03_linear_regression_keras.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:516: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint8 = np.dtype([(\"qint8\", np.int8, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:517: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint8 = np.dtype([(\"quint8\", np.uint8, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:518: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint16 = np.dtype([(\"qint16\", np.int16, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:519: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint16 = np.dtype([(\"quint16\", np.uint16, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:520: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint32 = np.dtype([(\"qint32\", np.int32, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorflow/python/framework/dtypes.py:525: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  np_resource = np.dtype([(\"resource\", np.ubyte, 1)])\n",
      "/Users/i550012/.pyenv/versions/3.7.17/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: compiletime version 3.6 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.7\n",
      "  return f(*args, **kwds)\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:541: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint8 = np.dtype([(\"qint8\", np.int8, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:542: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint8 = np.dtype([(\"quint8\", np.uint8, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:543: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint16 = np.dtype([(\"qint16\", np.int16, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:544: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint16 = np.dtype([(\"quint16\", np.uint16, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:545: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint32 = np.dtype([(\"qint32\", np.int32, 1)])\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:550: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  np_resource = np.dtype([(\"resource\", np.ubyte, 1)])\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Activation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# linear regression\n",
    "## steps  \n",
    "- prepare data\n",
    "- build model\n",
    "- define loss\n",
    "- optimize model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate data \n",
    "np.random.seed(42)\n",
    "# x is from 0 to 10, 100 points\n",
    "x = np.linspace(0, 10, 100)\n",
    "# y is a linear function of x plus some noise\n",
    "a = 2\n",
    "b = 1\n",
    "y = a * x + b + np.random.normal(0, 1, 100)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize the data to prevent over/underflow\n",
    "def norm(x):\n",
    "    return  (x - np.mean(x)) / np.std(x)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_norm = norm(x)\n",
    "y_norm = norm(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:74: The name tf.get_default_graph is deprecated. Please use tf.compat.v1.get_default_graph instead.\n",
      "\n",
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:517: The name tf.placeholder is deprecated. Please use tf.compat.v1.placeholder instead.\n",
      "\n",
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:4138: The name tf.random_uniform is deprecated. Please use tf.random.uniform instead.\n",
      "\n",
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/optimizers.py:790: The name tf.train.Optimizer is deprecated. Please use tf.compat.v1.train.Optimizer instead.\n",
      "\n",
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:986: The name tf.assign_add is deprecated. Please use tf.compat.v1.assign_add instead.\n",
      "\n",
      "WARNING:tensorflow:From /Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:973: The name tf.assign is deprecated. Please use tf.compat.v1.assign instead.\n",
      "\n",
      "Epoch 1/1000\n",
      "100/100 [==============================] - 0s 696us/step - loss: 0.9594\n",
      "Epoch 2/1000\n",
      " 32/100 [========>.....................] - ETA: 0s - loss: 0.7624"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/ipykernel_launcher.py:3: UserWarning: Update your `Dense` call to the Keras 2 API: `Dense(1, input_shape=(1,), activation=\"linear\", kernel_initializer=\"uniform\")`\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/Users/i550012/virtualenv/tensorflow1/lib/python3.7/site-packages/ipykernel_launcher.py:6: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.\n",
      "  \n",
      "2024-03-22 12:21:31.767542: I tensorflow/core/platform/cpu_feature_guard.cc:142] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX2 FMA\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100/100 [==============================] - 0s 46us/step - loss: 0.8261\n",
      "Epoch 3/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.6986\n",
      "Epoch 4/1000\n",
      "100/100 [==============================] - 0s 41us/step - loss: 0.5902\n",
      "Epoch 5/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.5097\n",
      "Epoch 6/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.4306\n",
      "Epoch 7/1000\n",
      "100/100 [==============================] - 0s 367us/step - loss: 0.3699\n",
      "Epoch 8/1000\n",
      "100/100 [==============================] - 0s 109us/step - loss: 0.3172\n",
      "Epoch 9/1000\n",
      "100/100 [==============================] - 0s 76us/step - loss: 0.2740\n",
      "Epoch 10/1000\n",
      "100/100 [==============================] - 0s 57us/step - loss: 0.2418\n",
      "Epoch 11/1000\n",
      "100/100 [==============================] - 0s 58us/step - loss: 0.2114\n",
      "Epoch 12/1000\n",
      "100/100 [==============================] - 0s 56us/step - loss: 0.1847\n",
      "Epoch 13/1000\n",
      "100/100 [==============================] - 0s 58us/step - loss: 0.1608\n",
      "Epoch 14/1000\n",
      "100/100 [==============================] - 0s 66us/step - loss: 0.1396\n",
      "Epoch 15/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.1212\n",
      "Epoch 16/1000\n",
      "100/100 [==============================] - 0s 58us/step - loss: 0.1060\n",
      "Epoch 17/1000\n",
      "100/100 [==============================] - 0s 56us/step - loss: 0.0942\n",
      "Epoch 18/1000\n",
      "100/100 [==============================] - 0s 48us/step - loss: 0.0850\n",
      "Epoch 19/1000\n",
      "100/100 [==============================] - 0s 44us/step - loss: 0.0766\n",
      "Epoch 20/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.0675\n",
      "Epoch 21/1000\n",
      "100/100 [==============================] - 0s 44us/step - loss: 0.0613\n",
      "Epoch 22/1000\n",
      "100/100 [==============================] - 0s 44us/step - loss: 0.0555\n",
      "Epoch 23/1000\n",
      "100/100 [==============================] - 0s 55us/step - loss: 0.0505\n",
      "Epoch 24/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.0454\n",
      "Epoch 25/1000\n",
      "100/100 [==============================] - 0s 41us/step - loss: 0.0419\n",
      "Epoch 26/1000\n",
      "100/100 [==============================] - 0s 48us/step - loss: 0.0395\n",
      "Epoch 27/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0371\n",
      "Epoch 28/1000\n",
      "100/100 [==============================] - 0s 58us/step - loss: 0.0350\n",
      "Epoch 29/1000\n",
      "100/100 [==============================] - 0s 52us/step - loss: 0.0332\n",
      "Epoch 30/1000\n",
      "100/100 [==============================] - 0s 49us/step - loss: 0.0315\n",
      "Epoch 31/1000\n",
      "100/100 [==============================] - 0s 57us/step - loss: 0.0301\n",
      "Epoch 32/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0290\n",
      "Epoch 33/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.0278\n",
      "Epoch 34/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0269\n",
      "Epoch 35/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0265\n",
      "Epoch 36/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0259\n",
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      "100/100 [==============================] - 0s 34us/step - loss: 0.0232\n",
      "Epoch 865/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0232\n",
      "Epoch 866/1000\n",
      "100/100 [==============================] - 0s 34us/step - loss: 0.0232\n",
      "Epoch 867/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0232\n",
      "Epoch 868/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0232\n",
      "Epoch 869/1000\n",
      "100/100 [==============================] - 0s 72us/step - loss: 0.0232\n",
      "Epoch 870/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 871/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0231\n",
      "Epoch 872/1000\n",
      "100/100 [==============================] - 0s 28us/step - loss: 0.0231\n",
      "Epoch 873/1000\n",
      "100/100 [==============================] - 0s 45us/step - loss: 0.0231\n",
      "Epoch 874/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0232\n",
      "Epoch 875/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 876/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0232\n",
      "Epoch 877/1000\n",
      "100/100 [==============================] - 0s 38us/step - loss: 0.0232\n",
      "Epoch 878/1000\n",
      "100/100 [==============================] - 0s 26us/step - loss: 0.0231\n",
      "Epoch 879/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0231\n",
      "Epoch 880/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0232\n",
      "Epoch 881/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 882/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0231\n",
      "Epoch 883/1000\n",
      "100/100 [==============================] - 0s 26us/step - loss: 0.0232\n",
      "Epoch 884/1000\n",
      "100/100 [==============================] - 0s 27us/step - loss: 0.0231\n",
      "Epoch 885/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 886/1000\n",
      "100/100 [==============================] - 0s 35us/step - loss: 0.0231\n",
      "Epoch 887/1000\n",
      "100/100 [==============================] - 0s 35us/step - loss: 0.0231\n",
      "Epoch 888/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 889/1000\n",
      "100/100 [==============================] - 0s 32us/step - loss: 0.0231\n",
      "Epoch 890/1000\n",
      "100/100 [==============================] - 0s 27us/step - loss: 0.0231\n",
      "Epoch 891/1000\n",
      "100/100 [==============================] - 0s 29us/step - loss: 0.0231\n",
      "Epoch 892/1000\n",
      "100/100 [==============================] - 0s 29us/step - loss: 0.0231\n",
      "Epoch 893/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 894/1000\n",
      "100/100 [==============================] - 0s 32us/step - loss: 0.0231\n",
      "Epoch 895/1000\n",
      "100/100 [==============================] - 0s 33us/step - loss: 0.0231\n",
      "Epoch 896/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0232\n",
      "Epoch 897/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.0231\n",
      "Epoch 898/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 899/1000\n",
      "100/100 [==============================] - 0s 38us/step - loss: 0.0231\n",
      "Epoch 900/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 901/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 902/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.0231\n",
      "Epoch 903/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 904/1000\n",
      "100/100 [==============================] - 0s 32us/step - loss: 0.0231\n",
      "Epoch 905/1000\n",
      "100/100 [==============================] - 0s 34us/step - loss: 0.0232\n",
      "Epoch 906/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0231\n",
      "Epoch 907/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0231\n",
      "Epoch 908/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 909/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 910/1000\n",
      "100/100 [==============================] - 0s 41us/step - loss: 0.0231\n",
      "Epoch 911/1000\n",
      "100/100 [==============================] - 0s 50us/step - loss: 0.0231\n",
      "Epoch 912/1000\n",
      "100/100 [==============================] - 0s 49us/step - loss: 0.0231\n",
      "Epoch 913/1000\n",
      "100/100 [==============================] - 0s 41us/step - loss: 0.0232\n",
      "Epoch 914/1000\n",
      "100/100 [==============================] - 0s 45us/step - loss: 0.0232\n",
      "Epoch 915/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0232\n",
      "Epoch 916/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0232\n",
      "Epoch 917/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0232\n",
      "Epoch 918/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0232\n",
      "Epoch 919/1000\n",
      "100/100 [==============================] - 0s 25us/step - loss: 0.0232\n",
      "Epoch 920/1000\n",
      "100/100 [==============================] - 0s 25us/step - loss: 0.0231\n",
      "Epoch 921/1000\n",
      "100/100 [==============================] - 0s 27us/step - loss: 0.0231\n",
      "Epoch 922/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 923/1000\n",
      "100/100 [==============================] - 0s 28us/step - loss: 0.0231\n",
      "Epoch 924/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0232\n",
      "Epoch 925/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 926/1000\n",
      "100/100 [==============================] - 0s 50us/step - loss: 0.0231\n",
      "Epoch 927/1000\n",
      "100/100 [==============================] - 0s 35us/step - loss: 0.0231\n",
      "Epoch 928/1000\n",
      "100/100 [==============================] - 0s 33us/step - loss: 0.0231\n",
      "Epoch 929/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0232\n",
      "Epoch 930/1000\n",
      "100/100 [==============================] - 0s 35us/step - loss: 0.0232\n",
      "Epoch 931/1000\n",
      "100/100 [==============================] - 0s 28us/step - loss: 0.0231\n",
      "Epoch 932/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0231\n",
      "Epoch 933/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 934/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 935/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 936/1000\n",
      "100/100 [==============================] - 0s 45us/step - loss: 0.0232\n",
      "Epoch 937/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 938/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0231\n",
      "Epoch 939/1000\n",
      "100/100 [==============================] - 0s 24us/step - loss: 0.0232\n",
      "Epoch 940/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0232\n",
      "Epoch 941/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0232\n",
      "Epoch 942/1000\n",
      "100/100 [==============================] - 0s 26us/step - loss: 0.0232\n",
      "Epoch 943/1000\n",
      "100/100 [==============================] - 0s 185us/step - loss: 0.0232\n",
      "Epoch 944/1000\n",
      "100/100 [==============================] - 0s 349us/step - loss: 0.0232\n",
      "Epoch 945/1000\n",
      "100/100 [==============================] - 0s 33us/step - loss: 0.0232\n",
      "Epoch 946/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0231\n",
      "Epoch 947/1000\n",
      "100/100 [==============================] - 0s 56us/step - loss: 0.0232\n",
      "Epoch 948/1000\n",
      "100/100 [==============================] - 0s 56us/step - loss: 0.0232\n",
      "Epoch 949/1000\n",
      "100/100 [==============================] - 0s 58us/step - loss: 0.0232\n",
      "Epoch 950/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0231\n",
      "Epoch 951/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0231\n",
      "Epoch 952/1000\n",
      "100/100 [==============================] - 0s 38us/step - loss: 0.0231\n",
      "Epoch 953/1000\n",
      "100/100 [==============================] - 0s 57us/step - loss: 0.0232\n",
      "Epoch 954/1000\n",
      "100/100 [==============================] - ETA: 0s - loss: 0.024 - 0s 662us/step - loss: 0.0232\n",
      "Epoch 955/1000\n",
      "100/100 [==============================] - 0s 62us/step - loss: 0.0231\n",
      "Epoch 956/1000\n",
      "100/100 [==============================] - 0s 51us/step - loss: 0.0231\n",
      "Epoch 957/1000\n",
      "100/100 [==============================] - 0s 52us/step - loss: 0.0231\n",
      "Epoch 958/1000\n",
      "100/100 [==============================] - 0s 60us/step - loss: 0.0231\n",
      "Epoch 959/1000\n",
      "100/100 [==============================] - 0s 69us/step - loss: 0.0231\n",
      "Epoch 960/1000\n",
      "100/100 [==============================] - 0s 49us/step - loss: 0.0231\n",
      "Epoch 961/1000\n",
      "100/100 [==============================] - 0s 59us/step - loss: 0.0231\n",
      "Epoch 962/1000\n",
      "100/100 [==============================] - 0s 54us/step - loss: 0.0231\n",
      "Epoch 963/1000\n",
      "100/100 [==============================] - 0s 54us/step - loss: 0.0231\n",
      "Epoch 964/1000\n",
      "100/100 [==============================] - 0s 54us/step - loss: 0.0231\n",
      "Epoch 965/1000\n",
      "100/100 [==============================] - 0s 45us/step - loss: 0.0231\n",
      "Epoch 966/1000\n",
      "100/100 [==============================] - 0s 38us/step - loss: 0.0231\n",
      "Epoch 967/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0231\n",
      "Epoch 968/1000\n",
      "100/100 [==============================] - 0s 33us/step - loss: 0.0231\n",
      "Epoch 969/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0232\n",
      "Epoch 970/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0232\n",
      "Epoch 971/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.0232\n",
      "Epoch 972/1000\n",
      "100/100 [==============================] - 0s 41us/step - loss: 0.0231\n",
      "Epoch 973/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0231\n",
      "Epoch 974/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.0231\n",
      "Epoch 975/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 976/1000\n",
      "100/100 [==============================] - 0s 44us/step - loss: 0.0231\n",
      "Epoch 977/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0231\n",
      "Epoch 978/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0231\n",
      "Epoch 979/1000\n",
      "100/100 [==============================] - 0s 39us/step - loss: 0.0231\n",
      "Epoch 980/1000\n",
      "100/100 [==============================] - 0s 45us/step - loss: 0.0231\n",
      "Epoch 981/1000\n",
      "100/100 [==============================] - 0s 566us/step - loss: 0.0231\n",
      "Epoch 982/1000\n",
      "100/100 [==============================] - 0s 61us/step - loss: 0.0231\n",
      "Epoch 983/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.0231\n",
      "Epoch 984/1000\n",
      "100/100 [==============================] - 0s 59us/step - loss: 0.0231\n",
      "Epoch 985/1000\n",
      "100/100 [==============================] - 0s 53us/step - loss: 0.0231\n",
      "Epoch 986/1000\n",
      "100/100 [==============================] - 0s 40us/step - loss: 0.0232\n",
      "Epoch 987/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0232\n",
      "Epoch 988/1000\n",
      "100/100 [==============================] - 0s 50us/step - loss: 0.0231\n",
      "Epoch 989/1000\n",
      "100/100 [==============================] - 0s 50us/step - loss: 0.0232\n",
      "Epoch 990/1000\n",
      "100/100 [==============================] - 0s 46us/step - loss: 0.0232\n",
      "Epoch 991/1000\n",
      "100/100 [==============================] - 0s 53us/step - loss: 0.0231\n",
      "Epoch 992/1000\n",
      "100/100 [==============================] - 0s 43us/step - loss: 0.0231\n",
      "Epoch 993/1000\n",
      "100/100 [==============================] - 0s 42us/step - loss: 0.0231\n",
      "Epoch 994/1000\n",
      "100/100 [==============================] - 0s 47us/step - loss: 0.0231\n",
      "Epoch 995/1000\n",
      "100/100 [==============================] - 0s 32us/step - loss: 0.0232\n",
      "Epoch 996/1000\n",
      "100/100 [==============================] - 0s 37us/step - loss: 0.0231\n",
      "Epoch 997/1000\n",
      "100/100 [==============================] - 0s 31us/step - loss: 0.0231\n",
      "Epoch 998/1000\n",
      "100/100 [==============================] - 0s 38us/step - loss: 0.0231\n",
      "Epoch 999/1000\n",
      "100/100 [==============================] - 0s 30us/step - loss: 0.0231\n",
      "Epoch 1000/1000\n",
      "100/100 [==============================] - 0s 36us/step - loss: 0.0232\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x10d965750>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define model\n",
    "model = Sequential()\n",
    "model.add(Dense(1, input_shape=(1,),init='uniform', activation='linear'))\n",
    "model.compile(optimizer='sgd', loss='mean_squared_error')\n",
    "\n",
    "model.fit(x_norm, y_norm, nb_epoch=1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100/100 [==============================] - 0s 142us/step\n",
      "score: 0.023147691902704538\n"
     ]
    }
   ],
   "source": [
    "score = model.evaluate(x_norm, y_norm)\n",
    "print('score:', score)"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.17"
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