01_liner_tf.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UPgo18-N1gSi"
      },
      "source": [
        "# 01. Neural Network Regression with TensorFlow\n",
        "\n",
        "There are many definitions for a [regression problem](https://en.wikipedia.org/wiki/Regression_analysis) but in our case, we're going to simplify it to be: predicting a number.\n",
        "\n",
        "For example, you might want to:\n",
        "- Predict the selling price of houses given information about them (such as number of rooms, size, number of bathrooms).\n",
        "- Predict the coordinates of a bounding box of an item in an image.\n",
        "- Predict the cost of medical insurance for an individual given their demographics (age, sex, gender, race).\n",
        "\n",
        "In this notebook, we're going to set the foundations for how you can take a sample of inputs (this is your data), build a neural network to discover patterns in those inputs and then make a prediction (in the form of a number) based on those inputs.\n",
        "\n",
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FMqsqKpk7TrH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "741c3cd9-99f5-4f58-b29b-2340679fc987"
      },
      "source": [
        "import tensorflow as tf\n",
        "print(tf.__version__) # check the version (should be 2.x+)\n",
        "\n"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.15.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8clMYxrF6Mzv"
      },
      "source": [
        "## Creating data to view and fit\n",
        "\n",
        "Since we're working on a **regression problem** (predicting a number) let's create some linear data (a straight line) to model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G43tWFof6i7T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "outputId": "10bf79cf-bd52-4963-dc94-8900d1897b3d"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Create features\n",
        "X = np.array([-7.0, -4.0, -1.0, 2.0, 5.0, 8.0, 11.0, 14.0])\n",
        "\n",
        "# Create labels\n",
        "y = np.array([3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0])\n",
        "\n",
        "# Visualize it\n",
        "plt.scatter(X, y);"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ONZF8un7_xy"
      },
      "source": [
        "Before we do any modelling, can you calculate the pattern between `X` and `y`?\n",
        "\n",
        "For example, say I asked you, based on this data what the `y` value would be if `X` was 17.0?\n",
        "\n",
        "Or how about if `X` was -10.0?\n",
        "\n",
        "This kind of pattern discovery is the essence of what we'll be building neural networks to do for us."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zaPxco6E9i1_"
      },
      "source": [
        "Our goal here will be to use `X` to predict `y`.\n",
        "\n",
        "So our **input** will be `X` and our **output** will be `y`.\n",
        "\n",
        "Knowing this, what do you think our input and output shapes will be?\n",
        "\n",
        "Let's take a look."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j1oT1gmB9iX-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0f551008-ac72-48bb-c9f7-0a6d79264300"
      },
      "source": [
        "# Take a single example of X\n",
        "input_shape = X[0].shape\n",
        "\n",
        "# Take a single example of y\n",
        "output_shape = y[0].shape\n",
        "\n",
        "input_shape, output_shape # these are both scalars (no shape)"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((), ())"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m4txxFTL_EEX"
      },
      "source": [
        "Huh?\n",
        "\n",
        "From this it seems our inputs and outputs have no shape?\n",
        "\n",
        "How could that be?\n",
        "\n",
        "It's because no matter what kind of data we pass to our model, it's always going to take as input and return as output some kind of tensor.\n",
        "\n",
        "But in our case because of our dataset (only 2 small lists of numbers), we're looking at a special kind of tensor, more specifically a rank 0 tensor or a scalar."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dag5y4MPaTmc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aab0c543-75e3-407c-be15-e3e3efc71a1c"
      },
      "source": [
        "# Let's take a look at the single examples invidually\n",
        "X[0], y[0]"
      ],
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-7.0, 3.0)"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PhAIqjrn6olF"
      },
      "source": [
        "## Steps in modelling with TensorFlow\n",
        "\n",
        "Now we know what data we have as well as the input and output shapes, let's see how we'd build a neural network to model it.\n",
        "\n",
        "In TensorFlow, there are typically 3 fundamental steps to creating and training a model.\n",
        "\n",
        "1. **Creating a model** - piece together the layers of a neural network yourself (using the [Functional](https://www.tensorflow.org/guide/keras/functional) or [Sequential API](https://www.tensorflow.org/api_docs/python/tf/keras/Sequential)) or import a previously built model (known as transfer learning).\n",
        "2. **Compiling a model** - defining how a models performance should be measured (loss/metrics) as well as defining how it should improve (optimizer).\n",
        "3. **Fitting a model** - letting the model try to find patterns in the data (how does `X` get to `y`).\n",
        "\n",
        "Let's see these in action using the [Keras Sequential API](https://www.tensorflow.org/api_docs/python/tf/keras/Sequential) to build a model for our regression data. And then we'll step through each.\n",
        "\n",
        "> **Note:** If you're using [TensorFlow 2.7.0](https://github.com/tensorflow/tensorflow/releases/tag/v2.7.0)+, the `fit()` function no longer upscales input data to go from `(batch_size, )` to `(batch_size, 1)`. To fix this, you'll need to expand the dimension of input data using `tf.expand_dims(input_data, axis=-1)`.\n",
        ">\n",
        "> In our case, this means instead of using `model.fit(X, y, epochs=5)`, use `model.fit(tf.expand_dims(X, axis=-1), y, epochs=5)`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P9jj-OE16yCn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d1e189c6-924f-4722-89c9-0f70f82df79c"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model using the Sequential API\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model.compile(loss=tf.keras.losses.mae, # mae is short for mean absolute error\n",
        "              optimizer=tf.keras.optimizers.SGD(), # SGD is short for stochastic gradient descent\n",
        "              metrics=[\"mae\"])\n",
        "\n",
        "# Fit the model\n",
        "# model.fit(X, y, epochs=5) # this will break with TensorFlow 2.7.0+\n",
        "model.fit(tf.expand_dims(X, axis=-1), y, epochs=5)"
      ],
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/5\n",
            "1/1 [==============================] - 0s 346ms/step - loss: 20.1022 - mae: 20.1022\n",
            "Epoch 2/5\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 19.8209 - mae: 19.8209\n",
            "Epoch 3/5\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 19.5397 - mae: 19.5397\n",
            "Epoch 4/5\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 19.2584 - mae: 19.2584\n",
            "Epoch 5/5\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 18.9772 - mae: 18.9772\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.History at 0x7b381a747400>"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bbjCwkEtetB9"
      },
      "source": [
        "Boom!\n",
        "\n",
        "We've just trained a model to figure out the patterns between `X` and `y`.\n",
        "\n",
        "How do you think it went?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VWLpG2U3erWo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5aa21528-f04e-43e1-a3ac-03ceabced6b2"
      },
      "source": [
        "# Check out X and y\n",
        "X, y"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([-7., -4., -1.,  2.,  5.,  8., 11., 14.]),\n",
              " array([ 3.,  6.,  9., 12., 15., 18., 21., 24.]))"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ZpkaI_Oe6no"
      },
      "source": [
        "What do you think the outcome should be if we passed our model an `X` value of 17.0?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X86cD66Qeo-8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8e4dafb7-3766-44fb-ed55-61879caf72fe"
      },
      "source": [
        "# Make a prediction with the model\n",
        "model.predict([17.0])"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 54ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-19.307014]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2YoKIqhffq33"
      },
      "source": [
        "It doesn't go very well... it should've output something close to 27.0.\n",
        "\n",
        "> 🤔 **Question:** What's Keras? I thought we were working with TensorFlow but every time we write TensorFlow code, `keras` comes after `tf` (e.g. `tf.keras.layers.Dense()`)?\n",
        "\n",
        "Before TensorFlow 2.0+, [Keras](https://keras.io/) was an API designed to be able to build deep learning models with ease. Since TensorFlow 2.0+, its functionality has been tightly integrated within the TensorFlow library."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qAPk1T3xgOm4"
      },
      "source": [
        "## Improving a model\n",
        "\n",
        "How do you think you'd improve upon our current model?\n",
        "\n",
        "If you guessed by tweaking some of the things we did above, you'd be correct.\n",
        "\n",
        "To improve our model, we alter almost every part of the 3 steps we went through before.\n",
        "\n",
        "1. **Creating a model** - here you might want to add more layers, increase the number of hidden units (also called neurons) within each layer, change the activation functions of each layer.\n",
        "2. **Compiling a model** - you might want to choose optimization function or perhaps change the **learning rate** of the optimization function.\n",
        "3. **Fitting a model** - perhaps you could fit a model for more **epochs** (leave it training for longer) or on more data (give the model more examples to learn from).\n",
        "\n",
        "![various options you can use to improve a neural network model](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-improving-a-model-from-model-perspective.png)\n",
        "*There are many different ways to potentially improve a neural network. Some of the most common include: increasing the number of layers (making the network deeper), increasing the number of hidden units (making the network wider) and changing the learning rate. Because these values are all human-changeable, they're referred to as [hyperparameters](https://en.wikipedia.org/wiki/Hyperparameter_(machine_learning)) and the practice of trying to find the best hyperparameters is referred to as [hyperparameter tuning](https://en.wikipedia.org/wiki/Hyperparameter_optimization).*\n",
        "\n",
        "Woah. We just introduced a bunch of possible steps. The important thing to remember is how you alter each of these will depend on the problem you're working on.\n",
        "\n",
        "And the good thing is, over the next few problems, we'll get hands-on with all of them.\n",
        "\n",
        "For now, let's keep it simple, all we'll do is train our model for longer (everything else will stay the same)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MI0LammMgWcN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a2d1bffa-0a9f-40cb-b33f-922cced6f4a7"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model (same as above)\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "# Compile model (same as above)\n",
        "model.compile(loss=tf.keras.losses.mae,\n",
        "              optimizer=tf.keras.optimizers.SGD(),\n",
        "              metrics=[\"mae\"])\n",
        "\n",
        "# Fit model (this time we'll train for longer)\n",
        "model.fit(tf.expand_dims(X, axis=-1), y, epochs=100) # train for 100 epochs not 10"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "1/1 [==============================] - 0s 331ms/step - loss: 8.8981 - mae: 8.8981\n",
            "Epoch 2/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 8.7656 - mae: 8.7656\n",
            "Epoch 3/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 8.6331 - mae: 8.6331\n",
            "Epoch 4/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 8.5006 - mae: 8.5006\n",
            "Epoch 5/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 8.3681 - mae: 8.3681\n",
            "Epoch 6/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 8.2356 - mae: 8.2356\n",
            "Epoch 7/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 8.1031 - mae: 8.1031\n",
            "Epoch 8/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.9706 - mae: 7.9706\n",
            "Epoch 9/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.8381 - mae: 7.8381\n",
            "Epoch 10/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.7056 - mae: 7.7056\n",
            "Epoch 11/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.5731 - mae: 7.5731\n",
            "Epoch 12/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.4406 - mae: 7.4406\n",
            "Epoch 13/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.4100 - mae: 7.4100\n",
            "Epoch 14/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.4044 - mae: 7.4044\n",
            "Epoch 15/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 7.3987 - mae: 7.3987\n",
            "Epoch 16/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.3931 - mae: 7.3931\n",
            "Epoch 17/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3875 - mae: 7.3875\n",
            "Epoch 18/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3819 - mae: 7.3819\n",
            "Epoch 19/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3763 - mae: 7.3763\n",
            "Epoch 20/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 7.3706 - mae: 7.3706\n",
            "Epoch 21/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3650 - mae: 7.3650\n",
            "Epoch 22/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.3594 - mae: 7.3594\n",
            "Epoch 23/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3538 - mae: 7.3538\n",
            "Epoch 24/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3481 - mae: 7.3481\n",
            "Epoch 25/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.3425 - mae: 7.3425\n",
            "Epoch 26/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3369 - mae: 7.3369\n",
            "Epoch 27/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 7.3313 - mae: 7.3313\n",
            "Epoch 28/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3256 - mae: 7.3256\n",
            "Epoch 29/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.3200 - mae: 7.3200\n",
            "Epoch 30/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3144 - mae: 7.3144\n",
            "Epoch 31/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 7.3087 - mae: 7.3087\n",
            "Epoch 32/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.3031 - mae: 7.3031\n",
            "Epoch 33/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2975 - mae: 7.2975\n",
            "Epoch 34/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 7.2919 - mae: 7.2919\n",
            "Epoch 35/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.2863 - mae: 7.2863\n",
            "Epoch 36/100\n",
            "1/1 [==============================] - 0s 13ms/step - loss: 7.2806 - mae: 7.2806\n",
            "Epoch 37/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.2750 - mae: 7.2750\n",
            "Epoch 38/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 7.2694 - mae: 7.2694\n",
            "Epoch 39/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2638 - mae: 7.2638\n",
            "Epoch 40/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2581 - mae: 7.2581\n",
            "Epoch 41/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.2525 - mae: 7.2525\n",
            "Epoch 42/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.2469 - mae: 7.2469\n",
            "Epoch 43/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.2413 - mae: 7.2413\n",
            "Epoch 44/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.2356 - mae: 7.2356\n",
            "Epoch 45/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.2300 - mae: 7.2300\n",
            "Epoch 46/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2244 - mae: 7.2244\n",
            "Epoch 47/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2188 - mae: 7.2188\n",
            "Epoch 48/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2131 - mae: 7.2131\n",
            "Epoch 49/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2075 - mae: 7.2075\n",
            "Epoch 50/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.2019 - mae: 7.2019\n",
            "Epoch 51/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1962 - mae: 7.1962\n",
            "Epoch 52/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1906 - mae: 7.1906\n",
            "Epoch 53/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1850 - mae: 7.1850\n",
            "Epoch 54/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1794 - mae: 7.1794\n",
            "Epoch 55/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1738 - mae: 7.1738\n",
            "Epoch 56/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1681 - mae: 7.1681\n",
            "Epoch 57/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1625 - mae: 7.1625\n",
            "Epoch 58/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1569 - mae: 7.1569\n",
            "Epoch 59/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1513 - mae: 7.1513\n",
            "Epoch 60/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.1456 - mae: 7.1456\n",
            "Epoch 61/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1400 - mae: 7.1400\n",
            "Epoch 62/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1344 - mae: 7.1344\n",
            "Epoch 63/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 7.1287 - mae: 7.1287\n",
            "Epoch 64/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1231 - mae: 7.1231\n",
            "Epoch 65/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1175 - mae: 7.1175\n",
            "Epoch 66/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.1119 - mae: 7.1119\n",
            "Epoch 67/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1063 - mae: 7.1063\n",
            "Epoch 68/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.1006 - mae: 7.1006\n",
            "Epoch 69/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0950 - mae: 7.0950\n",
            "Epoch 70/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 7.0894 - mae: 7.0894\n",
            "Epoch 71/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.0838 - mae: 7.0838\n",
            "Epoch 72/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0781 - mae: 7.0781\n",
            "Epoch 73/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.0725 - mae: 7.0725\n",
            "Epoch 74/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0669 - mae: 7.0669\n",
            "Epoch 75/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0612 - mae: 7.0612\n",
            "Epoch 76/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.0556 - mae: 7.0556\n",
            "Epoch 77/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0500 - mae: 7.0500\n",
            "Epoch 78/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.0444 - mae: 7.0444\n",
            "Epoch 79/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0387 - mae: 7.0387\n",
            "Epoch 80/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 7.0331 - mae: 7.0331\n",
            "Epoch 81/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 7.0275 - mae: 7.0275\n",
            "Epoch 82/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 7.0219 - mae: 7.0219\n",
            "Epoch 83/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 7.0163 - mae: 7.0163\n",
            "Epoch 84/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.0106 - mae: 7.0106\n",
            "Epoch 85/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 7.0050 - mae: 7.0050\n",
            "Epoch 86/100\n",
            "1/1 [==============================] - 0s 8ms/step - loss: 6.9994 - mae: 6.9994\n",
            "Epoch 87/100\n",
            "1/1 [==============================] - 0s 11ms/step - loss: 6.9938 - mae: 6.9938\n",
            "Epoch 88/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9881 - mae: 6.9881\n",
            "Epoch 89/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 6.9825 - mae: 6.9825\n",
            "Epoch 90/100\n",
            "1/1 [==============================] - 0s 12ms/step - loss: 6.9769 - mae: 6.9769\n",
            "Epoch 91/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9713 - mae: 6.9713\n",
            "Epoch 92/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9656 - mae: 6.9656\n",
            "Epoch 93/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9600 - mae: 6.9600\n",
            "Epoch 94/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9544 - mae: 6.9544\n",
            "Epoch 95/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9488 - mae: 6.9488\n",
            "Epoch 96/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 6.9431 - mae: 6.9431\n",
            "Epoch 97/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 6.9375 - mae: 6.9375\n",
            "Epoch 98/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 6.9319 - mae: 6.9319\n",
            "Epoch 99/100\n",
            "1/1 [==============================] - 0s 9ms/step - loss: 6.9263 - mae: 6.9263\n",
            "Epoch 100/100\n",
            "1/1 [==============================] - 0s 10ms/step - loss: 6.9206 - mae: 6.9206\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.History at 0x7b37f06cff40>"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1CIKSm7filgj"
      },
      "source": [
        "You might've noticed the loss value decrease from before (and keep decreasing as the number of epochs gets higher).\n",
        "\n",
        "What do you think this means for when we make a prediction with our model?\n",
        "\n",
        "How about we try predict on 17.0 again?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_YcacZsfi4zZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ad87d6e-be67-46e5-9b14-9689e7974b41"
      },
      "source": [
        "# Remind ourselves of what X and y are\n",
        "X, y"
      ],
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([-7., -4., -1.,  2.,  5.,  8., 11., 14.]),\n",
              " array([ 3.,  6.,  9., 12., 15., 18., 21., 24.]))"
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e6k5V08ZivNO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bd2b453b-e3a2-4c0a-ebed-cd89fd3bdd4b"
      },
      "source": [
        "# Try and predict what y would be if X was 17.0\n",
        "model.predict([17.0]) # the right answer is 27.0 (y = X + 10)"
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 51ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[30.272028]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sYi5V8ZYi_dy"
      },
      "source": [
        "Much better!\n",
        "\n",
        "We got closer this time. But we could still be better.\n",
        "\n",
        "Now we've trained a model, how could we evaluate it?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HvC98q_h6zvG"
      },
      "source": [
        "## Evaluating a model\n",
        "\n",
        "A typical workflow you'll go through when building neural networks is:\n",
        "\n",
        "```\n",
        "Build a model -> evaluate it -> build (tweak) a model -> evaulate it -> build (tweak) a model -> evaluate it...\n",
        "```\n",
        "\n",
        "The tweaking comes from maybe not building a model from scratch but adjusting an existing one.\n",
        "\n",
        "### Visualize, visualize, visualize\n",
        "\n",
        "When it comes to evaluation, you'll want to remember the words: \"visualize, visualize, visualize.\"\n",
        "\n",
        "This is because you're probably better looking at something (doing) than you are thinking about something.\n",
        "\n",
        "It's a good idea to visualize:\n",
        "* **The data** - what data are you working with? What does it look like?\n",
        "* **The model itself** - what does the architecture look like? What are the different shapes?\n",
        "* **The training of a model** - how does a model perform while it learns?\n",
        "* **The predictions of a model** - how do the predictions of a model line up against the ground truth (the original labels)?\n",
        "\n",
        "Let's start by visualizing the model.\n",
        "\n",
        "But first, we'll create a little bit of a bigger dataset and a new model we can use (it'll be the same as before, but the more practice the better).\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "srxuqbeYopns",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9158f17d-507d-44e7-cafc-6d4471e146a6"
      },
      "source": [
        "# Make a bigger dataset\n",
        "X = np.arange(-100, 100, 4)\n",
        "X"
      ],
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-100,  -96,  -92,  -88,  -84,  -80,  -76,  -72,  -68,  -64,  -60,\n",
              "        -56,  -52,  -48,  -44,  -40,  -36,  -32,  -28,  -24,  -20,  -16,\n",
              "        -12,   -8,   -4,    0,    4,    8,   12,   16,   20,   24,   28,\n",
              "         32,   36,   40,   44,   48,   52,   56,   60,   64,   68,   72,\n",
              "         76,   80,   84,   88,   92,   96])"
            ]
          },
          "metadata": {},
          "execution_count": 101
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pQcC0nSko3kJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d8f8fcd3-4efb-443f-fe08-3a16655ef6ec"
      },
      "source": [
        "# Make labels for the dataset (adhering to the same pattern as before)\n",
        "y = np.arange(-90, 110, 4)\n",
        "y"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-90, -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42,\n",
              "       -38, -34, -30, -26, -22, -18, -14, -10,  -6,  -2,   2,   6,  10,\n",
              "        14,  18,  22,  26,  30,  34,  38,  42,  46,  50,  54,  58,  62,\n",
              "        66,  70,  74,  78,  82,  86,  90,  94,  98, 102, 106])"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KNIw5tgGpKjb"
      },
      "source": [
        "Since $y=X+10$, we could make the labels like so:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ACgbmrAOpJwW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "36fa37be-37c6-4a4e-a1f4-2d96310e22e4"
      },
      "source": [
        "# Same result as above\n",
        "y = X + 10\n",
        "y"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-90, -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42,\n",
              "       -38, -34, -30, -26, -22, -18, -14, -10,  -6,  -2,   2,   6,  10,\n",
              "        14,  18,  22,  26,  30,  34,  38,  42,  46,  50,  54,  58,  62,\n",
              "        66,  70,  74,  78,  82,  86,  90,  94,  98, 102, 106])"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ax3MnQDupeBp"
      },
      "source": [
        "## Split data into training/test set\n",
        "\n",
        "One of the other most common and important steps in a machine learning project is creating a training and test set (and when required, a validation set).\n",
        "\n",
        "Each set serves a specific purpose:\n",
        "* **Training set** - the model learns from this data, which is typically 70-80% of the total data available (like the course materials you study during the semester).\n",
        "* **Validation set** - the model gets tuned on this data, which is typically 10-15% of the total data available (like the practice exam you take before the final exam).\n",
        "* **Test set** - the model gets evaluated on this data to test what it has learned, it's typically 10-15% of the total data available (like the final exam you take at the end of the semester).\n",
        "\n",
        "For now, we'll just use a training and test set, this means we'll have a dataset for our model to learn on as well as be evaluated on.\n",
        "\n",
        "We can create them by splitting our `X` and `y` arrays.\n",
        "\n",
        "> 🔑 **Note:** When dealing with real-world data, this step is typically done right at the start of a project (the test set should always be kept separate from all other data). We want our model to learn on training data and then evaluate it on test data to get an indication of how well it **generalizes** to unseen examples."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5G0RDMnZrgvK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "377c5f4a-1743-4e4b-8741-db54f9d2ab26"
      },
      "source": [
        "# Check how many samples we have\n",
        "len(X)"
      ],
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "50"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4Q9ptcQkrGfO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2ad91d55-1726-4ef6-b3d0-71f58df06aa2"
      },
      "source": [
        "# Split data into train and test sets\n",
        "X_train = X[:40] # first 40 examples (80% of data)\n",
        "y_train = y[:40]\n",
        "\n",
        "X_test = X[40:] # last 10 examples (20% of data)\n",
        "y_test = y[40:]\n",
        "\n",
        "len(X_train), len(X_test)"
      ],
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(40, 10)"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rz2cIdECsLH5"
      },
      "source": [
        "## Visualizing the data\n",
        "\n",
        "Now we've got our training and test data, it's a good idea to visualize it.\n",
        "\n",
        "Let's plot it with some nice colours to differentiate what's what."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "os30CXBHsOAH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 599
        },
        "outputId": "6f737a96-5040-4ade-d6a9-5cabb5c56908"
      },
      "source": [
        "plt.figure(figsize=(10, 7))\n",
        "# Plot training data in blue\n",
        "plt.scatter(X_train, y_train, c='b', label='Training data')\n",
        "# Plot test data in green\n",
        "plt.scatter(X_test, y_test, c='g', label='Testing data')\n",
        "# Show the legend\n",
        "plt.legend();"
      ],
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxRcHZFgtS_B"
      },
      "source": [
        "Beautiful! Any time you can visualize your data, your model, your anything, it's a good idea.\n",
        "\n",
        "With this graph in mind, what we'll be trying to do is build a model which learns the pattern in the blue dots (`X_train`) to draw the green dots (`X_test`).\n",
        "\n",
        "Time to build a model. We'll make the exact same one from before (the one we trained for longer)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zMXKFtFBuWgJ"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model (same as above)\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1, input_shape=[1]) # define the input_shape to our model\n",
        "])\n",
        "\n",
        "# Compile model (same as above)\n",
        "model.compile(loss=tf.keras.losses.mae,\n",
        "              optimizer=tf.keras.optimizers.SGD(),\n",
        "              metrics=[\"mae\"])"
      ],
      "execution_count": 131,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Kywg4q9u051",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "02417af7-4cf8-4464-dbbc-57c85bc721c5"
      },
      "source": [
        "# Fit the model to the training data\n",
        "model.fit(X_train, y_train, epochs=100 , verbose=0 ) # verbose controls how much gets output"
      ],
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.History at 0x7b37844f2290>"
            ]
          },
          "metadata": {},
          "execution_count": 132
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RRzj7LJMYftb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "767121e3-5f96-45a3-b069-e02d7391198a"
      },
      "source": [
        "# Make predictions\n",
        "y_preds = model.predict(X_test)"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 42ms/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_hKpW-KOZiAW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "576e3769-b664-4a71-d466-9c972dbf33ac"
      },
      "source": [
        "# View the predictions\n",
        "\n",
        "y_preds"
      ],
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[53.56951 ],\n",
              "       [57.05473 ],\n",
              "       [60.539948],\n",
              "       [64.02517 ],\n",
              "       [67.51038 ],\n",
              "       [70.995605],\n",
              "       [74.48082 ],\n",
              "       [77.96604 ],\n",
              "       [81.451256],\n",
              "       [84.93647 ]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_test"
      ],
      "metadata": {
        "id": "nAi3o6IGeluq",
        "outputId": "3a8bb54d-2a5d-4177-e18b-ac69d5728544",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 70,  74,  78,  82,  86,  90,  94,  98, 102, 106])"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "rM6YY3y0fSzs"
      },
      "execution_count": 111,
      "outputs": []
    }
  ]
}