lab15_Williams.ipynb

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    "colab": {
      "name": "lab15_Williams.ipynb",
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    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Lab 15: Tensor Flow \n",
        "\n",
        "Kobie Williams \n",
        "\n",
        "4/12/2022 \n",
        "\n",
        "The purpose of this file is to make a simple artificial neural network using Keras and Tensorflow "
      ],
      "metadata": {
        "id": "vQL0oq0n_-IL"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "id": "WwgUwGYG_h4u"
      },
      "outputs": [],
      "source": [
        "import numpy as np \n",
        "import matplotlib.pyplot as plt \n",
        "import tensorflow as tf"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Load the MNIST dataset \n",
        "mnist = tf.keras.datasets.mnist \n",
        "\n",
        "# Separate into train and test data and labels \n",
        "(x_train, y_train), (x_test, y_test) = mnist.load_data() \n",
        "\n",
        "#Preprocess for more stable training of the neural network \n",
        "# by normalizing the data values to be between 0 and 1 \n",
        "x_train = x_train / 255.0 \n",
        "x_test = x_test / 255.0 "
      ],
      "metadata": {
        "id": "icLdxVimAgw4"
      },
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_train.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dwBSlHmCC7AD",
        "outputId": "e2e26176-ec51-443d-f5dc-b5f96aeb9843"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_train.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FKkXw-ACC-cF",
        "outputId": "429624e7-969c-4860-dc6d-39d52ff5a274"
      },
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000,)"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_test.shape"
      ],
      "metadata": {
        "id": "5bPS8egAC_0M",
        "outputId": "7e09cc15-541d-4c00-de7c-50e65cfb193e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_test.shape"
      ],
      "metadata": {
        "id": "POUiun-oDCqj",
        "outputId": "8fe0ce11-d35d-49a8-d3f4-ef04eb2ed560",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000,)"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_idx = 2 \n",
        "plt.imshow(x_train[train_idx], cmap='gray') \n",
        "plt.title('Label: {}'.format(y_train[train_idx])) \n",
        "plt.show() \n"
      ],
      "metadata": {
        "id": "_utdaogoDE2S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "dac5ba3f-273f-42a5-da68-985f974a1e91"
      },
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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ZXwN8OSLeGt9W57aboK6ebLc6wr4TmDfu+dxiXl+IiJ3Fz73AWhqHHf1kz4ERdIufe2uu50MRsSci3o+ID4BvUeO2K4YZXwPcFxEPFLNr33YT1dWr7VZH2EeABZLmSzoc+DzwcA11fIykI4sTJ0g6EriI/huK+mFgZTG9Enioxlo+ol+G8W42zDg1b7vahz+PiJ4/gGU0zsj/N/CXddTQpK7fAH5aPDbVXRtwP43dul/QOLdxJXAssB7YCvwQmNNHtd1DY2jv52gEa7Cm2s6jsYv+HPBs8VhW97Yrqasn2823y5ol4RN0Zkk47GZJOOxmSTjsZkk47GZJOOxmSTjsZkn8P02Jjs5fwpdQAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model = tf.keras.models.Sequential([\n",
        "  tf.keras.layers.Flatten(input_shape=(28,28)), \n",
        "  tf.keras.layers.Dense(40,activation='relu'),\n",
        "  tf.keras.layers.Dense(16), \n",
        "  tf.keras.layers.Dropout(0.2), \n",
        "  tf.keras.layers.Dense(10) \n",
        "])"
      ],
      "metadata": {
        "id": "OAKlJs0GGK5m"
      },
      "execution_count": 76,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "predictions = model(x_train[:1]).numpy() \n",
        "predictions"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oB3UsKsjH-cy",
        "outputId": "4b8c4e47-b7c4-4efd-eb9a-cdc710db4bfc"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.225468  ,  0.25006944, -0.343845  , -0.02234282,  0.4332015 ,\n",
              "        -0.55791193,  0.33313355, -0.08753837, -0.10407096,  0.10575063]],\n",
              "      dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tf.nn.softmax(predictions).numpy() "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hZv79dmDIEDf",
        "outputId": "b08b55b7-a677-4d1a-ce4f-8f611c0f1716"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.07818785, 0.12579475, 0.06945904, 0.09579777, 0.1510761 ,\n",
              "        0.05607389, 0.13669002, 0.08975142, 0.08827978, 0.10888942]],\n",
              "      dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True) \n"
      ],
      "metadata": {
        "id": "RjUyFyE8IPnF"
      },
      "execution_count": 79,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model.compile(optimizer='adam',\n",
        "              loss=loss_fn, \n",
        "              metrics=['accuracy']) \n"
      ],
      "metadata": {
        "id": "jr0uRVmfIXWD"
      },
      "execution_count": 80,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model.fit(x_train, y_train, epochs=4) \n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xMT5CCTZIfa-",
        "outputId": "025a6b8e-4c26-416e-b775-12a1fb17ee44"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/4\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.4013 - accuracy: 0.8824\n",
            "Epoch 2/4\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.2068 - accuracy: 0.9403\n",
            "Epoch 3/4\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.1607 - accuracy: 0.9526\n",
            "Epoch 4/4\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1349 - accuracy: 0.9594\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f01326dfc50>"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model.evaluate(x_train,y_train,verbose=2) "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GT4nvR6y3uR7",
        "outputId": "6d34d41f-a7b2-4b95-e66c-5d26d28ff2cf"
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1875/1875 - 3s - loss: 0.0807 - accuracy: 0.9754 - 3s/epoch - 2ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.08074792474508286, 0.9753833413124084]"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model.evaluate(x_test, y_test, verbose=2) "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tT2MQB1LN8GH",
        "outputId": "2964d7f2-59ab-45b0-8ced-a164147f86c2"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 - 1s - loss: 0.1076 - accuracy: 0.9678 - 966ms/epoch - 3ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.10758572816848755, 0.9678000211715698]"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "probability_model = tf.keras.Sequential([\n",
        "  model, tf.keras.layers.Softmax() \n",
        "])"
      ],
      "metadata": {
        "id": "8xJNpvI_OB-A"
      },
      "execution_count": 84,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "test_idx = 200 \n",
        "plt.imshow(x_test[test_idx], cmap=plt.cm.gray) \n",
        "plt.title('Correct label: {}'.format(y_test[test_idx])) \n",
        "plt.show() \n",
        "print('Predicted probabilities:') \n",
        "probability_model(x_test[test_idx:test_idx+1]) \n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "id": "fyQEElbQOPwE",
        "outputId": "e19f8c5d-fa48-46ec-e741-fbb8ae14421c"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Predicted probabilities:\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(1, 10), dtype=float32, numpy=\n",
              "array([[3.6754397e-08, 2.0402865e-07, 2.4569363e-04, 9.9973971e-01,\n",
              "        1.7989955e-10, 1.0481653e-05, 4.8807380e-10, 3.3469456e-07,\n",
              "        3.2442665e-06, 1.6802478e-07]], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1) The test set had an accuracy of about 94.5% while the training set had an accuracy of about 94.9%. \n",
        "\n",
        "2a) Done \n",
        "\n",
        "2b) Done \n",
        "\n",
        "2c) Done \n",
        "\n",
        "2d) The accuracy that I ended up getting was 97.5% for the training data and 96.8% for the test data. \n",
        "\n",
        "3) Our model is not overfitting because the training data and test data accuracy has continouosly improved and the training data accuracy is still greater than the test data. Once we see a decrease, then we can know that there is overfitting. "
      ],
      "metadata": {
        "id": "dXdTlH1tOsS-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "_2J7ykdOOlbp"
      },
      "execution_count": 85,
      "outputs": []
    }
  ]
}