Linear_Regression_with_TensorFlow.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/github/NurFortuna/Deep_Learning_with_Tensorflow_notes/blob/main/Linear_Regression_with_TensorFlow.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Linear Regression with TensorFlow"
      ],
      "metadata": {
        "id": "xo8uIlRXT2pU"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
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          "base_uri": "https://localhost:8080/"
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        "id": "YbeDwY5SO7hX",
        "outputId": "1f5136c9-9f7b-4c0f-f4e3-9d41337e76f2"
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          "text": [
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            "Installing collected packages: tensorflow-estimator, scipy, h5py, gast, cachetools, google-auth, tensorboard, tensorflow\n",
            "  Attempting uninstall: tensorflow-estimator\n",
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            "      Successfully uninstalled tensorflow-estimator-2.9.0\n",
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            "    Found existing installation: gast 0.4.0\n",
            "    Uninstalling gast-0.4.0:\n",
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            "  Attempting uninstall: cachetools\n",
            "    Found existing installation: cachetools 5.2.0\n",
            "    Uninstalling cachetools-5.2.0:\n",
            "      Successfully uninstalled cachetools-5.2.0\n",
            "  Attempting uninstall: google-auth\n",
            "    Found existing installation: google-auth 2.15.0\n",
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            "    Found existing installation: tensorboard 2.9.1\n",
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            "      Successfully uninstalled tensorboard-2.9.1\n",
            "  Attempting uninstall: tensorflow\n",
            "    Found existing installation: tensorflow 2.9.2\n",
            "    Uninstalling tensorflow-2.9.2:\n",
            "      Successfully uninstalled tensorflow-2.9.2\n",
            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
            "xarray-einstats 0.4.0 requires scipy>=1.6, but you have scipy 1.4.1 which is incompatible.\n",
            "plotnine 0.8.0 requires scipy>=1.5.0, but you have scipy 1.4.1 which is incompatible.\n",
            "jaxlib 0.3.25+cuda11.cudnn805 requires scipy>=1.5, but you have scipy 1.4.1 which is incompatible.\n",
            "jax 0.3.25 requires scipy>=1.5, but you have scipy 1.4.1 which is incompatible.\n",
            "google-cloud-bigquery 3.4.1 requires grpcio<2.0dev,>=1.47.0, but you have grpcio 1.24.3 which is incompatible.\n",
            "google-api-core 2.11.0 requires google-auth<3.0dev,>=2.14.1, but you have google-auth 1.35.0 which is incompatible.\u001b[0m\u001b[31m\n",
            "\u001b[0mSuccessfully installed cachetools-4.2.4 gast-0.3.3 google-auth-1.35.0 h5py-2.10.0 scipy-1.4.1 tensorboard-2.2.2 tensorflow-2.2.0 tensorflow-estimator-2.2.0\n"
          ]
        }
      ],
      "source": [
        "!pip install grpcio==1.24.3\n",
        "!pip install tensorflow==2.2.0"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import pylab as pl\n",
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "import matplotlib.patches as mpatches\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.rcParams['figure.figsize'] = (10, 6)"
      ],
      "metadata": {
        "id": "FnpRTFxcUrjZ"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "if not tf.__version__ == '2.2.0':\n",
        "    print(tf.__version__)\n",
        "    raise ValueError('please upgrade to TensorFlow 2.2.0, or restart your Kernel (Kernel->Restart & Clear Output)')"
      ],
      "metadata": {
        "id": "5i4gU7z9TzGo"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X = np.arange(0.0, 10.0, 0.2)\n",
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9GKBQeYqUwq1",
        "outputId": "7819512f-39c6-4d5d-8973-68e928a2eeec"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2, 1.4, 1.6, 1.8, 2. , 2.2, 2.4,\n",
              "       2.6, 2.8, 3. , 3.2, 3.4, 3.6, 3.8, 4. , 4.2, 4.4, 4.6, 4.8, 5. ,\n",
              "       5.2, 5.4, 5.6, 5.8, 6. , 6.2, 6.4, 6.6, 6.8, 7. , 7.2, 7.4, 7.6,\n",
              "       7.8, 8. , 8.2, 8.4, 8.6, 8.8, 9. , 9.2, 9.4, 9.6, 9.8])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "##You can adjust the slope and intercept to verify the changes in the graph\n",
        "a = 3\n",
        "b = 1\n",
        "\n",
        "Y= a * X + b \n",
        "\n",
        "plt.plot(X, Y) \n",
        "plt.ylabel('Dependent Variable')\n",
        "plt.xlabel('Indepdendent Variable')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "HbGGPrtXVbLc",
        "outputId": "e475571b-8665-496a-e06e-f4c553eca3dd"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv(\"FuelConsumption.csv\")\n",
        "\n",
        "# take a look at the dataset\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        },
        "id": "san5B2khVh7Z",
        "outputId": "7d9cc293-148a-40bd-c414-9bf5cfc2e158"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n",
              "0       2014  ACURA         ILX      COMPACT         2.0          4   \n",
              "1       2014  ACURA         ILX      COMPACT         2.4          4   \n",
              "2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n",
              "3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n",
              "4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n",
              "\n",
              "  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n",
              "0          AS5        Z                   9.9                  6.7   \n",
              "1           M6        Z                  11.2                  7.7   \n",
              "2          AV7        Z                   6.0                  5.8   \n",
              "3          AS6        Z                  12.7                  9.1   \n",
              "4          AS6        Z                  12.1                  8.7   \n",
              "\n",
              "   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n",
              "0                   8.5                        33           196  \n",
              "1                   9.6                        29           221  \n",
              "2                   5.9                        48           136  \n",
              "3                  11.1                        25           255  \n",
              "4                  10.6                        27           244  "
            ],
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              "      <th></th>\n",
              "      <th>MODELYEAR</th>\n",
              "      <th>MAKE</th>\n",
              "      <th>MODEL</th>\n",
              "      <th>VEHICLECLASS</th>\n",
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              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX HYBRID</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.5</td>\n",
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              "      <th>3</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>MDX 4WD</td>\n",
              "      <td>SUV - SMALL</td>\n",
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              "      <td>6</td>\n",
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              "      <td>8.7</td>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Lets say we want to use linear regression to predict Co2Emission of cars based on their engine size. So, lets define X and Y value for the linear regression, that is, train_x and train_y:"
      ],
      "metadata": {
        "id": "mTyki6-bX6b2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "train_x = np.asanyarray(df[['ENGINESIZE']])\n",
        "train_y = np.asanyarray(df[['CO2EMISSIONS']])"
      ],
      "metadata": {
        "id": "9CgP95rbWJ5_"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "First, we initialize the variables a and b, with any random guess, and then we define the linear function:"
      ],
      "metadata": {
        "id": "-QhMBBr_YMXN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = tf.Variable(20.0)\n",
        "b = tf.Variable(30.2)\n",
        "\n",
        "\n",
        "def h(x):\n",
        "   y = a*x + b\n",
        "   return y"
      ],
      "metadata": {
        "id": "RyKJRPEbX8Vw"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "In a linear regression, we minimize the squared error of the difference between the predicted values(obtained from the equation) and the target values (the data that we have). In other words we want to minimize the square of the predicted values minus the target value. So we define the equation to be minimized as loss."
      ],
      "metadata": {
        "id": "FsgDiQlJYdyM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To find value of our loss, we use tf.reduce_mean(). This function finds the mean of a multidimensional tensor, and the result can have a different dimension.\n",
        "To find value of our loss, we use tf.reduce_mean(). This function finds the mean of a multidimensional tensor, and the result can have a different dimension."
      ],
      "metadata": {
        "id": "e12V2amEZAOY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def loss_object(y,train_y) :\n",
        "    return tf.reduce_mean(tf.square(y - train_y))\n",
        "    # Below is a predefined method offered by TensorFlow to calculate loss function\n",
        "    #loss_object = tf.keras.losses.MeanSquaredLogarithmicError()"
      ],
      "metadata": {
        "id": "WsDSUdgzX-C4"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        " We use GradientTape to calculate gradients:"
      ],
      "metadata": {
        "id": "pKVMBw8iZnqe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "learning_rate = 0.01\n",
        "train_data = []\n",
        "loss_values =[]\n",
        "a_values = []\n",
        "b_values = []\n",
        "# steps of looping through all your data to update the parameters\n",
        "training_epochs = 200\n",
        "\n",
        "# train model\n",
        "for epoch in range(training_epochs):\n",
        "    with tf.GradientTape() as tape:\n",
        "        y_predicted = h(train_x)\n",
        "        loss_value = loss_object(train_y,y_predicted)\n",
        "        loss_values.append(loss_value)\n",
        "\n",
        "        # get gradients\n",
        "        gradients = tape.gradient(loss_value, [b,a])\n",
        "        \n",
        "        # compute and adjust weights\n",
        "        a_values.append(a.numpy())\n",
        "        b_values.append(b.numpy())\n",
        "        b.assign_sub(gradients[0]*learning_rate)\n",
        "        a.assign_sub(gradients[1]*learning_rate)\n",
        "        if epoch % 5 == 0:\n",
        "            train_data.append([a.numpy(), b.numpy()])"
      ],
      "metadata": {
        "id": "JaW7rqJ1ZXDb"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.xlabel(\"Epoch\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.plot(loss_values, 'ro')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 405
        },
        "id": "7VuSvMhRbZ5-",
        "outputId": "17a1236e-636b-4065-f851-a8e2c0386557"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb811aeed60>]"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(train_x, train_y, color='green')\n",
        "for a,b in zip(a_values[0:len(a_values)], b_values[0:len(b_values)]):\n",
        "    plt.plot(train_x,a*train_x+b, color='red', linestyle='dashed')\n",
        "plt.plot(train_x,a_values[-1]*train_x+b_values[-1], color='black')\n",
        "\n",
        "final = mpatches.Patch(color='Black', label='Final')\n",
        "estimates = mpatches.Patch(color='Red', label='Estimates')\n",
        "data = mpatches.Patch(color='Green', label='Data Points')\n",
        "\n",
        "plt.legend(handles=[data, estimates, final])\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "id": "S_vCemNlbZ8x",
        "outputId": "40520739-77f1-4126-ff68-c628e27b60d6"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}