lab-03-1-Linear-Regression-and-Minimizing-Cost-eager.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "qa55_des11wj",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 03 - Multi-variable Linear Regression\n",
    "\n",
    "<img width=\"200\" src=\"https://i.imgur.com/hbPVe1T.png\">\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 741,
     "status": "ok",
     "timestamp": 1549799444433,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "BbOQ25cb11wl",
    "outputId": "149c17c0-c9ca-443f-91df-997c86f09f21",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.13.0-rc0'"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "tf.enable_eager_execution()\n",
    "tf.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gosQaP-B11wt",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Hypothesis and Cost\n",
    "\n",
    "$$ H(x) = Wx + b $$ \n",
    "\n",
    "$$ cost(W, b)=\\frac { 1 }{ m } \\sum _{i=1}^{m}{ { (H{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "# Simplifed hypothesis\n",
    "\n",
    "$$ H(x) = Wx $$ \n",
    "\n",
    "$$ cost(W)=\\frac { 1 }{ m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8_RLcYZe11wu",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "b를 W 행렬에 넣어 표현할 수 있기 때문에 생략 가능"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SgferLHt11ww",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cost function\n",
    "$$ cost(W)=\\frac { 1 }{ m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "W = -1, cost(W) = 18.67\n",
    "$$ cost(W)=\\frac { 1 }{ 3 } ( (-1 * 1 - 1)^2 + (-1 * 2 - 2)^2 + (-1 * 3 - 3)^2) $$\n",
    "\n",
    "W = 0, cost(W) = 4.67\n",
    "$$ cost(W)=\\frac { 1 }{ 3 } ( (0 * 1 - 1)^2 + (0 * 2 - 2)^2 + (0 * 3 - 3)^2) $$\n",
    "\n",
    "W = 1, cost(W) = 0\n",
    "$$ cost(W)=\\frac { 1 }{ 3 } ( (1 * 1 - 1)^2 + (1 * 2 - 2)^2 + (1 * 3 - 3)^2) $$\n",
    "\n",
    "W = 2, cost(W) = 4.67\n",
    "$$ cost(W)=\\frac { 1 }{ 3 } ( (2 * 1 - 1)^2 + (2 * 2 - 2)^2 + (2 * 3 - 3)^2) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jjICfKEk11wx",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cost function in pure Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 726,
     "status": "ok",
     "timestamp": 1549799444435,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "K-FN3gLt11wz",
    "outputId": "b55058bd-f228-4609-cced-0ac14b51292b",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.000 |   74.66667\n",
      "-2.429 |   54.85714\n",
      "-1.857 |   38.09524\n",
      "-1.286 |   24.38095\n",
      "-0.714 |   13.71429\n",
      "-0.143 |    6.09524\n",
      " 0.429 |    1.52381\n",
      " 1.000 |    0.00000\n",
      " 1.571 |    1.52381\n",
      " 2.143 |    6.09524\n",
      " 2.714 |   13.71429\n",
      " 3.286 |   24.38095\n",
      " 3.857 |   38.09524\n",
      " 4.429 |   54.85714\n",
      " 5.000 |   74.66667\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = np.array([1, 2, 3])\n",
    "Y = np.array([1, 2, 3])\n",
    "\n",
    "def cost_func(W, X, Y):\n",
    "    c = 0\n",
    "    for i in range(len(X)):\n",
    "        c += (W * X[i] - Y[i]) ** 2\n",
    "    return c / len(X)\n",
    "\n",
    "for feed_W in np.linspace(-3, 5, num=15):\n",
    "    curr_cost = cost_func(feed_W, X, Y)\n",
    "    print(\"{:6.3f} | {:10.5f}\".format(feed_W, curr_cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "r6i-reEG34GK",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cost function in TensorFlow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 715,
     "status": "ok",
     "timestamp": 1549799444437,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "t0zWozvW4tza",
    "outputId": "1f27299e-f3a8-4688-e1e9-aaff19752ed2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.000 |   74.66667\n",
      "-2.429 |   54.85714\n",
      "-1.857 |   38.09524\n",
      "-1.286 |   24.38095\n",
      "-0.714 |   13.71429\n",
      "-0.143 |    6.09524\n",
      " 0.429 |    1.52381\n",
      " 1.000 |    0.00000\n",
      " 1.571 |    1.52381\n",
      " 2.143 |    6.09524\n",
      " 2.714 |   13.71429\n",
      " 3.286 |   24.38095\n",
      " 3.857 |   38.09524\n",
      " 4.429 |   54.85714\n",
      " 5.000 |   74.66667\n"
     ]
    }
   ],
   "source": [
    "X = np.array([1, 2, 3])\n",
    "Y = np.array([1, 2, 3])\n",
    "\n",
    "def cost_func(W, X, Y):\n",
    "  hypothesis = X * W\n",
    "  return tf.reduce_mean(tf.square(hypothesis - Y))\n",
    "\n",
    "W_values = np.linspace(-3, 5, num=15)\n",
    "cost_values = []\n",
    "\n",
    "for feed_W in W_values:\n",
    "    curr_cost = cost_func(feed_W, X, Y)\n",
    "    cost_values.append(curr_cost)\n",
    "    print(\"{:6.3f} | {:10.5f}\".format(feed_W, curr_cost))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oFminhBFFlil"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (8,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 388
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1098,
     "status": "ok",
     "timestamp": 1549799444836,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "_b7ootOQ8Bx-",
    "outputId": "ee72e564-19cd-4136-dc9e-5c11011a9d14"
   },
   "outputs": [
    {
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BAz8NG/pYs8bBvn0x+tMjIhJB0tMdGIbJrbfG5tA4KLRDqkcPD16vwdKl6m2LiITSf/9r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\nAEV8ALvbQ9K6UzvLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(W_values, cost_values, \"b\")\n",
    "plt.ylabel('Cost(W)')\n",
    "plt.xlabel('W')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mZsgJWKW11w_",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# How to minimize cost?\n",
    "* 현재 데이터 X와 Y에 대해 W가 1일 때 cost 가 가장 작다\n",
    "* cost 가 최소가 되는 W를 어떻게 찾을 수 있을까?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IMPZVD0o11xA",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient descent algorithm\n",
    "* Minimize cost function\n",
    "* used many minimization problems\n",
    "* For a given cost (W, b), it will find W, b to minimize cost\n",
    "* It can be applied to more general function: cost (w1, w2, ...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-gFKqZ8111xC",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# How does it work?\n",
    "* Start with initial guesses\n",
    " * Start at 0,0 (or any other value)\n",
    " * Keeping changing $W$ and $b$ a little bit to try and reduce $cost(W,b)$\n",
    "* Each time you change the parameters, you select the gradient which reduces $cost(W,b)$ the most possible \n",
    "* Repeat\n",
    "* Do so until you converge to a local minimum\n",
    "* Has an interesting property\n",
    " * Where you start can determine which minimum you end up\n",
    "\n",
    "http://www.holehouse.org/mlclass/01_02_Introduction_regression_analysis_and_gr.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cLq7dmOc11xD",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Formal definition\n",
    "$$ cost(W)=\\frac { 1 }{ m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "$$ \\Downarrow $$\n",
    "\n",
    "$$ cost(W)=\\frac { 1 }{ 2m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "* m 혹은 2m 나누는 것이 cost 최소화에 영향 없음\n",
    "* 제곱을 미분할 때, 2가 앞으로 나오면서 공식이 단순하게 되는 효과"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8jVtv-Up11xE",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Formal definition\n",
    "$$ cost(W)=\\frac { 1 }{ 2m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "$$ W:=W - \\alpha\\frac{ \\partial } {\\partial W } cost(W) $$\n",
    "\n",
    "* W = W - 변화량\n",
    "* 변화량 = 현 위치(W)에서 비용곡선의 기울기(=미분값) X $\\alpha$ <br> $\\alpha$ : learning rate (시도 간격)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JCcthfl111xF",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Formal definition\n",
    "\n",
    "$$ W:=W - \\alpha\\frac{ \\partial } {\\partial W } \\frac { 1 }{ 2m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } } $$\n",
    "\n",
    "$$ W:=W-\\alpha \\frac { 1 }{ 2m } \\sum _{ i=1 }^{ m }{ { 2(W{ x }^{ i }-y^{ i } })x^{ i } }  $$\n",
    "\n",
    "$$ W:=W-\\alpha \\frac { 1 }{ m } \\sum _{ i=1 }^{ m }{ { (W{ x }^{ i }-y^{ i } })x^{ i } }  $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qb0l2j-g11xG",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient descent algorithm\n",
    "$$ W:=W-\\alpha \\frac { 1 }{ m } \\sum _{ i=1 }^{ m }{ { (W{ x }^{ i }-y^{ i } })x^{ i } }  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uK8NeKEj11xH",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Convex function\n",
    "<img width=\"40%\" src=\"http://i.imgur.com/TSKliup.png\" >\n",
    "<img width=\"40%\" src=\"http://i.imgur.com/GyCwshy.png\" >\n",
    "\n",
    "Gradient descent algorithm을 사용하려면, 비용함수 cost(W,b)가 Convex function 이어야 한다\n",
    "\n",
    "http://www.holehouse.org/mlclass/01_02_Introduction_regression_analysis_and_gr.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SIB932rR11xJ",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient descent 구현"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5ze9yS4_NCuC"
   },
   "outputs": [],
   "source": [
    "tf.set_random_seed(0)  # for reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 646,
     "status": "ok",
     "timestamp": 1549801133459,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "s4PdNwqWMlFb",
    "outputId": "9c3e40cc-f550-4eac-8612-fd1668f3e5a0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    0 | 11716.3086 |  48.767971\n",
      "   10 |  4504.9126 |  30.619968\n",
      "   20 |  1732.1364 |  19.366755\n",
      "   30 |   666.0052 |  12.388859\n",
      "   40 |   256.0785 |   8.062004\n",
      "   50 |    98.4620 |   5.379007\n",
      "   60 |    37.8586 |   3.715335\n",
      "   70 |    14.5566 |   2.683725\n",
      "   80 |     5.5970 |   2.044044\n",
      "   90 |     2.1520 |   1.647391\n",
      "  100 |     0.8275 |   1.401434\n",
      "  110 |     0.3182 |   1.248922\n",
      "  120 |     0.1223 |   1.154351\n",
      "  130 |     0.0470 |   1.095710\n",
      "  140 |     0.0181 |   1.059348\n",
      "  150 |     0.0070 |   1.036801\n",
      "  160 |     0.0027 |   1.022819\n",
      "  170 |     0.0010 |   1.014150\n",
      "  180 |     0.0004 |   1.008774\n",
      "  190 |     0.0002 |   1.005441\n",
      "  200 |     0.0001 |   1.003374\n",
      "  210 |     0.0000 |   1.002092\n",
      "  220 |     0.0000 |   1.001297\n",
      "  230 |     0.0000 |   1.000804\n",
      "  240 |     0.0000 |   1.000499\n",
      "  250 |     0.0000 |   1.000309\n",
      "  260 |     0.0000 |   1.000192\n",
      "  270 |     0.0000 |   1.000119\n",
      "  280 |     0.0000 |   1.000074\n",
      "  290 |     0.0000 |   1.000046\n"
     ]
    }
   ],
   "source": [
    "x_data = [1., 2., 3., 4.]\n",
    "y_data = [1., 3., 5., 7.]\n",
    "\n",
    "W = tf.Variable(tf.random_normal([1], -100., 100.))\n",
    "\n",
    "for step in range(300):\n",
    "    hypothesis = W * X\n",
    "    cost = tf.reduce_mean(tf.square(hypothesis - Y))\n",
    "\n",
    "    alpha = 0.01\n",
    "    gradient = tf.reduce_mean(tf.multiply(tf.multiply(W, X) - Y, X))\n",
    "    descent = W - tf.multiply(alpha, gradient)\n",
    "    W.assign(descent)\n",
    "    \n",
    "    if step % 10 == 0:\n",
    "        print('{:5} | {:10.4f} | {:10.6f}'.format(\n",
    "            step, cost.numpy(), W.numpy()[0]))\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 553,
     "status": "ok",
     "timestamp": 1549799480748,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "7uwjdzO9PziL",
    "outputId": "dab64b1a-e163-4a81-a65c-6793ebcf7479"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor([5.000017], shape=(1,), dtype=float32)\n",
      "tf.Tensor([2.5000086], shape=(1,), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(5.0 * W)\n",
    "print(2.5 * W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 580,
     "status": "ok",
     "timestamp": 1549801357771,
     "user": {
      "displayName": "Sean-June Lee",
      "photoUrl": "https://lh3.googleusercontent.com/-j96Pvw9LbEw/AAAAAAAAAAI/AAAAAAACQxw/aY8i4PoItwc/s64/photo.jpg",
      "userId": "12576390002043678893"
     },
     "user_tz": -540
    },
    "id": "bdFpBmDmWsrD",
    "outputId": "150e5258-8873-407d-c867-42868bd41506"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    0 |    74.6667 |   4.813334\n",
      "   10 |    28.7093 |   3.364572\n",
      "   20 |    11.0387 |   2.466224\n",
      "   30 |     4.2444 |   1.909177\n",
      "   40 |     1.6320 |   1.563762\n",
      "   50 |     0.6275 |   1.349578\n",
      "   60 |     0.2413 |   1.216766\n",
      "   70 |     0.0928 |   1.134412\n",
      "   80 |     0.0357 |   1.083346\n",
      "   90 |     0.0137 |   1.051681\n",
      "  100 |     0.0053 |   1.032047\n",
      "  110 |     0.0020 |   1.019871\n",
      "  120 |     0.0008 |   1.012322\n",
      "  130 |     0.0003 |   1.007641\n",
      "  140 |     0.0001 |   1.004738\n",
      "  150 |     0.0000 |   1.002938\n",
      "  160 |     0.0000 |   1.001822\n",
      "  170 |     0.0000 |   1.001130\n",
      "  180 |     0.0000 |   1.000700\n",
      "  190 |     0.0000 |   1.000434\n",
      "  200 |     0.0000 |   1.000269\n",
      "  210 |     0.0000 |   1.000167\n",
      "  220 |     0.0000 |   1.000103\n",
      "  230 |     0.0000 |   1.000064\n",
      "  240 |     0.0000 |   1.000040\n",
      "  250 |     0.0000 |   1.000025\n",
      "  260 |     0.0000 |   1.000015\n",
      "  270 |     0.0000 |   1.000009\n",
      "  280 |     0.0000 |   1.000006\n",
      "  290 |     0.0000 |   1.000004\n"
     ]
    }
   ],
   "source": [
    "x_data = [1., 2., 3., 4.]\n",
    "y_data = [1., 3., 5., 7.]\n",
    "\n",
    "W = tf.Variable([5.0])\n",
    "\n",
    "for step in range(300):\n",
    "    hypothesis = W * X\n",
    "    cost = tf.reduce_mean(tf.square(hypothesis - Y))\n",
    "\n",
    "    alpha = 0.01\n",
    "    gradient = tf.reduce_mean(tf.multiply(tf.multiply(W, X) - Y, X))\n",
    "    descent = W - tf.multiply(alpha, gradient)\n",
    "    W.assign(descent)\n",
    "    \n",
    "    if step % 10 == 0:\n",
    "        print('{:5} | {:10.4f} | {:10.6f}'.format(\n",
    "            step, cost.numpy(), W.numpy()[0]))\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sWizNKZl11xO",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Liner regression Summary\n",
    "\n",
    "## 1) Hypothesis \n",
    "\n",
    "$$ H(x) = Wx + b $$\n",
    "\n",
    "## 2) Cost function\n",
    "\n",
    "$$ cost(W)=\\frac { 1 }{ m } \\sum _{i=1}^{m}{ { (W{ x }^{ i }-y^{ i } })^{ 2 } }  $$\n",
    "\n",
    "## 3) Gradient descent\n",
    "\n",
    "$$ W := W-\\alpha \\frac { \\partial  }{ \\partial W } cost(W) $$"
   ]
  }
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