byoyo2018-giris-3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sınıflandırma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Kaggle\n",
    "https://www.kaggle.com/datasets\n",
    "\n",
    "UCI Machine Learning Repository\n",
    "https://archive.ics.uci.edu/ml/datasets.html\n",
    "\n",
    "Scikit-learn \n",
    "http://scikit-learn.org/stable/datasets/\n",
    "\n",
    "Türkiye İstatistik Kurumu\n",
    "http://www.tuik.gov.tr\n",
    "\n",
    "A Handbook of Small Data Sets\n",
    "edited by D.J. Hand, F. Daly, A.D. Lunn, K.J. McConway and E. Ostrowski \n",
    "from Chapman and Hall, ISBN 0 412 39920 2.\n",
    "https://www.stat.ncsu.edu/research/sas/sicl/data/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <a src=\"data/iris.txt\">Iris (Süsen Çiçeği) Veri Kümesi</a>\n",
    "\n",
    " (Fisher, 1926)\n",
    "\n",
    "|Sınıf 1 | Sınıf 2 | Sınıf 3 | ? | ? |\n",
    "|-------------|\n",
    "| Iris Setosa | Iris Versicolour | Iris Virginica | ? | ? |\n",
    "| <img src=\"data/iris1.png\" width=\"200\"> </img> | <img src=\"data/iris2.png\" width=\"200\"> </img> | <img src=\"data/iris3.png\" width=\"200\"> </img> | <img src=\"data/versi1.jpeg\" width=\"200\"> | <img src=\"data/versi2.jpeg\" width=\"200\">  </img>  \n",
    "\n",
    "__Features__\n",
    "- çanak yaprağı boyu (sepal length) cm\n",
    "- çanak yaprağı genişliği (sepal width) cm\n",
    "- taç yaprağı boyu (petal length) cm\n",
    "- taç yaprağı genişliği (petal width) cm\n",
    "\n",
    "<img src=\"data/564px-Petal-sepal.jpg\" width=\"200\"> </img>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    sl   sw   pl   pw  c\n",
      "0  5.1  3.5  1.4  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "1  4.9  3.0  1.4  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "2  4.7  3.2  1.3  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "3  4.6  3.1  1.5  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "4  5.0  3.6  1.4  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "5  5.4  3.9  1.7  0.4  1\n",
      "    sl   sw   pl   pw  c\n",
      "6  4.6  3.4  1.4  0.3  1\n",
      "    sl   sw   pl   pw  c\n",
      "7  5.0  3.4  1.5  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "8  4.4  2.9  1.4  0.2  1\n",
      "    sl   sw   pl   pw  c\n",
      "9  4.9  3.1  1.5  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "10  5.4  3.7  1.5  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "11  4.8  3.4  1.6  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "12  4.8  3.0  1.4  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "13  4.3  3.0  1.1  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "14  5.8  4.0  1.2  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "15  5.7  4.4  1.5  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "16  5.4  3.9  1.3  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "17  5.1  3.5  1.4  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "18  5.7  3.8  1.7  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "19  5.1  3.8  1.5  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "20  5.4  3.4  1.7  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "21  5.1  3.7  1.5  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "22  4.6  3.6  1.0  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "23  5.1  3.3  1.7  0.5  1\n",
      "     sl   sw   pl   pw  c\n",
      "24  4.8  3.4  1.9  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "25  5.0  3.0  1.6  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "26  5.0  3.4  1.6  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "27  5.2  3.5  1.5  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "28  5.2  3.4  1.4  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "29  4.7  3.2  1.6  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "30  4.8  3.1  1.6  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "31  5.4  3.4  1.5  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "32  5.2  4.1  1.5  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "33  5.5  4.2  1.4  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "34  4.9  3.1  1.5  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "35  5.0  3.2  1.2  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "36  5.5  3.5  1.3  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "37  4.9  3.1  1.5  0.1  1\n",
      "     sl   sw   pl   pw  c\n",
      "38  4.4  3.0  1.3  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "39  5.1  3.4  1.5  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "40  5.0  3.5  1.3  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "41  4.5  2.3  1.3  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "42  4.4  3.2  1.3  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "43  5.0  3.5  1.6  0.6  1\n",
      "     sl   sw   pl   pw  c\n",
      "44  5.1  3.8  1.9  0.4  1\n",
      "     sl   sw   pl   pw  c\n",
      "45  4.8  3.0  1.4  0.3  1\n",
      "     sl   sw   pl   pw  c\n",
      "46  5.1  3.8  1.6  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "47  4.6  3.2  1.4  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "48  5.3  3.7  1.5  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "49  5.0  3.3  1.4  0.2  1\n",
      "     sl   sw   pl   pw  c\n",
      "50  7.0  3.2  4.7  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "51  6.4  3.2  4.5  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "52  6.9  3.1  4.9  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "53  5.5  2.3  4.0  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "54  6.5  2.8  4.6  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "55  5.7  2.8  4.5  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "56  6.3  3.3  4.7  1.6  2\n",
      "     sl   sw   pl   pw  c\n",
      "57  4.9  2.4  3.3  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "58  6.6  2.9  4.6  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "59  5.2  2.7  3.9  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "60  5.0  2.0  3.5  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "61  5.9  3.0  4.2  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "62  6.0  2.2  4.0  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "63  6.1  2.9  4.7  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "64  5.6  2.9  3.6  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "65  6.7  3.1  4.4  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "66  5.6  3.0  4.5  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "67  5.8  2.7  4.1  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "68  6.2  2.2  4.5  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "69  5.6  2.5  3.9  1.1  2\n",
      "     sl   sw   pl   pw  c\n",
      "70  5.9  3.2  4.8  1.8  2\n",
      "     sl   sw   pl   pw  c\n",
      "71  6.1  2.8  4.0  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "72  6.3  2.5  4.9  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "73  6.1  2.8  4.7  1.2  2\n",
      "     sl   sw   pl   pw  c\n",
      "74  6.4  2.9  4.3  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "75  6.6  3.0  4.4  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "76  6.8  2.8  4.8  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "77  6.7  3.0  5.0  1.7  2\n",
      "     sl   sw   pl   pw  c\n",
      "78  6.0  2.9  4.5  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "79  5.7  2.6  3.5  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "80  5.5  2.4  3.8  1.1  2\n",
      "     sl   sw   pl   pw  c\n",
      "81  5.5  2.4  3.7  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "82  5.8  2.7  3.9  1.2  2\n",
      "     sl   sw   pl   pw  c\n",
      "83  6.0  2.7  5.1  1.6  2\n",
      "     sl   sw   pl   pw  c\n",
      "84  5.4  3.0  4.5  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "85  6.0  3.4  4.5  1.6  2\n",
      "     sl   sw   pl   pw  c\n",
      "86  6.7  3.1  4.7  1.5  2\n",
      "     sl   sw   pl   pw  c\n",
      "87  6.3  2.3  4.4  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "88  5.6  3.0  4.1  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "89  5.5  2.5  4.0  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "90  5.5  2.6  4.4  1.2  2\n",
      "     sl   sw   pl   pw  c\n",
      "91  6.1  3.0  4.6  1.4  2\n",
      "     sl   sw   pl   pw  c\n",
      "92  5.8  2.6  4.0  1.2  2\n",
      "     sl   sw   pl   pw  c\n",
      "93  5.0  2.3  3.3  1.0  2\n",
      "     sl   sw   pl   pw  c\n",
      "94  5.6  2.7  4.2  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "95  5.7  3.0  4.2  1.2  2\n",
      "     sl   sw   pl   pw  c\n",
      "96  5.7  2.9  4.2  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "97  6.2  2.9  4.3  1.3  2\n",
      "     sl   sw   pl   pw  c\n",
      "98  5.1  2.5  3.0  1.1  2\n",
      "     sl   sw   pl   pw  c\n",
      "99  5.7  2.8  4.1  1.3  2\n",
      "      sl   sw   pl   pw  c\n",
      "100  6.3  3.3  6.0  2.5  3\n",
      "      sl   sw   pl   pw  c\n",
      "101  5.8  2.7  5.1  1.9  3\n",
      "      sl   sw   pl   pw  c\n",
      "102  7.1  3.0  5.9  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "103  6.3  2.9  5.6  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "104  6.5  3.0  5.8  2.2  3\n",
      "      sl   sw   pl   pw  c\n",
      "105  7.6  3.0  6.6  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "106  4.9  2.5  4.5  1.7  3\n",
      "      sl   sw   pl   pw  c\n",
      "107  7.3  2.9  6.3  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "108  6.7  2.5  5.8  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "109  7.2  3.6  6.1  2.5  3\n",
      "      sl   sw   pl   pw  c\n",
      "110  6.5  3.2  5.1  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "111  6.4  2.7  5.3  1.9  3\n",
      "      sl   sw   pl   pw  c\n",
      "112  6.8  3.0  5.5  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "113  5.7  2.5  5.0  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "114  5.8  2.8  5.1  2.4  3\n",
      "      sl   sw   pl   pw  c\n",
      "115  6.4  3.2  5.3  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "116  6.5  3.0  5.5  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "117  7.7  3.8  6.7  2.2  3\n",
      "      sl   sw   pl   pw  c\n",
      "118  7.7  2.6  6.9  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "119  6.0  2.2  5.0  1.5  3\n",
      "      sl   sw   pl   pw  c\n",
      "120  6.9  3.2  5.7  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "121  5.6  2.8  4.9  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "122  7.7  2.8  6.7  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "123  6.3  2.7  4.9  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "124  6.7  3.3  5.7  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "125  7.2  3.2  6.0  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "126  6.2  2.8  4.8  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "127  6.1  3.0  4.9  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "128  6.4  2.8  5.6  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "129  7.2  3.0  5.8  1.6  3\n",
      "      sl   sw   pl   pw  c\n",
      "130  7.4  2.8  6.1  1.9  3\n",
      "      sl   sw   pl   pw  c\n",
      "131  7.9  3.8  6.4  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "132  6.4  2.8  5.6  2.2  3\n",
      "      sl   sw   pl   pw  c\n",
      "133  6.3  2.8  5.1  1.5  3\n",
      "      sl   sw   pl   pw  c\n",
      "134  6.1  2.6  5.6  1.4  3\n",
      "      sl   sw   pl   pw  c\n",
      "135  7.7  3.0  6.1  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "136  6.3  3.4  5.6  2.4  3\n",
      "      sl   sw   pl   pw  c\n",
      "137  6.4  3.1  5.5  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "138  6.0  3.0  4.8  1.8  3\n",
      "      sl   sw   pl   pw  c\n",
      "139  6.9  3.1  5.4  2.1  3\n",
      "      sl   sw   pl   pw  c\n",
      "140  6.7  3.1  5.6  2.4  3\n",
      "      sl   sw   pl   pw  c\n",
      "141  6.9  3.1  5.1  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "142  5.8  2.7  5.1  1.9  3\n",
      "      sl   sw   pl   pw  c\n",
      "143  6.8  3.2  5.9  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "144  6.7  3.3  5.7  2.5  3\n",
      "      sl   sw   pl   pw  c\n",
      "145  6.7  3.0  5.2  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "146  6.3  2.5  5.0  1.9  3\n",
      "      sl   sw   pl   pw  c\n",
      "147  6.5  3.0  5.2  2.0  3\n",
      "      sl   sw   pl   pw  c\n",
      "148  6.2  3.4  5.4  2.3  3\n",
      "      sl   sw   pl   pw  c\n",
      "149  5.9  3.0  5.1  1.8  3\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "df_iris = pd.read_csv(u'data/iris.txt',sep=' ')\n",
    "\n",
    "for i in range(150):\n",
    "    print(df_iris[i:i+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Regresyondan çok farklı değil, sadece çıktılar kategorik."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "\n",
    "* Girdi: Öznitelik vektörü \n",
    "* Çıktı: Evet/Hayır cevabı\n",
    "\n",
    "| Sınıf | Öznitelik1 | Öznitelik2  |\n",
    "|---| |---|\n",
    "| 0 |5.7| 3.1|\n",
    "| 1|-0.3|2 |\n",
    "|---| |---|\n",
    "|  $y_i$| $x_{i,1}$ | $x_{i,2}$ |\n",
    "|---| |---|\n",
    "| 1|0.4|5 |\n",
    "\n",
    "Yeni veri:\n",
    "\n",
    "| Sınıf | Öznitelik1 | Öznitelik2  |\n",
    "|---| |---|\n",
    "| ? |4.8| 3.2|\n",
    "| ? |-0.7|2.4 |\n",
    "|---| |---|\n",
    "\n",
    "\n",
    "\\begin{eqnarray}\n",
    "X & = &  \\begin{pmatrix}\n",
    "  x_{1,1} & x_{1,2} & \\dots & x_{1,D} \\\\\n",
    "  x_{2,1} & x_{2,2} & \\dots & x_{2,D} \\\\\n",
    "  \\vdots & \\vdots & \\vdots & \\vdots  \\\\\n",
    "  x_{i,1} & x_{i,2} & \\dots & x_{i,D}  \\\\\n",
    "  \\vdots & \\vdots & \\vdots & \\vdots  \\\\\n",
    "  x_{N,1} & x_{N,2} & \\dots & x_{N,D} \\\\\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "x_1^\\top \\\\\n",
    "x_2^\\top \\\\\n",
    "\\dots \\\\\n",
    "x_i^\\top \\\\\n",
    "\\dots \\\\\n",
    "x_N^\\top\n",
    "\\end{pmatrix} \n",
    "\\\\\n",
    "{y} & = & \\begin{pmatrix}\n",
    "y_1 \\\\\n",
    "y_2 \\\\\n",
    "\\vdots \\\\\n",
    "y_i \\\\\n",
    "\\vdots \\\\\n",
    "y_N\n",
    "\\end{pmatrix}\n",
    "\\end{eqnarray}\n",
    "\n",
    "İki sınıf:  $y_i \\in \\{0,1\\}$.  \n",
    "\n",
    "$$\n",
    "\\Pr\\{y_i = 1\\} = \\pi_i = \\sigma(x_i^\\top w)\n",
    "$$\n",
    "\n",
    "$\\sigma(x)$: sigmoid fonksyonu\n",
    "\\begin{eqnarray}\n",
    "\\sigma(x) & = & \\frac{1}{1+e^{-x}}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\pi_i & = & \\sigma(x_i^\\top w) \\\\\n",
    "y_i & \\sim &\\mathcal{BE}(\\pi)\n",
    "\\end{eqnarray}\n",
    "\n",
    "Her etiket için bir para atıyoruz ve paranın $1$ gelme olasılığını özniteliklere bağlıyoruz.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(y|\\pi) = \\pi^y(1-\\pi)^{1-y}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2e5b30d144944d5a2fa907df8e0f87b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='w', max=3.0, min=-3.0), FloatSlider(value=0.0, description='b', max=10.0, min=-10.0), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy as sc\n",
    "import pandas as pd\n",
    "\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import clear_output, display, HTML\n",
    "from matplotlib import rc\n",
    "\n",
    "import scipy as sc\n",
    "import scipy.optimize as opt\n",
    "\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "\n",
    "def inv_sigmoid(p=0.5):\n",
    "    xs = opt.bisect(lambda x: sigmoid(x)-p, a=-100, b=100)\n",
    "    return xs\n",
    "\n",
    "def inv_sigmoid1D(w, b, p=0.5):\n",
    "    xs = opt.bisect(lambda x: sigmoid(w*x+b)-p, a=-100, b=100)\n",
    "    return xs\n",
    "    \n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = fig.gca()\n",
    "ax.set_ylim([-0.1,1.1])\n",
    "x = np.linspace(-10,10,100)\n",
    "ax.set_xlim([-10,10])\n",
    "\n",
    "ln = plt.Line2D(x, sigmoid(x))\n",
    "ln2 = plt.axvline([0], ls= ':', color='k')\n",
    "ln_left = plt.axvline([0], ls= ':', color='b')\n",
    "ln_right = plt.axvline([0], ls= ':', color='r')\n",
    "\n",
    "ax.add_line(ln)\n",
    "plt.close(fig)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$\\sigma(wx + b)$')\n",
    "\n",
    "def plot_fun(w, b):\n",
    "    ln.set_ydata(sigmoid(w*x+b))\n",
    "    if np.abs(w)>0.00001:\n",
    "        ln2.set_xdata(inv_sigmoid1D(w,b,0.5))\n",
    "        ln_left.set_xdata(inv_sigmoid1D(w,b,0.25))\n",
    "        ln_right.set_xdata(inv_sigmoid1D(w,b,0.75))\n",
    "    display(fig)\n",
    "    \n",
    "res = interact(plot_fun, w=(-3, 3, 0.1), b=(-10.0,10.0,0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parametreleri öğrenmek\n",
    "\n",
    "Verilen özniteliklerle etiketleri gözlemleme ihtimali:\n",
    "\n",
    "$\\begin{eqnarray}\n",
    "p(y_1, y_2, \\dots, y_N|w, X ) &=& \\left(\\prod_{i : y_i=1} \\sigma(x_i^\\top w) \\right) \\left(\\prod_{i : y_i=0}(1- \\sigma(x_i^\\top w)) \\right)\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "{\\cal L}(w) & = & \\log p(y_1, y_2, \\dots, y_N|w, x_1, x_2, \\dots, x_N ) \\\\\n",
    "& = & \\sum_{i : y_i=1} \\log \\sigma(x_i^\\top w) + \\sum_{i : y_i=0} \\log (1- \\sigma(x_i^\\top w)) \\\\\n",
    "& = & \\sum_{i : y_i=1} x_i^\\top w - \\sum_{i : y_i=1} \\log(1+e^{x_i^\\top w}) - \\sum_{i : y_i=0}\\log({1+e^{x_i^\\top w}}) \\\\\n",
    "& = & \\sum_i y_i x_i^\\top w - \\sum_{i} \\log(1+e^{x_i^\\top w}) \\\\\n",
    "& = & y^\\top X w - \\mathbf{1}^\\top \\text{logsumexp}(0, X w)\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "w^* & = & \\arg\\max_{w} {\\cal L}(w)\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "$\\mathbf{1}^T v = \\sum_i v_i$.\n",
    "\n",
    "$$\n",
    "f = \\text{logsumexp}(a, b) \\equiv \\log(e^a + e^b)\n",
    "$$\n",
    "\n",
    "$$\n",
    "f_i = \\text{logsumexp}(a_i, b_i) \\equiv \\log(e^{a_i} + e^{b_i})\n",
    "$$\n",
    "\n",
    "En küçük kare hata yaklaşımından farklı olarak burada gerçekten bayır çıkışı kullanmamız gerkiyor. \n",
    "\n",
    "Hinge (Menteşe) hata fonksyonu\n",
    "$$\n",
    "h(x) = \\left\\{ \\begin{array}{cc} 0 & x < 0 \\\\x & x \\geq 0  \\end{array} \\right.\n",
    "$$\n",
    "\n",
    "$$\n",
    "f_\\alpha(x) = \\frac{1}{\\alpha}\\text{logsumexp}(0, \\alpha x)\n",
    "$$\n",
    "$\\alpha = 1$, orjinal logsumexp. Büyük $\\alpha$: hinge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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MqFEDMnj75+SoMPbQ4MGDad68udevGxoaSo0aNa667/yjjz7KxIkTvX5vkSxvwgQ4cYJ/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\n9NN8++232X48M6NVq1bs27fvpPtcc8017N27N9uPLZIXzB89mpYLFvB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mw0+y22dAt/Qr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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1520c93828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "def logsumexp(a,b):\n",
    "    m = np.max([a,b])\n",
    "    return m + np.log(np.exp(a-m) + np.exp(b-m))\n",
    "\n",
    "def hinge(x):\n",
    "    return x if x>0 else 0\n",
    "\n",
    "xx = np.arange(-5,3,0.1)\n",
    "\n",
    "plt.figure(figsize=(12,10))\n",
    "for i,alpha in enumerate([1,2,5,10]):\n",
    "    f = [logsumexp(0, alpha*z)/alpha for z in xx]\n",
    "    h = [hinge(z) for z in xx]\n",
    "    \n",
    "    plt.subplot(2,2,i+1)\n",
    "    plt.plot(xx, f, 'r')\n",
    "    plt.plot(xx, h, 'k:')\n",
    "    plt.xlabel('z')\n",
    "    #plt.title('a = '+ str(alpha))\n",
    "    if alpha==1:\n",
    "        plt.legend([ 'logsumexp(0,z)','hinge(z)' ], loc=2 )    \n",
    "    else:\n",
    "        plt.legend([ 'logsumexp(0,{a} z)/{a}'.format(a=alpha),'hinge(z)' ], loc=2 )\n",
    "  \n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Negatif olabilirlik azaltmak - Hata düşürmek\n",
    "\n",
    "$$\n",
    "- \\mathcal{L}(\\pi) = - \\sum_i l_i(w) \n",
    "$$\n",
    "\n",
    "$$\n",
    "E_i(w) \\equiv -l_i(w) = - y_i x_i^\\top w + \\text{logsumexp}(0, x_i^\\top w) = - y_i z_i + \\text{logsumexp}(0, z_i)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CBbnTSCoN22ypXrzySlo18YADYOutc6epO+0pqs8segrl0aVLmlrv+efh4otz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\nSR1kUS1JkiR1kEW1JEmS1EH/H0O/STU18Hz8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e2ca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.arange(-10,10,0.1)\n",
    "y = 1\n",
    "f = [-y*z + logsumexp(0, z) for z in xx]\n",
    "f0 = [logsumexp(0, z) for z in xx]\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(xx, f, 'r')\n",
    "plt.xlabel('$z_i$')\n",
    "plt.ylabel('$-l_i$')\n",
    "plt.title('Pozitif örnekler için hata. $y = $'+str(y))\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(xx, f0, 'r')\n",
    "plt.xlabel('$z_i$')\n",
    "plt.ylabel('$-l_i$')\n",
    "plt.title('Negatif örnekler için hata. $y = 0$')\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sentetik veri kümesi üzerinde gösterim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "# Generate a random logistic regression problem\n",
    "\n",
    "def sigmoid(t):\n",
    "    return np.exp(t)/(1+np.exp(t))\n",
    "\n",
    "\n",
    "def generate_toy_dataset(number_of_features=3, number_of_datapoints=20, styles = ['ob', 'xr']):\n",
    "\n",
    "    D = number_of_features\n",
    "    N = number_of_datapoints\n",
    "    \n",
    "\n",
    "    # Some random features\n",
    "    X = 2*np.random.rand(N,D)-1\n",
    "    X[:,0] = 1\n",
    "\n",
    "    # Generate a random paramater vector\n",
    "    w_true = np.random.randn(D,1)\n",
    "\n",
    "    # Generate class labels\n",
    "    pi = sigmoid(np.dot(X, w_true))\n",
    "    y = np.array([1 if u else 0 for u in np.random.rand(N,1) < pi]).reshape((N))\n",
    "\n",
    "    return X, y, w_true, D, N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x151fa0aa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "styles = ['ob', 'xr']\n",
    "X, y, w_true, D, N = generate_toy_dataset(number_of_features=3, number_of_datapoints=20, styles=styles)\n",
    "\n",
    "xl = -1.5; xr = 1.5; yl = -1.5; yr = 1.5\n",
    "\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(X[y==1,1],X[y==1,2],styles[1])\n",
    "plt.plot(X[y==0,1],X[y==0,2],styles[0])\n",
    "\n",
    "ax = fig.gca()\n",
    "ax.set_ylim([yl, yr])\n",
    "ax.set_xlim([xl, xr])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Implement Gradient Descent\n",
    "w = np.random.randn(D)\n",
    "\n",
    "# Learnig rate\n",
    "eta = 0.05\n",
    "\n",
    "W = []\n",
    "MAX_ITER = 200\n",
    "for epoch in range(MAX_ITER):\n",
    "    W.append(w)\n",
    "    dL = np.dot(X.T, y-sigmoid(np.dot(X,w)))\n",
    "    w = w + eta*dL\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
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       "model_id": "431ac47a5cf64a1c8d91cbf3f2ed20a2",
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      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
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       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
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       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
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      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='iteration', max=199), Output()), _dom_classes=('widget-interact',))"
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     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "<function __main__.plot_boundry_of_weight>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xl = -1.5\n",
    "xr = 1.5\n",
    "yl = -1.5\n",
    "yr = 1.5\n",
    "\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = fig.gca()\n",
    "ax.set_ylim([yl, yr])\n",
    "ax.set_xlim([xl, xr])\n",
    "\n",
    "plt.plot(X[y==1,1],X[y==1,2],styles[1])\n",
    "plt.plot(X[y==0,1],X[y==0,2],styles[0])\n",
    "\n",
    "\n",
    "ln = plt.Line2D([],[],color='k')\n",
    "ln_left  = plt.Line2D([],[],ls= ':', color=styles[0][1])\n",
    "ln_right = plt.Line2D([],[],ls= ':', color=styles[1][1])\n",
    "\n",
    "ax.add_line(ln)\n",
    "ax.add_line(ln_left)\n",
    "ax.add_line(ln_right)\n",
    "plt.close(fig)\n",
    "ax.set_xlabel('$x_1$')\n",
    "ax.set_ylabel('$x_2$')\n",
    "ax.set_xticks(np.arange(xl,xr))\n",
    "ax.set_yticks(np.arange(yl,yr))\n",
    "ax.grid(True)\n",
    "def plot_boundry(w0,w1,w2):\n",
    "    if w1 != 0:\n",
    "        xa = -(w0+w2*yl)/w1\n",
    "        xb = -(w0+w2*yr)/w1\n",
    "        ln.set_xdata([xa, xb])\n",
    "        ln.set_ydata([yl, yr])\n",
    "\n",
    "        xa = -(-inv_sigmoid(0.25) + w0+w2*yl)/w1\n",
    "        xb = -(-inv_sigmoid(0.25) + w0+w2*yr)/w1\n",
    "        ln_left.set_xdata([xa, xb])\n",
    "        ln_left.set_ydata([yl, yr])\n",
    "\n",
    "        xa = -(-inv_sigmoid(0.75) + w0+w2*yl)/w1\n",
    "        xb = -(-inv_sigmoid(0.75) + w0+w2*yr)/w1\n",
    "        ln_right.set_xdata([xa, xb])\n",
    "        ln_right.set_ydata([yl, yr])\n",
    "        \n",
    "        \n",
    "    elif w2!=0:\n",
    "        ya = -(w0+w1*xl)/w2\n",
    "        yb = -(w0+w1*xr)/w2\n",
    "        ln.set_xdata([xl, xr])\n",
    "        ln.set_ydata([ya, yb])\n",
    "\n",
    "        ya = -(-inv_sigmoid(0.25) + w0+w1*xl)/w2\n",
    "        yb = -(-inv_sigmoid(0.25) + w0+w1*xr)/w2\n",
    "        ln_left.set_xdata([xl, xr])\n",
    "        ln_left.set_ydata([ya, yb])\n",
    "\n",
    "        ya = -(-inv_sigmoid(0.75) + w0+w1*xl)/w2\n",
    "        yb = -(-inv_sigmoid(0.75) + w0+w1*xr)/w2\n",
    "        ln_right.set_xdata([xl, xr])\n",
    "        ln_right.set_ydata([ya, yb])      \n",
    "        \n",
    "    else:\n",
    "        ln.set_xdata([])\n",
    "        ln.set_ydata([])\n",
    "        \n",
    "    display(fig)\n",
    "\n",
    "def plot_boundry_of_weight(iteration=0):\n",
    "    i = iteration\n",
    "    w = W[i]\n",
    "    plot_boundry(w[0],w[1],w[2])\n",
    "    \n",
    "interact(plot_boundry_of_weight, iteration=(0,len(W)-1))\n"
   ]
  }
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