exe1_logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_data.shape =  (10, 1) , t_data.shape =  (10, 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_data = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]).reshape(10,1)   \n",
    "t_data = np.array([0, 0, 0, 0,  0,  0,  1,  1,  1,  1]).reshape(10,1)\n",
    "\n",
    "print(\"x_data.shape = \", x_data.shape, \", t_data.shape = \", t_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W =  [[0.86484539]] , W.shape =  (1, 1) , b =  [0.33222796] , b.shape =  (1,)\n"
     ]
    }
   ],
   "source": [
    "W = np.random.rand(1,1)  \n",
    "b = np.random.rand(1)  \n",
    "print(\"W = \", W, \", W.shape = \", W.shape, \", b = \", b, \", b.shape = \", b.shape)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 최종출력은 y = sigmoid(Wx+b) 이며, 손실함수는 cross-entropy 로 나타냄\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1+np.exp(-x))\n",
    "\n",
    "def loss_func(x, t):\n",
    "    \n",
    "    delta = 1e-7    # log 무한대 발산 방지\n",
    "    \n",
    "    z = np.dot(x,W) + b\n",
    "    y = sigmoid(z)\n",
    "    \n",
    "    # cross-entropy \n",
    "    return  -np.sum( t*np.log(y + delta) + (1-t)*np.log((1 - y)+delta ) ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def numerical_derivative(f, x):\n",
    "    delta_x = 1e-4 # 0.0001\n",
    "    grad = np.zeros_like(x)\n",
    "    \n",
    "    it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])\n",
    "    \n",
    "    while not it.finished:\n",
    "        idx = it.multi_index        \n",
    "        tmp_val = x[idx]\n",
    "        x[idx] = float(tmp_val) + delta_x\n",
    "        fx1 = f(x) # f(x+delta_x)\n",
    "        \n",
    "        x[idx] = tmp_val - delta_x \n",
    "        fx2 = f(x) # f(x-delta_x)\n",
    "        grad[idx] = (fx1 - fx2) / (2*delta_x)\n",
    "        \n",
    "        x[idx] = tmp_val \n",
    "        it.iternext()   \n",
    "        \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 손실함수 값 계산 함수\n",
    "# 입력변수 x, t : numpy type\n",
    "def error_val(x, t):\n",
    "    delta = 1e-7    # log 무한대 발산 방지\n",
    "    \n",
    "    z = np.dot(x,W) + b\n",
    "    y = sigmoid(z)\n",
    "    \n",
    "    # cross-entropy \n",
    "    return  -np.sum( t*np.log(y + delta) + (1-t)*np.log((1 - y)+delta ) ) \n",
    "\n",
    "# 학습을 마친 후, 임의의 데이터에 대해 미래 값 예측 함수\n",
    "# 입력변수 x : numpy type\n",
    "def predict(x):\n",
    "    \n",
    "    z = np.dot(x,W) + b\n",
    "    y = sigmoid(z)\n",
    "    \n",
    "    if y >= 0.5:\n",
    "        result = 1  # True\n",
    "    else:\n",
    "        result = 0  # False\n",
    "    \n",
    "    return y, result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial error value =  16.539615246674526 Initial W =  [[0.24074049]] \n",
      " , b =  [0.97732743]\n",
      "step =  0 error value =  11.256566637475201 W =  [[-0.15112129]] , b =  [0.98148434]\n",
      "step =  400 error value =  2.8683377881474006 W =  [[0.27240015]] , b =  [-4.05326616]\n",
      "step =  800 error value =  1.7913715512265722 W =  [[0.45142765]] , b =  [-5.61525634]\n",
      "step =  1200 error value =  1.5223035171207158 W =  [[0.52923725]] , b =  [-6.65141023]\n",
      "step =  1600 error value =  1.3553664865002537 W =  [[0.59075854]] , b =  [-7.46840938]\n",
      "step =  2000 error value =  1.2381160302888912 W =  [[0.6424462]] , b =  [-8.15331079]\n",
      "step =  2400 error value =  1.1494776730690062 W =  [[0.68746987]] , b =  [-8.7488453]\n",
      "step =  2800 error value =  1.0791287702741297 W =  [[0.72763863]] , b =  [-9.27938008]\n",
      "step =  3200 error value =  1.0213341375475669 W =  [[0.76409026]] , b =  [-9.76022414]\n",
      "step =  3600 error value =  0.9726150484303496 W =  [[0.7975908]] , b =  [-10.20167309]\n",
      "step =  4000 error value =  0.9307201440728496 W =  [[0.82868274]] , b =  [-10.61100989]\n",
      "step =  4400 error value =  0.8941178334413025 W =  [[0.85776556]] , b =  [-10.99359166]\n",
      "step =  4800 error value =  0.8617240505991438 W =  [[0.88514271]] , b =  [-11.35348346]\n",
      "step =  5200 error value =  0.8327463327764959 W =  [[0.9110506]] , b =  [-11.6938492]\n",
      "step =  5600 error value =  0.8065896622165475 W =  [[0.93567733]] , b =  [-12.01720393]\n",
      "step =  6000 error value =  0.7827970680577995 W =  [[0.95917524]] , b =  [-12.32558284]\n",
      "step =  6400 error value =  0.7610107572790576 W =  [[0.98166962]] , b =  [-12.62065816]\n",
      "step =  6800 error value =  0.7409458730477071 W =  [[1.00326486]] , b =  [-12.90382211]\n",
      "step =  7200 error value =  0.7223722949137212 W =  [[1.02404893]] , b =  [-13.17624732]\n",
      "step =  7600 error value =  0.7051017168945638 W =  [[1.04409676]] , b =  [-13.43893151]\n",
      "step =  8000 error value =  0.6889782817329568 W =  [[1.0634727]] , b =  [-13.69273135]\n",
      "step =  8400 error value =  0.6738716674551101 W =  [[1.08223251]] , b =  [-13.93838835]\n",
      "step =  8800 error value =  0.6596719002042547 W =  [[1.10042481]] , b =  [-14.17654903]\n",
      "step =  9200 error value =  0.6462854048726486 W =  [[1.11809232]] , b =  [-14.40778084]\n",
      "step =  9600 error value =  0.6336319581180295 W =  [[1.13527276]] , b =  [-14.63258481]\n",
      "step =  10000 error value =  0.621642309186399 W =  [[1.15199965]] , b =  [-14.85140575]\n"
     ]
    }
   ],
   "source": [
    "learning_rate = 1e-2  # 발산하는 경우, 1e-3 ~ 1e-6 등으로 바꾸어서 실행\n",
    "\n",
    "f = lambda x : loss_func(x_data,t_data)  # f(x) = loss_func(x_data, t_data)\n",
    "\n",
    "print(\"Initial error value = \", error_val(x_data, t_data), \"Initial W = \", W, \"\\n\", \", b = \", b )\n",
    "\n",
    "for step in  range(10001):  \n",
    "    \n",
    "    W -= learning_rate * numerical_derivative(f, W)\n",
    "    \n",
    "    b -= learning_rate * numerical_derivative(f, b)\n",
    "    \n",
    "    if (step % 400 == 0):\n",
    "        print(\"step = \", step, \"error value = \", error_val(x_data, t_data), \"W = \", W, \", b = \",b )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.12468997e-05]] 0\n"
     ]
    }
   ],
   "source": [
    "(real_val, logical_val) = predict(3) \n",
    "\n",
    "print(real_val, logical_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99127317]] 1\n"
     ]
    }
   ],
   "source": [
    "(real_val, logical_val) = predict(17) \n",
    "\n",
    "print(real_val, logical_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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