=2, label=f\"degree {degree}\")\n",
    "plt.ylim([0,250])\n",
    "plt.xlim([0,100])\n",
    "degree"
   ]
  }
 ],
 "metadata": {
  "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",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}