10-逻辑回归中sigmoid和损失函数原理.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a435752fd0>]"
      ]
     },
     "execution_count": 2,
     "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": [
    "x = np.linspace(-10, 10, 100)\n",
    "def y(x):\n",
    "    return 1/(1 + np.exp(-x))\n",
    "y = y(x)\n",
    "\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### x < 0 ==> p = 0\n",
    "##### x == 0 ==> p = 0.5\n",
    "##### x > 0 ==> p = 1\n",
    "##### ==> x > 0  p > 0.5\n",
    "##### ==> x < 0  p < 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "        <img src = './img/7.jpg', width=600, height=200/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "        <img src = './img/12.jpg', width=600, height=200/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "    <img src='./img/9.jpg', width= 600, height = 200>\n",
    "    <img src='./img/10.jpg', width= 600, height = 200>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "END"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}