Regressão Polinomial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 0. Dependências "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Introdução "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Dados "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10c27bda0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c209320>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1, 11).reshape(-1, 1)\n",
    "y = np.array([1, 3, 7, 15, 20, 30, 40, 60, 85, 120]).reshape(-1, 1)\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Implementação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PolynomialRegression():\n",
    "    def __init__(self, degree=2):\n",
    "        self.degree = degree\n",
    "        self.b = None\n",
    "        \n",
    "    def fit(self, x, y):\n",
    "        powers = self.__compute_powers(x)\n",
    "        \n",
    "        b1 = np.linalg.inv(np.dot(powers.T, powers))\n",
    "        b2 = np.dot(powers.T, y)\n",
    "        self.b = np.dot(b1, b2)\n",
    "    \n",
    "    def predict(self, x):\n",
    "        powers = self.__compute_powers(x)\n",
    "        return np.dot(powers, self.b)\n",
    "    \n",
    "    def __compute_powers(self, x):\n",
    "        x = x.ravel()\n",
    "        powers = np.empty((x.shape[0], self.degree + 1))\n",
    "        powers[:, 0] = np.ones(x.shape[0])\n",
    "        powers[:, 1] = x\n",
    "        \n",
    "        for p in range(2, self.degree+1):\n",
    "            powers[:, p] = x**p\n",
    "        return powers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Teste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão Quadrática"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 10.76666667]\n",
      " [ -7.49242424]\n",
      " [  1.78030303]]\n"
     ]
    }
   ],
   "source": [
    "reg = PolynomialRegression()\n",
    "reg.fit(x, y)\n",
    "\n",
    "print(reg.b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10c204d68>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f39cc18>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = reg.predict(x)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Comparação com o Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 10.76666667] [[ 0.         -7.49242424  1.78030303]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "poly.fit(x, y)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(poly.transform(x), y)\n",
    "\n",
    "print(reg.intercept_, reg.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão Cúbica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_cubic(n_samples, x_min, x_max, a=1, b=0, c=0, d=0, noise=0.0, random_state=None):\n",
    "    np.random.seed(random_state)\n",
    "    x = np.linspace(x_min, x_max, n_samples)\n",
    "    y = a*x**3 + b*x**2 + c*x + d + (2*noise*np.random.random(n_samples) - noise)\n",
    "    return x.reshape(-1,1), y.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 1) (100, 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x111bf47f0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4242b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = make_cubic(n_samples=100, x_min=-4, x_max=4, a=1, b=0, c=-10, d=0, noise=3)\n",
    "\n",
    "print(x.shape, y.shape)\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -0.18147954]\n",
      " [-10.22969684]\n",
      " [  0.03369393]\n",
      " [  1.02064375]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x111c25c18>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f41b240>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = PolynomialRegression(degree=3)\n",
    "reg.fit(x, y)\n",
    "\n",
    "print(reg.b)\n",
    "\n",
    "y_pred = reg.predict(x)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Comparação com o Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.18147954] [[  0.         -10.22969684   0.03369393   1.02064375]]\n"
     ]
    }
   ],
   "source": [
    "poly = PolynomialFeatures(degree=3)\n",
    "poly.fit(x, y)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(poly.transform(x), y)\n",
    "\n",
    "print(reg.intercept_, reg.coef_)"
   ]
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}