Lingfeng_Zhang/DL_A1_hands_on.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8a1b088710>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy, math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 200\n",
    "theta = 1\n",
    "def getData():\n",
    "    \n",
    "    x = numpy.random.uniform(0,1,N)\n",
    "\n",
    "    def fun(xi):\n",
    "        yi = math.cos(2*math.pi*xi)+(1/math.sqrt(2*math.pi*math.pow(theta,2)))*math.exp(-1*math.pow(xi,2)/(2*math.pow(theta,2)))\n",
    "        return yi\n",
    "\n",
    "    y=[]\n",
    "    for xi in x:\n",
    "        y.append(fun(xi))\n",
    "    return x,y\n",
    "\n",
    "x,y=getData()\n",
    "plt.plot(x,y,'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "d = 20 \n",
    "a = []\n",
    "for i in range(0,d):\n",
    "    a.append(random.random())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8a1ae83780>]"
      ]
     },
     "execution_count": 3,
     "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": [
    "def predict_function(d,a,xi):\n",
    "    yi_hat = 0\n",
    "    for i in range(d):\n",
    "        yi_hat = yi_hat + a[i]*math.pow(xi,i)\n",
    "    return yi_hat\n",
    "\n",
    "y_hat = []\n",
    "for xi in x:\n",
    "    y_hat.append(predict_function(d,a,xi))\n",
    "    \n",
    "plt.plot(x,y_hat,'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getMSE(y,y_hat):\n",
    "    mse = 0\n",
    "    for i in range(len(y)):\n",
    "        mse = mse + math.pow((y[i]-y_hat[i]),2)\n",
    "        mse = mse/N\n",
    "    return mse\n",
    "\n",
    "getMSE(y,y_hat)\n",
    "learning_rate = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitData_SGD(y,y_hat,x,a,running_threshold):\n",
    "    k = 0\n",
    "    number = 0\n",
    "    while 1:\n",
    "        a_old = a\n",
    "        for i in range(1,d):\n",
    "            derivative = 2*(y[k]-y_hat[k])*math.pow(x[k],i)\n",
    "            a[i] = a[i] + learning_rate*derivative\n",
    "        k = k+1\n",
    "        number = number+1\n",
    "        if(a==a_old):\n",
    "            break\n",
    "        if(k==N):\n",
    "            k=0\n",
    "        if(number == running_threshold):\n",
    "            break\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.012104850960232637\n",
      "0.0026535329362651753\n",
      "0.0003646120428829085\n",
      "7.417861870246073e-06\n",
      "9.70131955824461e-05\n",
      "0.00024212186396472366\n",
      "0.00035812965798409044\n",
      "0.000438869166406858\n",
      "0.0004935814354473365\n",
      "0.0005313876347805682\n",
      "0.0005586463493969014\n",
      "0.0005793335448402841\n",
      "0.0005958295727410436\n",
      "0.0006095382129310432\n",
      "0.0006212890469243091\n",
      "0.0006315802729453213\n",
      "0.0006407201773492392\n",
      "0.0006489080835597578\n",
      "0.0006562802343431621\n",
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      "0.0006743880656954272\n",
      "0.0006792997201310514\n",
      "0.0006837315847399691\n",
      "0.0006877241523438605\n",
      "0.0006913137108956604\n",
      "0.0006945330091914652\n",
      "0.0006974117236267671\n",
      "0.0006999768089311022\n",
      "0.0007022527787494613\n",
      "0.0007042619414864888\n",
      "0.000706024605586188\n",
      "0.0007075592622651638\n",
      "0.0007088827503641552\n",
      "0.0007100104061641833\n",
      "0.0007109562000309252\n",
      "0.000711732861219679\n",
      "0.0007123519918829829\n",
      "0.0007128241711595257\n",
      "0.0007131590501249216\n",
      "0.0007133654383195541\n",
      "0.0007134513825192294\n",
      "0.0007134242383721513\n",
      "0.0007132907354869049\n",
      "0.0007130570365187116\n",
      "0.0007127287907648494\n",
      "0.0007123111827445433\n",
      "0.0007118089762042087\n",
      "0.0007112265539555873\n",
      "0.0007105679539225623\n",
      "0.0007098369017422466\n",
      "0.0007090368402374035\n",
      "0.0007081709560505692\n",
      "0.0007072422037052733\n",
      "0.0007062533273365834\n",
      "0.0007052068803117087\n",
      "0.0007041052429415944\n",
      "0.0007029506384661807\n",
      "0.0007017451474792546\n",
      "0.0007004907209434726\n",
      "0.0006991891919320856\n",
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    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8a1ae45198>]"
      ]
     },
     "execution_count": 6,
     "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": [
    "def fitData_GD(y,y_hat,x,a):\n",
    "    for i in range(0,d):\n",
    "        derivative = 0\n",
    "        for k in range(N):\n",
    "            derivative += 2*(y[k]-y_hat[k])*math.pow(x[k],i)\n",
    "        derivative = derivative / N\n",
    "        a[i] = a[i] + learning_rate*derivative\n",
    "    return a\n",
    "plt.plot(x,y,'go')\n",
    "learning_threshold = 2000\n",
    "for time in range(learning_threshold):\n",
    "    a_old = a\n",
    "#     print(\"a_old\",sum(a_old))\n",
    "    a = fitData_GD(y,y_hat,x,a)\n",
    "#     print(\"a\",sum(a))\n",
    "#     a = fitData_SGD(y,y_hat,x,a,1000)\n",
    "#     print(\"y_hat_init\",sum(y_hat))\n",
    "    for i in range(N):\n",
    "        y_hat[i]=predict_function(d,a,x[i])\n",
    "#     print(\"y_hat\",sum(y_hat))\n",
    "    if True:\n",
    "        print(getMSE(y,y_hat))\n",
    "        plt.plot(x,y_hat,'ro')\n",
    "    \n",
    "#     if(a_old == a):\n",
    "#         print(\"break\")\n",
    "#         break;\n",
    "print(getMSE(y,y_hat))\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# learning rate higher- mse-nan - gradient explosion? e.g. lr=10\n",
    "# 学着学着学不动了，derivative太小，\n",
    "#learning rate 大一点 >1，mse变大, <1变小\n",
    "#学习中mse越来越大，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(x,y_hat,'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}