Neuron.ipynb

neuron.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Neuron.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/x1001000/34aa1900ccecf34e93b5426158ad6081/neuron.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "id": "motxQ-WfV9vO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Data"
      ]
    },
    {
      "metadata": {
        "id": "86D8fM6-33Yk",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 資料要數據化成Ｎ維陣列  \n",
        "資料要視覺化以幫助理解\n",
        "\n",
        "- 匯入Ｎ維陣列運算要用的函式庫 numpy  \n",
        "匯入作圖要用的函式庫 matplotlib.pyplot"
      ]
    },
    {
      "metadata": {
        "id": "jRG5EitZxlcO",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "id": "L-WBfUAK_QB1",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 串列(list)與陣列(array)的元素，皆有序可供索引  \n",
        "串列的元素可以不同類別  \n",
        "陣列的元素必須相同類別，儲存在連續的記憶體位址上，故運算效率高\n",
        "\n",
        "- 複習一下串列"
      ]
    },
    {
      "metadata": {
        "id": "pCnkWRWq4uTb",
        "colab_type": "code",
        "outputId": "0ba87b7f-0b42-4346-830b-af6855a9ebc3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "a = [ 1001000, 3.14, [5,5,6,6], 'Hello Python!' ]\n",
        "print(type(a))\n",
        "print(len(a))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'list'>\n",
            "4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "axn22aoT9nGX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 把串列轉成陣列，陣列 = np.array(串列)\n",
        "\n",
        "- 查看陣列的形狀(shape)及維度(ndim)"
      ]
    },
    {
      "metadata": {
        "id": "hWJFxi7H5WnJ",
        "colab_type": "code",
        "outputId": "d40bbd80-c2d6-4c04-9565-4f3a44b2a6a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        }
      },
      "cell_type": "code",
      "source": [
        "a = [5, 5, 6, 6]\n",
        "b = [a, a]\n",
        "c = [b, b, b, b, b]\n",
        "d = np.array( c )\n",
        "print(d)\n",
        "print(type(d))\n",
        "print(len(c))\n",
        "print(len(d))\n",
        "print(d.shape)\n",
        "print(d.ndim)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[[5 5 6 6]\n",
            "  [5 5 6 6]]\n",
            "\n",
            " [[5 5 6 6]\n",
            "  [5 5 6 6]]\n",
            "\n",
            " [[5 5 6 6]\n",
            "  [5 5 6 6]]\n",
            "\n",
            " [[5 5 6 6]\n",
            "  [5 5 6 6]]\n",
            "\n",
            " [[5 5 6 6]\n",
            "  [5 5 6 6]]]\n",
            "<class 'numpy.ndarray'>\n",
            "5\n",
            "5\n",
            "(5, 2, 4)\n",
            "3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "aF3ceYqmED3q",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 一維陣列 aka 向量  \n",
        "二維陣列 aka 矩陣  \n",
        "Ｎ維陣列 aka 張量"
      ]
    },
    {
      "metadata": {
        "id": "Ww97ynVlHelS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Linear Regression"
      ]
    },
    {
      "metadata": {
        "id": "nd3tbvdjx6yS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 函數是一對一或多對一的關係，可用來模型化一個系統的輸入和輸出的關係  \n",
        "線性迴歸就是求最接近全部樣本的一個線性函數，線性函數的示意圖像神經元  \n",
        "用一堆線性函數串並聯模型化一個複雜系統（例如輸入貓圖片輸出貓答案）的示意圖像神經網路\n",
        "\n",
        "- 用一個極簡的例子來理解何謂線性迴歸  \n",
        "用五筆特徵x及其標籤y，反覆更新w(weight)和b(bias)，使得線性函數y=wx+b更接近這五個資料點，反覆更新的過程就稱為「訓練」或「學習」"
      ]
    },
    {
      "metadata": {
        "id": "A5Nogo-RGqen",
        "colab_type": "code",
        "outputId": "40ea18de-64b4-4321-ac7d-601ceb7d3893",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "cell_type": "code",
      "source": [
        "# 五筆特徵xs\n",
        "xs = np.array( [ 1, 2, 3, 4, 5] )\n",
        "# 及其標籤ys\n",
        "ys = np.array( [10,20,30,43,59] )\n",
        "# 繪製散佈圖，輸入X座標們xs及Y座標們ys\n",
        "plt.scatter(xs, ys)\n",
        "# 繪製折線圖，輸入X座標們xs及Y座標們ys\n",
        "plt.plot(xs, ys)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb590afa518>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IhS7ix3ZlFfDwou3szyliyvAuPKFFQvIdVOgifqiisopX1h/g+TVaJCTuU6GL+JkvXYuE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\niEiA+F+UBrnRbwq2xwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "nO1Vgsk9XRzQ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Model"
      ]
    },
    {
      "metadata": {
        "id": "K27ixz0BBeDZ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 初學者用Keras函式庫（之後再用TensorFlow函式庫）  \n",
        "初學者用順序式模型（之後再用函數式模型）"
      ]
    },
    {
      "metadata": {
        "id": "ub7Iwo_0A-I1",
        "colab_type": "code",
        "outputId": "4061e9c0-b38f-4033-f625-9fd538bc4dea",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.models import Sequential\n",
        "model = Sequential()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "QSEXUNnHFgSa",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- Dense(全連接)層有三個引數要設：\n",
        "    1. 每筆資料的特徵x只有1個數（長度為1的向量），故這個Dense層的input_dim=1\n",
        "    2. 每筆資料的標籤y只有1個數（長度為1的向量），故這個Dense層需units=1個神經元\n",
        "    3. 激活函數activation=None，讓y直接等於f(x)"
      ]
    },
    {
      "metadata": {
        "id": "CEQ_nRkpBRVh",
        "colab_type": "code",
        "outputId": "91d1fc66-d0b4-4742-e2f8-da7023eb7be1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.layers import Dense\n",
        "model.add(Dense(input_dim=1, units=1, activation=None))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Colocations handled automatically by placer.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "FdoF649QSkQ_",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 這個模型的概要檢視  \n",
        "這個模型只有一個Dense層，這個Dense層只有一個神經元，這個神經元只有兩個Param要訓練  \n",
        "任何模型的每一層的Param數量要知道怎麼算，才能對該模型有概念"
      ]
    },
    {
      "metadata": {
        "id": "_wiZcpqlItVQ",
        "colab_type": "code",
        "outputId": "22f5e72f-3e6f-4c54-e940-fb5b58880ccd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "cell_type": "code",
      "source": [
        "model.summary()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dense_1 (Dense)              (None, 1)                 2         \n",
            "=================================================================\n",
            "Total params: 2\n",
            "Trainable params: 2\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "htqdwNnUkpBy",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 尚未訓練的Param們的初始值"
      ]
    },
    {
      "metadata": {
        "id": "EJqHRLvnjPTZ",
        "colab_type": "code",
        "outputId": "0ceb5d27-d213-42f4-95ec-f537225bd1da",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "w, b = model.layers[0].get_weights()\n",
        "print('w =', w[0])\n",
        "print('b =', b[0])"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "w = [-0.25288296]\n",
            "b = 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "fHFbYjNHTNdY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Training"
      ]
    },
    {
      "metadata": {
        "id": "ePRDFrxVI3KD",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- [Before training a model, you need to configure the learning process, which is done via the compile method.](https://keras.io/getting-started/sequential-model-guide/)\n",
        "\n",
        "- Param的誤差函數Loss(w,b)的算法，在此採用MSE(均方誤差法)  \n",
        "Param的最佳解的找法，在此採用SGD(隨機梯度下降法)"
      ]
    },
    {
      "metadata": {
        "id": "yne07GxQFB_f",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "model.compile(loss='MSE',\n",
        "              optimizer='SGD')"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "metadata": {
        "id": "_-qG1KEGHs-G",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 訓練10個回合(epochs)"
      ]
    },
    {
      "metadata": {
        "id": "PFBLINzWLcVK",
        "colab_type": "code",
        "outputId": "20429659-8ecb-42e4-bca7-f8c04cf5c3e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 445
        }
      },
      "cell_type": "code",
      "source": [
        "model.fit(xs, ys, epochs=10)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.cast instead.\n",
            "Epoch 1/10\n",
            "5/5 [==============================] - 1s 145ms/step - loss: 1408.1034\n",
            "Epoch 2/10\n",
            "5/5 [==============================] - 0s 1ms/step - loss: 825.4548\n",
            "Epoch 3/10\n",
            "5/5 [==============================] - 0s 601us/step - loss: 485.8926\n",
            "Epoch 4/10\n",
            "5/5 [==============================] - 0s 906us/step - loss: 287.9895\n",
            "Epoch 5/10\n",
            "5/5 [==============================] - 0s 542us/step - loss: 172.6384\n",
            "Epoch 6/10\n",
            "5/5 [==============================] - 0s 619us/step - loss: 105.3945\n",
            "Epoch 7/10\n",
            "5/5 [==============================] - 0s 543us/step - loss: 66.1855\n",
            "Epoch 8/10\n",
            "5/5 [==============================] - 0s 333us/step - loss: 43.3139\n",
            "Epoch 9/10\n",
            "5/5 [==============================] - 0s 516us/step - loss: 29.9630\n",
            "Epoch 10/10\n",
            "5/5 [==============================] - 0s 423us/step - loss: 22.1606\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fb590ad1828>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "metadata": {
        "id": "7Y6CSiUasrMe",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 更新後的Param們"
      ]
    },
    {
      "metadata": {
        "id": "DbIZphaXL6FM",
        "colab_type": "code",
        "outputId": "7538ee52-1839-4a32-dd03-58ac087a9b35",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "w, b = model.layers[0].get_weights()\n",
        "print('w =', w[0])\n",
        "print('b =', b[0])"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "w = [9.575648]\n",
            "b = 2.4785392\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "z9n9HHRaISJV",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Inference"
      ]
    },
    {
      "metadata": {
        "id": "zAC7coOHTsin",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 用訓練過的模型（神經網路）做推論（預測）  \n",
        "輸入訓練資料的feature，輸出的預測結果會接近但不會等於label"
      ]
    },
    {
      "metadata": {
        "id": "tdjspq_VLx9i",
        "colab_type": "code",
        "outputId": "c094a6c5-4637-47ee-9c57-2cc7be079ef7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "cell_type": "code",
      "source": [
        "prediction1 = model.predict(xs)\n",
        "prediction1"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12.054188],\n",
              "       [21.629835],\n",
              "       [31.205482],\n",
              "       [40.78113 ],\n",
              "       [50.35678 ]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "metadata": {
        "id": "vxR7GKyWtgaw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 訓練資料為藍色點  \n",
        "預測結果為紅色點  \n",
        "五點連線為一直線，因為此模型只有一個神經元，神經元是一個線性函數"
      ]
    },
    {
      "metadata": {
        "id": "k8Sk7LOPQEiD",
        "colab_type": "code",
        "outputId": "89a6c37a-3eb8-4d34-b807-a82f384e3b68",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "cell_type": "code",
      "source": [
        "plt.scatter(xs, ys)\n",
        "\n",
        "plt.scatter(xs, prediction1, color='red')\n",
        "plt.plot(xs, prediction1, color='red')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb53822ceb8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Kf1ep414EPFHT/6Ooz1M96or8XAFzgWbf83pkP385e4XuNS9Ova5jgUc9eB1o\numYVpRhripy7L3b3t1KPvwRmABs2iY/jXKVTV6RS//1fpZ42Tn1s+CbSugugjwYONTOLuabImVkb\n4FfAA7XsEul5qkdduSiyn7+cDfQ0tAYWrPN8ITEHRsr+qT+f/25m+0R54NSfvV0IV3nrivVcfU9d\nEPH5Sv25/jZh2cQJ7l7ruXL31cAyYOeYawI4PvXn+mgz2yWb9aTcDlwKVNfyeuTnKc26IPpz5cDL\nZjbFzPrX8HpkP3/5HOi56C3CFN1OwF3A2KgObGbbAk8DF7r78qiOW5c66or8fLl7lbt3BtoA3cxs\n32wfMwM1PQcUuntHYAJrr4yzwsyOApa6+5RsHqe+0qwr0nOV0t3duwJHAOeZ2UERHLNG+RzoZcC6\nv33bpLbFxt2Xr/nz2d1fBBqbWbNsH9fMGhNCs8Tdx9SwSyznqq664jpfqeNVAJOAwzd46btzZWZb\nAjsAn8VZk7t/5u7fpp4+APwky6UcCBxjZnOBp4BDzOzxDfaJ4zzVWVcM5wp3L0t9Xgo8A3TbYJfI\nfv7yOdCfBU5LvYO8H7DM3RfHWZCZ/WjNOKKZdSOc36z+I08d70FghrvfWstukZ+rdOqK+nyZWXMz\na5p6XAAcBszcYLd1F0A/AXjFU+9sxVXTBuOtxxDej8gadx/k7m3cvZDwhucr7n7KBrtFep7SrSvq\nc2VmPzCz7dY8Bn4JbHgXXGQ/f3UuEh0Xq3lx6sYA7n4f8CLh3ePZwArg9Byo6QTgHDNbDVQCJ2X7\nHznhquVUYFpqHBbgcqDtOnVFfq7SrCvq89USGGFmjQi/PEa5+/NmNgQodfdnCb+EHjOz2YQ3wE/K\nYj3p1nS+mR0DrE7V1C/LNdUo5vOUbl1Rn6sWwDOp65ItgSfc/SUzOxui//nTTFERkYTI5yEXERFZ\nhwJdRCQhFOgiIgmhQBcRSQgFuohIQijQRUQSQoEuIpIQCnQRkYT4f3M0kAqsDUayAAAAAElFTkSu\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "9MgPWwvCONjz",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 再訓練10個回合(epochs)"
      ]
    },
    {
      "metadata": {
        "id": "Wjei0gNSN6d0",
        "colab_type": "code",
        "outputId": "064966cd-395e-41b2-a971-947db1dce469",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "cell_type": "code",
      "source": [
        "model.fit(xs, ys, epochs=10)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/10\n",
            "5/5 [==============================] - 0s 1ms/step - loss: 17.5916\n",
            "Epoch 2/10\n",
            "5/5 [==============================] - 0s 748us/step - loss: 14.9071\n",
            "Epoch 3/10\n",
            "5/5 [==============================] - 0s 643us/step - loss: 13.3209\n",
            "Epoch 4/10\n",
            "5/5 [==============================] - 0s 820us/step - loss: 12.3749\n",
            "Epoch 5/10\n",
            "5/5 [==============================] - 0s 694us/step - loss: 11.8021\n",
            "Epoch 6/10\n",
            "5/5 [==============================] - 0s 654us/step - loss: 11.4469\n",
            "Epoch 7/10\n",
            "5/5 [==============================] - 0s 953us/step - loss: 11.2187\n",
            "Epoch 8/10\n",
            "5/5 [==============================] - 0s 659us/step - loss: 11.0647\n",
            "Epoch 9/10\n",
            "5/5 [==============================] - 0s 653us/step - loss: 10.9540\n",
            "Epoch 10/10\n",
            "5/5 [==============================] - 0s 899us/step - loss: 10.8687\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fb538279390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "metadata": {
        "id": "gGWd2Aids0Hh",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 再次更新後的Param們"
      ]
    },
    {
      "metadata": {
        "id": "jvG9O0g2N_AL",
        "colab_type": "code",
        "outputId": "781f4699-716a-4936-bebf-73e4907d245a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "w, b = model.layers[0].get_weights()\n",
        "print('w =', w[0])\n",
        "print('b =', b[0])"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "w = [10.292608]\n",
            "b = 2.4414377\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "hNHMwM1ep277",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "- 再次用訓練資料的feature做推論，顯示為棕色"
      ]
    },
    {
      "metadata": {
        "id": "qq282joVo-B3",
        "colab_type": "code",
        "outputId": "b3834feb-16f3-403e-91b9-78366c71fb7a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "cell_type": "code",
      "source": [
        "prediction2 = model.predict(xs)\n",
        "prediction2"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12.734046],\n",
              "       [23.026653],\n",
              "       [33.319263],\n",
              "       [43.61187 ],\n",
              "       [53.90448 ]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "metadata": {
        "id": "WLEEpzVUpOm4",
        "colab_type": "code",
        "outputId": "240ea5f8-367f-46c6-a534-53a4e0678904",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "cell_type": "code",
      "source": [
        "plt.scatter(xs, ys)\n",
        "\n",
        "plt.scatter(xs, prediction2, color='brown')\n",
        "plt.plot(xs, prediction2, color='brown')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb538224828>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LxRMnUl5SAkBxYSEb58/nrM6duTIzUwNPEan3GngdIFi5GRmVZX6sskOHVOYi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\nJf4/4ifZXJpiwb8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}