Hands-On Machine Learning/03_Classification.ipynb

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  "metadata": {
    "colab": {
      "name": "3.Classification.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNlvq9KyBFHQz2VR+/mgFCc"
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      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N-fKXrcdrdVO"
      },
      "source": [
        "# MNIST"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EQoSpb5rrmbT"
      },
      "source": [
        "In this chapter, we will be using the MNIST dataset, which is a set of 70,000 small images of digits handwritten by high school students and employees of the US Census Bureau\n",
        "\n",
        "Each image is labeled with the digit it represents. This set has been stud ied so much that it is often called the “Hello World” of Machine Learning: whenever people come up with a new classification algorithm, they are curious to see how it will perform on MNIST"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p8NVyPxIr94K"
      },
      "source": [
        "Scikit-Learn provides many helper functions to download popular datasets. MNIST is one of them. The following code fetches the MNIST dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UUFjQgdErTcQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "269b56e7-6c70-496d-b433-9df4f242b8dc"
      },
      "source": [
        "from sklearn.datasets import fetch_openml\n",
        "mnist = fetch_openml('mnist_784', version=1, cache=True, as_frame=False)\n",
        "mnist.keys()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'DESCR', 'details', 'categories', 'url'])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aLB5GQyFv2Lo"
      },
      "source": [
        "Datasets loaded by Scikit-Learn generally have a similar dictionary structure including:\n",
        "*   A DESCR key describing the dataset \n",
        "*   A data key containing an array with one row per instance and one column per feature\n",
        "*   A target key containing an array with the labels \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v7wnJ6iJwOc5"
      },
      "source": [
        "Let’s look at these arrays:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SPh-_A9KwOCU",
        "outputId": "4b2d2d82-3751-40bf-d860-16797177d54d"
      },
      "source": [
        "X, y = mnist['data'], mnist['target']\n",
        "X.shape"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(70000, 784)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qKkbtQ9Dwhcy",
        "outputId": "1acc4f65-1383-4ece-cad8-7bc5327a5ccd"
      },
      "source": [
        "y.shape"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(70000,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zI4S-9qMwud3"
      },
      "source": [
        "There are 70,000 images, and each image has 784 features. This is because each image is 28x28 pixels, and each feature simply represents one pixel’s intensity, from 0 (white) to 255 (black)\n",
        "\n",
        "Let’s take a peek at one digit from the dataset. All you need to do is grab an instance’s feature vector, reshape it to a array, and display it using Matplotlib’s imshow() function "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "yI0rleXewlui",
        "outputId": "e9fe572c-9b4e-4ea1-f5e3-af8304cffa6b"
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "some_digit = X[0]\n",
        "some_digit_image = some_digit.reshape(28, 28)\n",
        "\n",
        "plt.imshow(some_digit_image, cmap = matplotlib.cm.binary,\n",
        "           interpolation='nearest')\n",
        "plt.axis('off')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.5, 27.5, 27.5, -0.5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s7W_1mg_yIwT"
      },
      "source": [
        "This looks like a 5, and indeed that’s what the label tells us:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "uYmFOCcdyLDT",
        "outputId": "2ff104a1-17b2-4010-d728-9810bc46b1d4"
      },
      "source": [
        "y[0]"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'5'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "21AyUzKPH7be"
      },
      "source": [
        "There should be more than one value in the resulting array. If not, then perhaps what happened is that you used fetch_openml() to download MNIST, and it returns labels as strings so when you defined y_train_5 = (y_train == 5), it results an array full of False. A solution is to cast y_train to int8: y_train = y_train.astype(np.int8)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A8Qezlu_H3He"
      },
      "source": [
        "import numpy as np\n",
        "y = y.astype(np.uint8)"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZfPyOt7QyR-f"
      },
      "source": [
        "But wait! You should always create a test set and set it aside before inspecting the data closely. The MNIST dataset is actually already split into a training set (the first 60,000 images) and a test set (the last 10,000 images)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d6x3auaGyWVH"
      },
      "source": [
        "X_train, X_test, y_train, y_test = X[:60000], X[60000:], y[:60000], y[60000:]"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iq13P-3cyiUA"
      },
      "source": [
        "Let’s also shuffle the training set; this will guarantee that all cross-validation folds will be similar (you don’t want one fold to be missing some digits). Moreover, some learn ing algorithms are sensitive to the order of the training instances, and they perform poorly if they get many similar instances in a row. Shuffling the dataset ensures that this won’t happen"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iNoobRJeyn1e"
      },
      "source": [
        "shuffle_index = np.random.permutation(60000)\n",
        "X_train, y_train = X_train[shuffle_index], y_train[shuffle_index]"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c4VE5EjZy7w3"
      },
      "source": [
        "# Training a Binary Classifier"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ntDeySxxy-Gk"
      },
      "source": [
        "Let’s simplify the problem for now and only try to identify one digit—for example, the number 5. This “5-detector” will be an example of a binary classifier, capable of distinguishing between just two classes, 5 and not-5. Let’s create the target vectors for this classification task"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-iaxu4dezL6c"
      },
      "source": [
        "y_train_5 = (y_train == 5)\n",
        "y_test_5 = (y_test == 5)"
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KbkzwlZOzFJc"
      },
      "source": [
        "Okay, now let’s pick a classifier and train it. A good place to start is with a Stochastic Gradient Descent (SGD) classifier, using Scikit-Learn's SGDClassifier class. This clas sifier has the advantage of being capable of handling very large datasets efficiently\n",
        "\n",
        "This is in part because SGD deals with training instances independently, one at a time (which also makes SGD well suited for online learning), as we will see later. Let’s create an SGDClassifier and train it on the whole training set \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y-lTBuPo0F97",
        "outputId": "ed31c325-0933-44d7-a82b-364657125992"
      },
      "source": [
        "from sklearn.linear_model import SGDClassifier\n",
        "\n",
        "sgd_clf = SGDClassifier(random_state=42)\n",
        "sgd_clf.fit(X_train, y_train_5)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDClassifier(alpha=0.0001, average=False, class_weight=None,\n",
              "              early_stopping=False, epsilon=0.1, eta0=0.0, fit_intercept=True,\n",
              "              l1_ratio=0.15, learning_rate='optimal', loss='hinge',\n",
              "              max_iter=1000, n_iter_no_change=5, n_jobs=None, penalty='l2',\n",
              "              power_t=0.5, random_state=42, shuffle=True, tol=0.001,\n",
              "              validation_fraction=0.1, verbose=0, warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mlRmT2azXgZl"
      },
      "source": [
        "Now you can use it to detect images of the number 5"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QY6sOxETXiNt",
        "outputId": "94e09b9e-95db-4098-aa1d-57f21ce47085"
      },
      "source": [
        "sgd_clf.predict([some_digit])"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hPyOhx_6X8Aj"
      },
      "source": [
        "# Performance Measures"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5MFFUdVgYApz"
      },
      "source": [
        "Evaluating a classifier is often significantly trickier than evaluating a regressor, so we will spend a large part of this chapter on this topic. There are many performance measures available, so grab another coffee and get ready to learn many new concepts and acronyms!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4vXhITV3YJUL"
      },
      "source": [
        "## Measuring Accuracy Using Cross-Validation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BfabkYvpYS1j"
      },
      "source": [
        "Let’s use the cross_val_score() function to evaluate your SGDClassifier model using K-fold cross-validation, with three folds\n",
        "\n",
        "Remember that K-fold cross validation means splitting the training set into K-folds (in this case, three), then making predictions and evaluating them on each fold using a model trained on the remaining folds"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NnVqMA_AYibq",
        "outputId": "64c19df7-eadb-46e0-ea5a-a1c59a3136d8"
      },
      "source": [
        "from sklearn.model_selection import cross_val_score\n",
        "cross_val_score(sgd_clf, X_train, y_train_5, cv=3, scoring='accuracy')"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.9407 , 0.95045, 0.96015])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mi94bDGwZCnq"
      },
      "source": [
        "Wow! Above 95% accuracy (ratio of correct predictions) on all cross-validation folds? This looks amazing, doesn’t it?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pmGe3jXxZGRR"
      },
      "source": [
        "Well, before you get too excited, let’s look at a very dumb classifier that just classifies every single image in the “not-5” class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mOP0RLSvZI0j"
      },
      "source": [
        "from sklearn.base import BaseEstimator\n",
        "\n",
        "class Never5Classifier(BaseEstimator):\n",
        "  def fit(self, X, y=None):\n",
        "    pass\n",
        "  def predict(self, X):\n",
        "    return np.zeros((len(X), 1), dtype=bool)"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vTHDAmVoZcs_"
      },
      "source": [
        "Can you guess this model’s accuracy? Let’s find out"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fe5xQFUhZcBr",
        "outputId": "93c928a9-ae10-43a7-9b65-158408c3c96b"
      },
      "source": [
        "never_5_clf = Never5Classifier()\n",
        "cross_val_score(never_5_clf, X_train, y_train_5, cv=3, scoring='accuracy')"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.91015, 0.90895, 0.90985])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B7zmEC3KZqeN"
      },
      "source": [
        "That’s right, it has over 90% accuracy! This is simply because only about 10% of the images are 5s, so if you always guess that an image is not a 5, you will be right about 90% of the time. Beats Nostradamus\n",
        "\n",
        "This demonstrates why accuracy is generally not the preferred performance measure for classifiers, especially when you are dealing with skewed datasets (i.e., when some classes are much more frequent than others)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "53Db8-CsZvBS"
      },
      "source": [
        "## Confusion Matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Lzetq80bCsk"
      },
      "source": [
        "A much better way to evaluate the performance of a classifier is to look at the confu sion matrix. The general idea is to count the number of times instances of class A are classified as class B. For example, to know the number of times the classifier confused images of 5s with 3s, you would look in the 5th row and 3rd column of the confusion matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g5nboMZqbfJM"
      },
      "source": [
        "To compute the confusion matrix, you first need to have a set of predictions, so they can be compared to the actual targets. You could make predictions on the test set, but let’s keep it untouched for now (remember that you want to use the test set only at the very end of your project, once you have a classifier that you are ready to launch). Instead, you can use the cross_val_predict() function "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "epjPheHibjz_"
      },
      "source": [
        "from sklearn.model_selection import cross_val_predict\n",
        "\n",
        "y_train_pred = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3)"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1PD93BIkbxW6"
      },
      "source": [
        "Just like the cross_val_score() function, cross_val_predict() performs K-fold cross-validation, but instead of returning the evaluation scores, it returns the predictions made on each test fold. This means that you get a clean prediction for each instance in the training set (“clean” meaning that the prediction is made by a model that never saw the data during training)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ik5H7DR1cGXI"
      },
      "source": [
        "Now you are ready to get the confusion matrix using the confusion_matrix() function. Just pass it the target classes (y_train_5) and the predicted classes (y_train_pred) "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ph9VGpuKcUfC",
        "outputId": "da2a6a3c-71a7-443e-b5a4-14b1f74b7086"
      },
      "source": [
        "from sklearn.metrics import confusion_matrix\n",
        "confusion_matrix(y_train_5, y_train_pred)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[53000,  1579],\n",
              "       [ 1395,  4026]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iijh-0JTcqSg"
      },
      "source": [
        "Each row in a confusion matrix represents an actual class, while each column represents a predicted class\n",
        "\n",
        "The first row of this matrix considers non-5 images (the nega tive class): 53,272 of them were correctly classified as non-5s (they are called true negatives), while the remaining 1,307 were wrongly classified as 5s (false positives)\n",
        "\n",
        "The second row considers the images of 5s (the positive class): 1,077 were wrongly classified as non-5s (false negatives), while the remaining 4,344 were correctly classi fied as 5s (true positives)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "29fZou6E4VyF"
      },
      "source": [
        "A perfect classifier would have only true positives and true negatives, so its confusion matrix would have nonzero values only on its main diagonal (top left to bottom right)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MQ-nXEeP4ZOk",
        "outputId": "fd12306c-5b1b-467c-bf17-3b86c5894e62"
      },
      "source": [
        "y_train_perfect_predictions = y_train_5\n",
        "confusion_matrix(y_train_5, y_train_perfect_predictions)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[54579,     0],\n",
              "       [    0,  5421]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6qn2oP455mhy"
      },
      "source": [
        "## Precision and Recall"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ClKCZrr5qxY"
      },
      "source": [
        "Scikit-Learn provides several functions to compute classifier metrics, including precision and recall"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fPYXlrjz5uj9",
        "outputId": "4ec91183-f9b9-463d-c9f4-a5bc84ec0ee3"
      },
      "source": [
        "from sklearn.metrics import precision_score, recall_score\n",
        "precision_score(y_train_5, y_train_pred)\n"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7182872435325602"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zHqlKxzb6Ip0",
        "outputId": "ff293264-63ea-42b0-9aad-056859e5ccdc"
      },
      "source": [
        "recall_score(y_train_5, y_train_pred)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7426674045379081"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S1q2wcPW6agr"
      },
      "source": [
        "Now your 5-detector does not look as shiny as it did when you looked at its accuracy. When it claims an image represents a 5, it is correct only 72% of the time. Moreover, it only detects 70% of the 5s"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j-TiENsk6yri"
      },
      "source": [
        "To compute the F1 score, simply call the f1_score() function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "shAW2LS36yUH",
        "outputId": "8d10f788-546f-4a13-fab9-e815e630f406"
      },
      "source": [
        "from sklearn.metrics import f1_score\n",
        "f1_score(y_train_5, y_train_pred)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7302738980591329"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1SS8SjLZDEyL"
      },
      "source": [
        "## Precision/Recall Tradeof"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D7OQqWvkDGbQ"
      },
      "source": [
        "To understand this tradeoff, let’s look at how the SGDClassifier makes its classifiction decisions\n",
        "\n",
        "For each instance, it computes a score based on a decision function, and if that score is greater than a threshold, it assigns the instance to the positive class, or else it assigns it to the negative class"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q_PK5cbUDRsj"
      },
      "source": [
        "Scikit-Learn does not let you set the threshold directly, but it does give you access to the decision scores that it uses to make predictions. Instead of calling the classifier’ method, you can call its method, which returns a predict() decision_function() score for each instance, and then make predictions based on those scores using any threshold you want"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ER6JCgrxDYkm",
        "outputId": "7e828d70-0dea-42ca-d416-f0f1709f014a"
      },
      "source": [
        "y_scores = sgd_clf.decision_function([some_digit])\n",
        "y_scores"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([636.11998385])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M4Lkm8d3DkBF",
        "outputId": "5d138ba7-32d9-4e50-f2af-71bbbf033c09"
      },
      "source": [
        "thershold = 0\n",
        "y_some_digit_pred = (y_scores > thershold)\n",
        "y_some_digit_pred"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2GOJFwgQDwJG"
      },
      "source": [
        "The SGDClassifier uses a threshold equal to 0, so the previous code returns the same result as the predict() method (i.e., True). Let’s raise the threshold "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ShsuoSIzDmbs",
        "outputId": "87ec1012-c3b8-4658-adb6-e2f7ad3b8edc"
      },
      "source": [
        "thershold = 200000\n",
        "y_some_digit_pred = (y_scores > thershold)\n",
        "y_some_digit_pred"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vptoSn5vD_Yn"
      },
      "source": [
        "This confirms that raising the threshold decreases recall. The image actually repre sents a 5, and the classifier detects it when the threshold is 0, but it misses it when the threshold is increased to 200,000"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KOV91NBgEFJU"
      },
      "source": [
        "So how can you decide which threshold to use? For this you will first need to get the scores of all instances in the training set using the cross_val_predict() function again, but this time specifying that you want it to return decision scores instead of predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5bFnlx3KELy-"
      },
      "source": [
        "y_scores = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3,\n",
        "                             method='decision_function')"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mT6cd7NIGAKf"
      },
      "source": [
        "# hack to work around issue #9589 in Scikit-Learn 0.19.0\n",
        "if y_scores.ndim == 2:\n",
        "    y_scores = y_scores[:, 1]"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7rEWBM-TES8U"
      },
      "source": [
        "Now with these scores you can compute precision and recall for all possible thresh olds using the precision_recall_curve() function "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r2z42xL7EXlu"
      },
      "source": [
        "from sklearn.metrics import precision_recall_curve\n",
        "\n",
        "precisions, recalls, thersholds = precision_recall_curve(y_train_5, y_scores)"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q_xXojopEf3i"
      },
      "source": [
        "Finally, you can plot precision and recall as functions of the threshold value using\n",
        "Matplotlib"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SW7XRCRuEh-y"
      },
      "source": [
        "def plot_precision_recall_vs_thershold(precisions, recalls, thersholds):\n",
        "  plt.plot(thersholds, precisions[:-1], 'b--', label='Precision')\n",
        "  plt.plot(thersholds, recalls[:-1], 'g-', label='Recall')\n",
        "  plt.xlabel('Thershold')\n",
        "  plt.legend(loc='upper left')\n",
        "  plt.ylim([0,1])\n",
        "  plt.xlim([-100000, 45000]) "
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "XLR4f9GDE4Jj",
        "outputId": "237e5c5c-b966-466c-b78b-e7a4e3db47f7"
      },
      "source": [
        "plot_precision_recall_vs_thershold(precisions, recalls, thersholds)\n",
        "plt.show()"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Xrx9paWm88847zJgxg1dffZW+ffuSmprKRx99BMA//vEPFixYQJ8+fcjIyGDjxo2MGTOG4uJievbsycSJExk8eLCP34lSFV3a1Wprmbtjbp11jbGGvbv5Zk9HpZzmt000vlJ2krTMJ598cmb6iy++qFI/MTHxTLJ39fnnn1e7fteh9ipvSylvST8rnbbN2jJ722xu63dbrXW//RaOHQPthTrw6BG8UiFIRLg+9Xpmb53N6aLTtdYtG1Vy5EgvBKYcpQleqRA1MmUkhSWFdV6OfPnl1sAe2tIYePwuwftqhKlgoPtO1cegdoMA+G7vd7XWy8jQUZsClV8l+JiYGI4ePaqJqgGMMRw9epSYmBhfh6ICRFKLJLrFd2Pernk11snJga+/htO1t+IoP+VXJ1mTk5PZv38/R44c8XUoASkmJobk5GRfh6ECyIUpF/LGmjcoKikiMjyyyvxvvoErrrCehw3zQYCqUfwqwUdGRpKSkuLrMJQKGUM7DOWl5S+x5tAaMs+u2snM0qUQHg79+/sgONVoftVEo5TyrqEdhgLU2Lvk00/DOedAs2bejEo5xa0ELyJjRGSLiGwXkSqnW0Skg4gsEJFVIrJWRMY6H6pSymnJLZPp1KoTc3bMqTKvoMC6yUnvXg1cdSZ4EQkHJgOXAL2AG0WkV6VqfwTeM8b0A24AXnI6UKWU80SECzpdwOL9i6tc3LBggfX8+9/7IDDlCHeO4AcC240xO40xhcC7wJWV6higpT0dC/zoXIhKKU8akjyE7Lxsth7dWqG8Xz8YNAguu8xHgalGcyfBtwP2ubzeb5e5ehy4WUT2A58Bv6luRSJyp4gsF5HleqWMUv5hSPshACzat6hCeWKiNch2YqIvolJOcOok643AG8aYZGAs8JaIVFm3MWaaMSbTGJOZkJDg0KaVUo3RK6EXbZq24cudX1YoP/ts+PvffRSUcoQ7CT4LaO/yOtkuc3U78B6AMeYHIAZo40SASinPCpMwLux8IV/v+fpM2eHDcOAArF/vw8BUo7mT4JcBXUUkRUSisE6iflypzl5gFICI9MRK8NoGo1SA6H9Wf348+SPHTx8HoGxsm1tv9WFQqtHqTPDGmGLgHmAOsAnrapkNIvKkiFxhV3sAuENE1gDvAOOM9jegVMDo3bY3wJmOxz791CpPT/dVRMoJbt3Jaoz5DOvkqWvZYy7TG4HznA1NKeUtQ9oPQRC+3vM1F6RcwKRJVnlcnG/jUo3jV10VKKV8o1VMK/ol9eObPd8AkJxsjeKkApt2VaCUAmDA2QNYc8gaa3jnzvJ2eBW4NMErpQDoFt+NY6ePsS0rmylToLTU1xGpxtIEr5QCyk+0Pjp5Nffea10mqQKbJnilFAAD2w0E4Ps9SwBoV/l+dRVwNMErpQDrRGvPNj3Zb6yug7UXycCnCV4pdcbg5MGQvJiUznobSzDQBK+UOqNv/GBols2YG3f4OhTlAE3wSqkzzu1g9SzZaWj1IzypwKIJXil1Rv/kXjSPas6ekh98HYpygCZ4pdQZq1eFc06TgSzO0iP4YKAJXil1xosvwrZv0tl4ZCMlpSW+Dkc1kiZ4pdQZW7dCcnRv8ovz2X5su6/DUY2kCV4pdcb27dCjdS8A1h/W0T4CnSZ4pRQAOTlw5AgM7JhGmISx6uAqX4ekGkkTvFIKgG3brOeeXZvQPb47aw+t9W1AqtE0wSulAOjdG1auhAsugL5n9dUEHwQ0wSulAIiJgX79oFUr6JvYlz05e8jJz/F1WKoRNMErpQA4/3y45hprOi0xDUCP4gOcDtmnlALg22/Lp10T/LCOw3wUkWosTfBKKYyByEi4+27rdbsW7YiLidMj+ACnTTRKKQ4fhqIi6NLFei0i1onWw5rgA5kmeKUUu3ZZz507l5f1aduHdYfWUWp0cNZApQleKcWPP1rPKSnlZakJqZwqOsXenL2+CUo1miZ4pRRXXw15edC9e3lZattUQLssCGSa4JVSADRpAuHh5a/LrqRZd2idjyJSjaUJXinFvffCq69WLGsZ3ZL2Lduz/ogewQcqTfBKhThjrH7gV1XTt1i/pH6sPLDS+0EpR2iCVyrE7d9vPRcVVZ3X/6z+bM7ezKnCU94NSjlCE7xSIW67Pa7HuedWndcnsQ8AG49s9GJEyima4JUKcVlZ1vPAgVXn9TurHwArDqzwYkTKKZrglQpxpaXQtWvFm5zKdGrViZbRLfVKmgClCV6pEHfLLdZYrNHRVeeJCGmJaaw+tNr7galG0wSvlKpVzzY92ZK9xddhqAZwK8GLyBgR2SIi20VkYg11fiYiG0Vkg4i87WyYSilPGTwYnn++5vk92/Tk6OmjHMo95L2glCPq7C5YRMKBycBFwH5gmYh8bIzZ6FKnK/AQcJ4x5riItPVUwEop5+TmwpIl0LFjzXV6tOkBwPZj20lsnuilyJQT3DmCHwhsN8bsNMYUAu8CV1aqcwcw2RhzHMAYc9jZMJVSnlB2DfzQoTXX6RxnnX3dcXyHFyJSTnInwbcD9rm83m+XueoGdBOR70VksYiMqW5FInKniCwXkeVHjhxpWMRKKcfssHN2RkbNdVLiUgiTMG2HD0BOnWSNALoCI4Abgf8TkVaVKxljphljMo0xmQkJCQ5tWinVUF9+aT279iJZWVR4FL0SerHsx2XeCUo5xp0EnwW0d3mdbJe52g98bIwpMsbsArZiJXyllB8bMACSkiA+vvZ6A88eyKqDqzDGeCcw5Qh3EvwyoKuIpIhIFHAD8HGlOv/BOnpHRNpgNdnsdDBOpZQH3HRT+WAftemX1I/svGz2/7Tf80Epx9SZ4I0xxcA9wBxgE/CeMWaDiDwpIlfY1eYAR0VkI7AAmGCMOeqpoJVSzqiug7HqlHVZoINwBxa32uCNMZ8ZY7oZY7oYY562yx4zxnxsTxtjzP3GmF7GmD7GmHc9GbRSqvGKiqB5c3j22brrlo3utOHIBg9HpZykd7IqFaJ274bCQmjrxl0rrWJacXaLszXBBxhN8EqFqG3brOdzznGvfo82PbTb4ACjCV6pELVpk/XcpYt79QecPYBVB1ZRVOJmw73yOU3wSoWoF1+0nhPd7H2ge3x3SkwJe3P2ei4o5ShN8EqFqGeegTvvBBH36neNt25t2Zy92YNRKSdpglcqRF1/PUyd6n79tMQ0QC+VDCSa4JUKQcbAli3WVTTuahndkqTmSWw7ts1zgSlHaYJXKgQdOgQ9esC0afVbrnNcZ3Ye15vUA4UmeKVC0E47R1c3DmttUuJS2HVil/MBKY/QBK9UCGpogu8S14V9Ofs4XXTa+aCU4zTBKxWCyhJ8p071W653294YjN7RGiA0wSsVgnbvtroJjomp33J92vYBYMNhTfCBoM4xWZVSwWfcOLjwwvov16V1F6LCo/QIPkBoglcqBJ1/fsOWiwiLoHt8d03wAUKbaJQKMYWF8Pnn0NBhkVPbpmqnYwFCE7xSIWbHDhg7tnw81vpKTUhl94nd5BbmOhuYcpwmeKVCzNat1nO3bg1bPjXBGvxj05FNDkWkPEUTvFIhZssW67lr14Ytr6M7BQ5N8EqFmK1brS6CY2MbtnznuM7WlTR6qaTf0wSvVIjZurXhR+9gXUnTo00PNmbriVZ/p5dJKhVipk6FvLzGrSM1IZVF+xY5E5DyGD2CVyrE9OwJGRmNW0dqQip7cvbolTR+ThO8UiFk/36ri+DDhxu3nrITrXo9vH/TBK9UCPn+e7jrLvjxx8atp1dCL0D7pPF3muCVCiFlQ/R17Ni49XSJ60J0eLQewfs5TfBKhZCzz7ae4+Iat57wsHB6tOmh18L7OU3wSoWQHTvgggucWVdq21RN8H5OE7xSIWT7duje3Zl19WrTi705ezlZcNKZFSrH6XXwSoWQffvgtEOj7bleSTMoeZAzK1WO0iN4pUJITEzj29/LlHU6pida/ZcmeKVCxOzZcP/9kJ/vzPo6x3UmJiJG2+H9mCZ4pULE55/Dq69CdLQz6wsPC6dLXBd2Ht/pzAqV4zTBKxUiNmyA1FQQcW6dnVp1YteJXc6tUDlKE7xSIaIswTupa+uubMneQklpibMrVo7QBK9UCDhyBLKznU/wPdr04HTxaX482ci+D5RHuJXgRWSMiGwRke0iMrGWeteIiBGRTOdCVEo1VlaWNciH0wm+W7w17t+mbB2+zx/VmeBFJByYDFwC9AJuFJFe1dRrAdwHLHE6SKVU46Snw8GDcOGFzq63d9veACz/cbmzK1aOcOcIfiCw3Riz0xhTCLwLXFlNvaeAZwCHLsJSSjnNyROsAAnNEujUqhNrD611dsXKEe4k+HbAPpfX++2yM0SkP9DeGPNpbSsSkTtFZLmILD9y5Ei9g1VKNUxSEowZ45l1pyZonzT+qtEnWUUkDHgOeKCuusaYacaYTGNMZkJCQmM3rZRy08GD1mAfnpCakMqW7C0UlRR5ZgOqwdxJ8FlAe5fXyXZZmRZAb2ChiOwGBgMf64lWpfxD2X+Wb7/dM+sf2G4gRaVFLN6/2DMbUA3mToJfBnQVkRQRiQJuAD4um2mMyTHGtDHGdDLGdAIWA1cYY/Ssi1J+YN0667l3b8+sf1TnUQjC/F3zPbMB1WB1JnhjTDFwDzAH2AS8Z4zZICJPisgVng5QKdU469dbz336eGb9rWJa0TOhJysPrvTMBlSDudVdsDHmM+CzSmWP1VB3ROPDUko5pWVLa5CPxETPbaN7fHfWH17vuQ2oBtE7WZUKcuPGwfz5zl8i6WrA2QPYdmwbx08f99xGVL1pglcqiJWWQokXuokpG/xjc/Zmz29MuU0TvFJBbPNmq4nm01rvUGm8fmf1A2DFgRWe3ZCqF03wSgWxNWsgLw+Skz27neSWybSKaaWjO/kZTfBKBbFly6xh+npV6T3KWSJCr4Reekern9EEr1QQW70a0tIgMtLz20pNSGX94fUYYzy/MeUWTfBKBamSEli+HDIyvLO9/kn9OXb6mI7w5Ec0wSsVpPLzYcIEuO4672zv3PbnAmiXBX5EE7xSQapZM3j0UesmJ2/o2aYn0eHRrDygd7T6C03wSgWpDRvgxAnvbS8yPJJ+Sf1YkqVj/vgLTfBKBalrr4Wf/9y72xzcbjDLf1yuXQf7CU3wSgWhY8esm5zi47273UHJg8gvzmfd4XXe3bCqliZ4pYLQDz9Yz9df793tZp5tDQOx4ke9o9UfaIJXKgh9/z1ERMDIkd7dbpe4LsRGx+qJVj+hCV6pILR4MaSnQ9Om3t2uiNA/qT9Lf1zq3Q2rammCVyoITZkCzz/vm22f2/5cVh9czemi074JQJ2hCV6pINStGwwd6pttp5+VTqkp1Y7H/IAmeKWCzOzZMH06+KpLmLTENADWHlrrmwDUGW4N2aeUChx/+xucPAm33OKb7XeJ60KTiCaa4P2AHsErFURycmDRIhg71ncxhIeF07ttb9Ye1gTva5rglQoic+davUiOGePbONIS01hzcI12HexjmuCVCiKffw5xcTBkiG/j6J/Un6Onj7Lz+E7fBhLiNMErFUT27oVRo6ybnHzpvPbnAdp1sK9pglcqiHz1FfzrX76OAlLbptIiqgWL9i3ydSghTRO8UkGirLk7Otq3cQBEhEXQP6k/yw8s93UoIU0TvFJBYvRoa4APfzEkeQgrD6wktzDX16GELE3wSgWBvXvhyy+hSRNfR1JueKfhFJcWszRL+6XxFU3wSgWBBx+0nr3dPXBthiQPQRC+2/udr0MJWZrglQpwxsC771rTXbr4NhZXsTGx9EnsownehzTBKxXgVthja9x3n2/jqM7Q9kP5Yf8PFJcW+zqUkKQJXqkA164dPPII/M//+DqSqoZ2GEpuYa72S+MjmuCVCnBJSfCnP1l3sPqb8zpYNzx9v/d7H0cSmjTBKxXAvvwSPvkESkt9HUn1OsR2oENsBxbsXuDrUEKSdhesVAB75BHIzYXLLvN1JDW7qPNFfLDxA4pLi4kI05TjTW4dwYvIGBHZIiLbRWRiNfPvF5GNIrJWROaJSEfnQ1VKufrsM1i2DMaPBxFfR1OzUSmjyCnI0XZ4H6gzwYtIODAZuAToBdwoIr0qVVsFZBpj0oAPgL85HahSqgYly8cAABHASURBVKKnnrKex43zaRh1Gt5pOABfbP/Cx5GEHneO4AcC240xO40xhcC7wJWuFYwxC4wxefbLxUCys2EqpVytWAGLF8OECdCypa+jqd3ZLc6mf1J/5u6Y6+tQQo47Cb4dsM/l9X67rCa3A59XN0NE7hSR5SKy/MiRI+5HqZSqICfHuqlpwgRfR+Kec5PPZcWBFRQUF/g6lJDi6FU0InIzkAk8W918Y8w0Y0ymMSYzISHByU0rFVIuuACWL4dA+TMamTKS3MJc7ZfGy9xJ8FlAe5fXyXZZBSJyIfAIcIUxRn+mlfKA0lJ45RUoKoJWrXwdjfvO73g+gujlkl7mToJfBnQVkRQRiQJuAD52rSAi/YCpWMn9sPNhKqUAXngB7rjDuvY9kMQ3jSfz7Ezm7Jjj61BCSp0J3hhTDNwDzAE2Ae8ZYzaIyJMicoVd7VmgOfC+iKwWkY9rWJ1SqoE2bICHH4Yrr4Srr/Z1NPV3yTmXsGjfInaf2O3rUEKG+GrU88zMTLN8uY72opQ7Tp+GQYPg4EFYtw4SE30dUf1tPbqV7v/szktjX+JXA37l63ACloisMMZkulNXuypQKgA88ICV2KdPD8zkDtC1dVfatWjH/N3zfR1KyND7hpUKAHfdBT16wJgxvo6k4USEi7tczKzNs7TbAi/RI3il/Nju3dZz375w770+DcURo7uM5kT+CZb/qM2z3qAJXik/9d13kJoKzz3n60icc2HnCxGEOdv1ahpv0ASvlB+aOxcuuQSSk+Gmm3wdjXPim8YzpP0QZm6e6etQQoImeKX8iDEwaZKV3FNSYP78wD2pWpOre1zN2kNr9XJJL9AEr5Qf2bIF7r8fLr8cFi2yhuMLNlf3tC7if2XlKz6OJPhpglfKDxw4YD336GG1vc+cCc2b+zYmT0mJS2FUyig+3qL3Q3qaJnilfOjkSWtUpk6d4Au7u/TBgyEsyP8yR6WMYt3hdWT9VKVbK+WgIP8aKeWf8vNh8mTo2hX+/Ge49lro18/XUXnPpd0uBeDTbZ/6OJLgpgleKS8zBoYOhXvugW7dYMkSmDEj+E6m1qZP2z70SujFa6te83UoQU0TvFIeVlpqtavfcw8UFlrjpz70EMybB19/DQMH+jpC7xMRbkm7hSVZS1h/eL2vwwlamuCV8oCiIliwAO67z2pfHzYM3nzT6k8G4JprYORI/x4s29Nu63cbgvD2urd9HUrQ0gSvlAMKCqzLGjdvtl6vWWMl8KlTIT0d/vUv60qZjAzfxulP2jZry8iUkXo1jQdpgleqHkpKrOfSUnjmGesu07Q065LG886Dl16y5qenw6xZkJ0NH39s1QvWyx4b47Jul7HhyAZWH1zt61CCkvYHr0JeaSmcOgU//WQl8A4drPK33oKNG2HPHuuxY4d1cvSDD6z5SUkQGQl9+lidgQ0YYM0PlHFS/cHx08dJfj6ZG1Jv4NUrX/V1OAGhPv3Ba3+dyq8ZY7VnFxeXP1q3tuYdPAjHjlknLgsLITfXmn/xxdb8f//bair56SfrevOffoK4OHjNvnDj6qvhq6+s5cqOc/r3hxUrrOl//MNavn17qx398svh3HPLY9uxA5o29cpuCFpxTeK4uc/NvLrqVR4f8TjtY9vXvZByW8gn+N/9zvrjdzVkCNx+uzV9111W0nB1wQVw881W+R13VF3n2LFw3XXWUeGvf111/jXXWMkiO9u6Ld2Y8gRjDNxyC4weDfv2wYQJ5fPL6tx9txXD1q0wcWLV+X/4g9VcsGoVPPpo1flPPQWZmdaVHU8+WXX+P/4BvXtbN9789a9V57/+OpxzDnz4Ifz97+VxG2MdAX/0kXWL/f/9Hzz/vFVW9igtteJq3dq6/rtsfmlp+fOxYxAdbXWP++KLFfddZKSVzMF672++WXF+XJy1PFhH2rNmQcuW1qNFC+jSpbzu8OHQsWPF+a5dA3z1lVUWHl71MwRN7k55aNhDVoJf+LgexTss5BP8vHnlCaFMs2YV5xcUVJx/1lnl0/OrGZyme3frubgYFi6sOr/sRFtBgZVkwbqaouyKirIj0IICWL264nwROH7cKsvPh+3bq84/dcoqKyy0jnIrzy8qKo8vN7fq/NLSivGKWHdWutYBK9m2aFH+WsRKhmV3YSYkWD8UYWFWedkjwv7W9e4NP/tZ+XzXZ7B+5OLjrfoREdb2IiPL4xo/3voxjYqyyps3h9jY8vlvv20tV9OVKvfdV315mVatap+vnNGpVSfuH3I/zy56lvuH3E9q21RfhxQ0tA1eKeVz2XnZJD+XzB397+DFsS/WvUAI0zFZlVIBpU3TNlzV8yreWvsW2XnZvg4naGiCV0r5hYeHPsxPBT/xxMInfB1K0NAEr5TyC30S+3BH/zt4aflL7MvZ5+twgoImeKWU33hw6INEh0dz08ybKCop8nU4AU8TvFLKb3SO68zLl77Mt3u/5ZH5j/g6nICnCV4p5Vdu6XsLN6fdzLOLnuWTLZ/4OpyApgleKeVXRIRpl02j31n9uGnmTWw6ssnXIQUsTfBKKb/TJLIJs66fRURYBBO+nODrcAKWJnillF/q2KojE4dO5NNtn/LWmrd8HU5A0gSvlPJbvxv8O87veD63/udWnvvhOV+HE3A0wSul/FZkeCSf3PgJV/a4kgfmPsALi1/wdUgBRRO8UsqvtYxuyb+u+hdjzhnD7+b8jgfmPODrkAKGJnillN9rFtWM2TfO5rb023hu8XM8tuAxSk1p3QuGuJDvLlgpFRjCw8KZetlU8oryeOqbp/h+3/e8+V9vktwy2deh+S09gldKBYzI8EjeueYdXr70ZZbsX0LPyT15ZN4jbDi8wdeh+SW3EryIjBGRLSKyXUQmVjM/WkT+bc9fIiKdnA5UKaXAuhFqfOZ41oxfw4WdL+Qv3/2F3i/35pxJ53DPZ/cwe+tsThWe8nWYfqHOAT9EJBzYClwE7AeWATcaYza61LkbSDPGjBeRG4CrjDHX17ZeHfBDKeWEg7kH+XDjh8zZMYd5u+aRV5RHZFgkvdv2pnub7qS0SiGpeRJJLZJIap5Em6ZtiImIISo8iqjwKKIjookKjyIyLBKpafgvP1KfAT/cSfBDgMeNMaPt1w8BGGP+4lJnjl3nBxGJAA4CCaaWlWuCV0o5raC4gO/3fc9n2z5j7aG17Di+g705eykuLa57YWDKpVO4K/MuD0fZOPVJ8O6cZG0HuHbOvB8YVFMdY0yxiOQA8UCFoVlE5E7gTvtlgYisdydIP9OGSu8rgARq7Bq3d4Vs3OMfH894xjsUjtvqG3dHdyt69SoaY8w0YBqAiCx391fInwRq3BC4sWvc3qVxe5cn43bnJGsW0N7ldbJdVm0du4kmFjjqRIBKKaUaxp0EvwzoKiIpIhIF3AB8XKnOx8Ct9vS1wPza2t+VUkp5Xp1NNHab+j3AHCAceM0Ys0FEngSWG2M+Bl4F3hKR7cAxrB+BukxrRNy+FKhxQ+DGrnF7l8btXR6Lu86raJRSSgUmvZNVKaWClCZ4pZQKUo1K8CJynYhsEJFSEcmsNO8hu+uCLSIy2qW82m4P7JO4S+zyf9sndGvtBqGmbTTgfaSLyGIRWS0iy0VkoF0uIjLJ3sZaEenvssytIrLNftzqUp4hIuvsZSaJfWuciLQWkS/t+l+KSFxD460U+29EZLP9OfzNpdzj+9+B2B8QESMibezXfr2/ReRZe1+vFZFZItLKZZ7f728332Ot3ZJ4YfvtRWSBiGy0v9P32eXVfp5Ofmccij9cRFaJyGz7db0/5/p+l2pljGnwA+gJdAcWApku5b2ANUA0kALswDpBG25Pdwai7Dq97GXeA26wp6cAv7Kn7wam2NM3AP+ubRsNfB9zgUvs6bHAQpfpzwEBBgNL7PLWwE77Oc6ejrPnLbXrir1s2Xr/Bky0pycCzzRm39vruQD4Coi2X7f11v53IPb2WCfu9wBtAmR/XwxE2NPPlK0zEPa3m++vxni9GEMS0N+eboHVTUqvmj5PJ78zDsV/P/A2MLshn3NDvku1xuPQm1pIxQT/EPCQy+s5wBD7MadyPXtHZ7v88ZypV7asPR1h15OattHA+OcA19vTNwJv29NTsfrdKau3xf4C3ghMdSmfapclAZtdys/UK1vW5Uu8xYH9/h5wYTXlHt//DsT+AdAX2E15gvfr/V0p/quAGYGyv918T9XG641t1xLTR1j9YFX7eTr5nXEg1mRgHjASmN2Qz7m+36W6YvJUG3x13Ru0q6U8HjhhjCmuVF5hXfb8sm4QalpXQ/wWeFZE9gF/x9p5DXkf7ezp6mJKNMYcsKcPAokNjNVVN2CY/V+8r0VkQAPjbsj+bzARuRLIMsasqTTL3/e3q//GOvqjjvh8vr/rwcm/qUazmy36AUuo+fN08jvTWC8AfwDKRiJxMq816LOp8zp4EfkKOKuaWY8YYz6qa3l/Udv7AEYBvzPGfCgiP8O6rv9CT8VijDEi4tb1qXXEHYH1X9DBwADgPRHp7FigjVBH3A9jNXd4hVP7u+z7LiKPAMXADOeiVK5EpDnwIfBbY8xPrs3k9fk8vUVELgMOG2NWiMgIX8dTxp0bnRqS6Grr3qC68qNAKxGJsH/NXOuXrWu/VOwGwZ0uFNx6HyIyHbjPfvk+8Eod7yMLGFGpfKFdnlxNfYBDIpJkjDkgIknA4ZriqUfcvwJmGuv/bEtFpBSr4yJv7P8GxS0ifbDaFtfYf7TJwEqxTmz79f624x8HXAaMsvc7tcRNDeWO72+H1OtvylNEJBIruc8wxsy0i2v6PJ38zjTGecAVIjIWiAFaAv/A2bxW/8/GobanhVRsg0+l4omCnVgnCSLs6RTKTxSk2su8T8WTEXfb07+m4smI92rbRgPj3wSMsKdHASvs6UupeAJnqV3eGtiFdfImzp5ubc+rfAJnrF3+LBVPEv3Ngf0+HnjSnu6G9V848cb+d+pBxTZ4f9/fY4CNWF1hu5YHzP6u4/3VGK8XYxBgOvBCpfJqP08nvzMOvocRlJ9kdSSvNfSzaewbuQqrLagAOETFkwCPYJ313YLLWWqss95b7XmPuJR3tnf8dnunlF0ZEmO/3m7P71zXNhrwPoYCK+ydtgTIcPmyTba3sY6KP2L/bce0HbjNpTwTWG8v80/K7xaOxzoBsw3rypfWDnyRooB/2dtbCYz05v536I9hN+UJ3t/393asH9HV9mNKoO1vN95jtfF6cftDAQOsddnPY2v6PJ38zjj4HkZQnuAdy2sN+Wy0qwKllApSeierUkoFKU3wSikVpDTBK6VUkNIEr5RSQUoTvFJKBSlN8CrgiEi8WD1/rhaRgyKSZU+fEJGNHtjeiLLeAeuxzEKp1MOqXT5ORP7pXHRK1UwTvAo4xpijxph0Y0w61s0jz9vT6ZT3A1Jv9h2FSgUNTfAq2ISLyP/ZfYnPFZEmACLSRUS+EJEVIvKtiPSwy98QkSkisgT4m4gMd/nfwSoRaWGvt7mIfCBWf/AzyvoQF5FRdr11IvKaiERXDkhEbhORrSKyFOuWdqW8QhO8CjZdgcnGmFTgBHCNXT4N+I0xJgP4PfCSyzLJwLnGmPvteb+2/0cwDDht1+mH1etoL6y7E88TkRjgDayupvtg3U7+K9dg7H5TnsBK7EPt5ZXyCk3wKtjsMsastqdXAJ3sngnPBd4XkdVYfYMnuSzzvjGmxJ7+HnhORO4FWpnyrl6XGmP2G2NKsW6f74Q12M0uY8xWu86bwPmV4hmENYDMEWNMIfBvx96pUnXQNkcVbApcpkuAJlgHMifso/LqnCqbMMb8VUQ+xer343uXIdMqr1f/dpTf0yN4FfSMMT8Bu0TkOjgzjmff6uqKSBdjzDpjzDPAMqBHLavegvU/hHPs178Avq5UZwkw3L7yJxK4rjHvRan60ASvQsVNwO0isgbYAFxZQ73fish6EVkLFFE+alMVxph84Daspp91WFfwTKlU5wDwOPADVvPPpka+D6Xcpr1JKqVUkNIjeKWUClKa4JVSKkhpgldKqSClCV4ppYKUJnillApSmuCVUipIaYJXSqkg9f+CcuvPAztMtgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gFgka5WFI5w5"
      },
      "source": [
        "Now you can simply select the threshold value that gives you the best precision/recall tradeoff for your task. Another way to select a good precision/recall tradeoff is to plot precision directly against recall"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WHqDtKw1I-kX"
      },
      "source": [
        "def plot_precision_versus_recall(precisions, recalls):\n",
        "  plt.plot(recalls, precisions)\n",
        "  plt.xlabel('Recall')\n",
        "  plt.ylabel('Precisions')\n",
        "  plt.xlim(0, 1)\n",
        "  plt.ylim(0, 1)"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "wxuhDMdBJNkQ",
        "outputId": "a25ac7bc-2762-481f-c81d-c86ff31452fe"
      },
      "source": [
        "plot_precision_versus_recall(precisions, recalls)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tgg0HjLLJxRn"
      },
      "source": [
        "You can see that precision really starts to fall sharply around 80% recall. You will probably want to select a precision/recall tradeoff just before that drop—for example, at around 60% recall. But of course the choice depends on your project"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dSZgLkuJJ0nB"
      },
      "source": [
        "So let’s suppose you decide to aim for 90% precision. You look up the first plot (zooming in a bit) and find that you need to use a threshold of about 70,000 (5,000 for this case). To make predictions (on the training set for now), instead of calling the classifier’s predict() method, you can just run this code"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TOp8Q2bwKdnq"
      },
      "source": [
        "y_train_pred_90 = (y_scores > 5000)"
      ],
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q0Tk90Z7KiIo"
      },
      "source": [
        "Let’s check these predictions’ precision and recall"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1MhjqsElKjVl",
        "outputId": "22d916d7-8dbc-4622-caca-20fcc276a7f6"
      },
      "source": [
        "precision_score(y_train_5, y_train_pred_90)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9265625"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8ZMlkR3uKrhi",
        "outputId": "09376f35-2b25-4e15-bc42-c3bd0e04750f"
      },
      "source": [
        "recall_score(y_train_5, y_train_pred_90)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4375576461907397"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GXNqfJpkKqfM"
      },
      "source": [
        "Great, you have a 90% precision classifier (or close enough)! As you can see, it is fairly easy to create a classifier with virtually any precision you want: just set a high enough threshold, and you’re done. Hmm, not so fast. A high-precision classifier is not very useful if its recall is too low"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J0uybJHxLjlU"
      },
      "source": [
        "## The ROC Curve"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6TOASnaHMB0q"
      },
      "source": [
        "The receiver operating characteristic (ROC) curve is another common tool used with binary classifiers. It is very similar to the precision/recall curve, but instead of plot ting precision versus recall, the ROC curve plots the true positive rate (another name for recall) against the false positive rate\n",
        "\n",
        "The FPR is the ratio of negative instances that are incorrectly classified as positive. It is equal to one minus the true negative rate, which is the ratio of negative instances that are correctly classified as negative\n",
        "\n",
        "The TNR is also called specificity. Hence the ROC curve plots sensitivity (recall) versus 1 – specificity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XWoLdwbz3fYI"
      },
      "source": [
        "To plot the ROC curve, you first need to compute the TPR and FPR for various thres hold values, using the function roc_curve()"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SjJ8fmrpLlId"
      },
      "source": [
        "from sklearn.metrics import roc_curve\n",
        "\n",
        "fpr, tpr, thersholds = roc_curve(y_train_5, y_scores)"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P014pENk4lN8"
      },
      "source": [
        "Then you can plot the FPR against the TPR using Matplotlib"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "P_ljst8Y4ota",
        "outputId": "f13fbaa6-d1af-437d-98d1-bb51d56c7ddf"
      },
      "source": [
        "def plot_roc_curve(fpr, tpr, label=None):\n",
        "  plt.plot(fpr, tpr, linewidth=2, label=label)\n",
        "  plt.plot([0, 1], [0, 1], 'k--')\n",
        "  plt.axis([0, 1, 0, 1])\n",
        "  plt.xlabel('False Positive Rate')\n",
        "  plt.ylabel('True Positive Rate')\n",
        "\n",
        "plot_roc_curve(fpr, tpr)"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T8ktAOvL5E7i"
      },
      "source": [
        "Once again there is a tradeoff: the higher the recall (TPR), the more false positives (FPR) the classifier produces\n",
        "\n",
        "The dotted line represents the ROC curve of a purely random classifier; a good classifier stays as far away from that line as possible (toward the top-left corner)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JxWQ_J8q6UXk"
      },
      "source": [
        "One way to compare classifiers is to measure the area under the curve (AUC)\n",
        "\n",
        "A perfect classifier will have a ROC AUC equal to 1, whereas a purely random classifier will have a ROC AUC equal to 0.5. Scikit-Learn provides a function to compute the ROC AUC"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m1Peir2C6jJm",
        "outputId": "9379825a-c909-40ce-cc65-bab97626a9f2"
      },
      "source": [
        "from sklearn.metrics import roc_auc_score\n",
        "roc_auc_score(y_train_5, y_scores)"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9519021384459392"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AoCd7gGI6ydC"
      },
      "source": [
        "Let’s train a and compare its ROC curve and ROC AUC RandomForestClassifier score to the SGDClassifier\n",
        "\n",
        "First, you need to get scores for each instance in the training set. But due to the way it works (see Chapter 7), the RandomForestClassifier class does not have a decision_function() method. Instead it has a  predict_proba() method. Scikit-Learn classifiers generally have one or the other \n",
        "\n",
        "The method returns an array containing a row per instance and a col predict_proba() umn per class, each containing the probability that the given instance belongs to the given class (e.g., 70% chance that the image represents a 5)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNWxutqN7Urx"
      },
      "source": [
        "from sklearn.ensemble import RandomForestClassifier\n",
        "\n",
        "forest_clf = RandomForestClassifier(random_state=42)\n",
        "y_probas_forest = cross_val_predict(forest_clf, X_train, y_train_5, cv=3,\n",
        "                                    method='predict_proba')"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SFS1ApJb7kur"
      },
      "source": [
        "But to plot a ROC curve, you need scores, not probabilities. A simple solution is to use the positive class’s probability as the score"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y0n8m5kK7nt1"
      },
      "source": [
        "y_scores_forest = y_probas_forest[:, 1]\n",
        "fpr_forest, tpr_forest, thersholds_forest = roc_curve(y_train_5, y_scores_forest)"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nq-jpgQf73Ze"
      },
      "source": [
        "Now you are ready to plot the ROC curve. It is useful to plot the first ROC curve as well to see how they compare"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "fOvOqMcj7-Wi",
        "outputId": "9a9ce76d-1f5d-42e6-edf2-cfa151ed1abb"
      },
      "source": [
        "plt.plot(fpr, tpr, 'b:', label='SGD')\n",
        "plot_roc_curve(fpr_forest, tpr_forest, 'Random Forest')\n",
        "plt.legend(loc='lower right')"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fa30e5b8690>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wEiyHQUX8zgR"
      },
      "source": [
        "the RandomForestClassifier’s ROC curve looks much better than the SGDClassifier’s: it comes much closer to the top-left corner. As a result, its ROC AUC score is also significantly better"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KLXu1EAs9aPv",
        "outputId": "4130cb3e-5973-4f40-85ea-5f3899c55e7f"
      },
      "source": [
        "roc_auc_score(y_train_5, y_scores_forest)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9983247072096962"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hbye1d3T9kgG"
      },
      "source": [
        "Try measuring the precision and recall scores: you should find 98.5% precision and 82.8% recall. Not too bad\n",
        "\n",
        "Hopefully you now know how to train binary classifiers, choose the appropriate met ric for your task, evaluate your classifiers using cross-validation, select the precision/ recall tradeoff that fits your needs, and compare various models using ROC curves and ROC AUC scores. Now let’s try to detect more than just the 5s"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "timnaUpa9Z0m"
      },
      "source": [
        "# Multiclass Classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UB1Ppq9I-GK0"
      },
      "source": [
        "Whereas binary classifiers distinguish between two classes, multiclass classifiers (also called multinomial classifiers) can distinguish between more than two classes\n",
        "\n",
        "Some algorithms (such as Random Forest classifiers or naive Bayes classifiers) are capable of handling multiple classes directly. Others (such as Support Vector Machine classifiers or Linear classifiers) are strictly binary classifiers. However, there are vari ous strategies that you can use to perform multiclass classification using multiple binary classifiers\n",
        "\n",
        "For example, one way to create a system that can classify the digit images into 10 classes (from 0 to 9) is to train 10 binary classifiers, one for each digit (a 0-detector, a 1-detector, a 2-detector, and so on). Then when you want to classify an image, you get the decision score from each classifier for that image and you select the class whose classifier outputs the highest score. This is called the one-versus-all (OvA) strategy (also called one-versus-the-rest)\n",
        "\n",
        "Another strategy is to train a binary classifier for every pair of digits: one to distin guish 0s and 1s, another to distinguish 0s and 2s, another for 1s and 2s, and so on. This is called the one-versus-one (OvO) strategy. If there are N classes, you need to train N (N – 1) / 2 classifiers\n",
        "\n",
        "For the MNIST problem, this means training 45 binary classifiers! When you want to classify an image, you have to run the image through all 45 classifiers and see which class wins the most duels. The main advan tage of OvO is that each classifier only needs to be trained on the part of the training set for the two classes that it must distinguish\n",
        "\n",
        "Some algorithms (such as Support Vector Machine classifiers) scale poorly with the size of the training set, so for these algorithms OvO is preferred since it is faster to train many classifiers on small training sets than training few classifiers on large training sets. For most binary classification algorithms, however, OvA is preferred"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7GSUkslno-0T"
      },
      "source": [
        "Scikit-Learn detects when you try to use a binary classification algorithm for a multi class classification task, and it automatically runs OvA (except for SVM classifiers for which it uses OvO). Let’s try this with the SGDClassifier"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QMIP_4e0pKdk",
        "outputId": "80af1ed2-d931-4291-b09a-e75fd61a1e78"
      },
      "source": [
        "sgd_clf.fit(X_train, y_train)\n",
        "sgd_clf.predict([some_digit])"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5], dtype=uint8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HQMk6TUgpj2l"
      },
      "source": [
        "That was easy! This code trains the SGDClassifier on the training set using the original target classes from 0 to 9 (y_train), instead of the 5-versus-all target classes (y_train_5). Then it makes a prediction (a correct one in this case)\n",
        "\n",
        "Under the hood, Scikit-Learn actually trained 10 binary classifiers, got their decision scores for the image, and selected the class with the highest score"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TQ5gLBvep_8k"
      },
      "source": [
        "To see that this is indeed the case, you can call the method. decision_function() Instead of returning just one score per instance, it now returns 10 scores, one per class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hI3a54-tqDHJ",
        "outputId": "9b4845c6-5e7d-4669-9c32-52af99b35001"
      },
      "source": [
        "some_digit_scores = sgd_clf.decision_function([some_digit])\n",
        "some_digit_scores"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-21567.97120123, -46650.24829539,  -7999.78975411,\n",
              "          2461.72932294, -19474.42587923,   4516.78817377,\n",
              "        -24741.20843354, -19029.80088524,  -8668.06933717,\n",
              "        -13426.76295427]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z0iZ-W67qTIk"
      },
      "source": [
        "The highest score is indeed the one corresponding to class 5"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zEZAUtIlqWNo",
        "outputId": "6073bc5c-b99d-45a7-b22f-291ec3c50ded"
      },
      "source": [
        "np.argmax(some_digit_scores)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lZmTNVtsqY4G",
        "outputId": "15e2d803-3661-464f-f88b-7ca150bd44bc"
      },
      "source": [
        "sgd_clf.classes_"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3z_-n-IeqeFW",
        "outputId": "af9d0a09-94f0-4893-de80-157891bc4f6d"
      },
      "source": [
        "sgd_clf.classes_[5]"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OHBb0LOSqzQx"
      },
      "source": [
        "If you want to force ScikitLearn to use one-versus-one or one-versus-all, you can use the OneVsOneClassifier or classes OneVsRestClassifier\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Z6KKfboq8Wm"
      },
      "source": [
        "Simply create an instance and pass a binary classifier to its constructor. For example, this code creates a multiclass classifier using the OvO strategy, based on a SGDClassifier"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X4j2Gxk_qy7I",
        "outputId": "2bd13020-352c-4b5a-8b14-2462f61d2fb0"
      },
      "source": [
        "from sklearn.multiclass import OneVsOneClassifier\n",
        "ovo_clf = OneVsOneClassifier(SGDClassifier(random_state=42))\n",
        "ovo_clf.fit(X_train, y_train)\n",
        "ovo_clf.predict([some_digit])"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5], dtype=uint8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CXbt1Xo3rVZG",
        "outputId": "47f1533c-4807-4528-c49c-f483054dab47"
      },
      "source": [
        "len(ovo_clf.estimators_)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "45"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "15hXtwKerZGF"
      },
      "source": [
        "Training a is just as easy RandomForestClassifier"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bzdPG6dArcO8",
        "outputId": "bbae49b4-27f9-4c70-f0b2-59dfcbb3163d"
      },
      "source": [
        "forest_clf.fit(X_train, y_train)\n",
        "forest_clf.predict([some_digit])"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5], dtype=uint8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uDynYXORri3f"
      },
      "source": [
        "This time Scikit-Learn did not have to run OvA or OvO because Random Forest classifiers can directly classify instances into multiple classes\n",
        "\n",
        "You can call predict_proba() to get the list of probabilities that the classifier assigned to each instance for each class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4Vj5tBV8ru_4",
        "outputId": "126a5adb-451b-422b-86ac-76abf4cea882"
      },
      "source": [
        "forest_clf.predict_proba([some_digit])"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.01, 0.  , 0.03, 0.05, 0.  , 0.9 , 0.  , 0.  , 0.  , 0.01]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-VCo7P2Kr-nc"
      },
      "source": [
        "You can see that the classifier is fairly confident about its prediction: the 0.9 at the 5th index in the array means that the model estimates a 90% probability that the image represents a 5\n",
        "\n",
        "It also thinks that the image could instead be a 2, a 3 or a 8, respec tively with 1%, 8% and 1% probability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gisOjs2NsL9K"
      },
      "source": [
        "Now of course you want to evaluate these classifiers. As usual, you want to use cross validation. Let’s evaluate the SGDClassifier’s accuracy using the cross_val_score() function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TgHhY6jrr90T",
        "outputId": "bded9e5b-62a4-4ee8-9acd-4d934a78bc92"
      },
      "source": [
        "cross_val_score(sgd_clf, X_train, y_train, cv=3, scoring='accuracy')"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.8784 , 0.8658 , 0.87375])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0G8_HnXZsWCv"
      },
      "source": [
        "It gets over 84% on all test folds. If you used a random classifier, you would get 10% accuracy, so this is not such a bad score, but you can still do much better. For exam ple, simply scaling the inputs (as discussed in Chapter 2) increases accuracy above 89%"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i5a4q1tcsbq6",
        "outputId": "c06cec36-0d2a-4ecb-cf16-a53fbacf768b"
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "scaler = StandardScaler()\n",
        "X_train_scaled = scaler.fit_transform(X_train.astype(np.float64))\n",
        "cross_val_score(sgd_clf, X_train_scaled, y_train, cv=3, scoring='accuracy')"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.898  , 0.89915, 0.8996 ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "clACRWnkswa1"
      },
      "source": [
        "# Error Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CB8W1OPPs43w"
      },
      "source": [
        "Of course, if this were a real project, you would follow the steps in your Machine Learning project checklist: exploring data preparation options, trying out multiple models, shortlisting the best ones and fine-tuning their hyperparameters using GridSearchCV, and automating as much as possible, as you did in the previous chapter\n",
        "\n",
        "Here, we will assume that you have found a promising model and you want to find ways to improve it. One way to do this is to analyze the types of errors it makes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l5nMmjoVtEWL"
      },
      "source": [
        "First, you can look at the confusion matrix. You need to make predictions using the cross_val_predict() function, then call the confusion_matrix() function, just like you did earlier"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3IDRT6Rqs4sn",
        "outputId": "c2e34d77-0c76-422f-ac22-0ddfadaeb2a3"
      },
      "source": [
        "y_train_pred = cross_val_predict(sgd_clf, X_train_scaled, y_train, cv=3)\n",
        "conf_mx = confusion_matrix(y_train, y_train_pred)\n",
        "conf_mx"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[5580,    0,   19,    8,   10,   39,   33,    4,  229,    1],\n",
              "       [   2, 6413,   44,   27,    3,   43,    4,    7,  191,    8],\n",
              "       [  27,   28, 5244,   85,   70,   19,   65,   40,  371,    9],\n",
              "       [  24,   19,  109, 5252,    2,  198,   23,   45,  399,   60],\n",
              "       [  14,   14,   43,    9, 5219,    8,   29,   18,  352,  136],\n",
              "       [  27,   19,   26,  158,   49, 4419,   78,   16,  560,   69],\n",
              "       [  27,   18,   44,    3,   46,   88, 5549,    4,  139,    0],\n",
              "       [  26,   11,   52,   26,   53,   11,    3, 5695,  194,  194],\n",
              "       [  16,   55,   42,   91,    2,  113,   29,    8, 5458,   37],\n",
              "       [  22,   21,   27,   63,  121,   32,    1,  179,  377, 5106]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P-CSPwK2toPE"
      },
      "source": [
        "That’s a lot of numbers. It’s often more convenient to look at an image representation of the confusion matrix, using Matplotlib’s matshow() function "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "id": "zAvkFQ4lsvuq",
        "outputId": "c17c3933-43e7-4847-92c4-2ee8afcea29e"
      },
      "source": [
        "plt.matshow(conf_mx, cmap=plt.cm.gray)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fa30e4ae250>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QnqOnmlmtzhZ"
      },
      "source": [
        "This confusion matrix looks fairly good, since most images are on the main diagonal, which means that they were classified correctly\n",
        "\n",
        "The 5s look slightly darker than the other digits, which could mean that there are fewer images of 5s in the dataset or that the classifier does not perform as well on 5s as on other digits. In fact, you can verify that both are the case"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QfYXkpJUt8jL"
      },
      "source": [
        "Let’s focus the plot on the errors. First, you need to divide each value in the confusion matrix by the number of images in the corresponding class, so you can compare error rates instead of absolute number of errors (which would make abundant classes look unfairly bad)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wCuSlbDawAW7"
      },
      "source": [
        "row_sums = conf_mx.sum(axis=1, keepdims=True)\n",
        "norm_conf_mx = conf_mx / row_sums"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DTf_od8txLcu"
      },
      "source": [
        "Now let’s fill the diagonal with zeros to keep only the errors, and let’s plot the result"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "id": "FZ5CYs5lxOXZ",
        "outputId": "dee3aa97-5468-4e62-83c5-d44fc00fe50e"
      },
      "source": [
        "np.fill_diagonal(norm_conf_mx, 0)\n",
        "plt.matshow(norm_conf_mx, cmap=plt.cm.gray)"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fa30e48a610>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MSpkw8pBx6iT"
      },
      "source": [
        "Now you can clearly see the kinds of errors the classifier makes. Remember that rows represent actual classes, while columns represent predicted classes. The column for class 8 is quite bright, which tells you that many images get misclassified as 8s\n",
        "\n",
        "How ever, the row for class 8 is not that bad, telling you that actual 8s in general get prop erly classified as 8s. As you can see, the confusion matrix is not necessarily symmetrical. You can also see that 3s and 5s often get confused (in both directions)\n",
        "\n",
        "Analyzing the confusion matrix can often give you insights on ways to improve your classifier. Looking at this plot, it seems that your efforts should be spent on reducing the false 8s. For example, you could try to gather more training data for digits that look like 8s (but are not) so the classifier can learn to distinguish them from real 8s\n",
        "\n",
        "Or you could engineer new features that would help the classifier—for example, writ ing an algorithm to count the number of closed loops (e.g., 8 has two, 6 has one, 5 has none). Or you could preprocess the images (e.g., using Scikit-Image, Pillow, or OpenCV) to make some patterns stand out more, such as closed loops\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f8rG5MoTyZ5n"
      },
      "source": [
        "Analyzing individual errors can also be a good way to gain insights on what your classifier is doing and why it is failing, but it is more difficult and time-consuming\n",
        "\n",
        "For example, let’s plot examples of 3s and 5s (the function just uses plot_digits() Matplotlib’s imshow() function; see this chapter’s Jupyter notebook for details) "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y4p0nEhV7us_"
      },
      "source": [
        "import matplotlib as mpl\n",
        "def plot_digits(instances, images_per_row=10, **options):\n",
        "    size = 28\n",
        "    images_per_row = min(len(instances), images_per_row)\n",
        "    images = [instance.reshape(size,size) for instance in instances]\n",
        "    n_rows = (len(instances) - 1) // images_per_row + 1\n",
        "    row_images = []\n",
        "    n_empty = n_rows * images_per_row - len(instances)\n",
        "    images.append(np.zeros((size, size * n_empty)))\n",
        "    for row in range(n_rows):\n",
        "        rimages = images[row * images_per_row : (row + 1) * images_per_row]\n",
        "        row_images.append(np.concatenate(rimages, axis=1))\n",
        "    image = np.concatenate(row_images, axis=0)\n",
        "    plt.imshow(image, cmap = mpl.cm.binary, **options)\n",
        "    plt.axis(\"off\")"
      ],
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "JNEy3Y897lij",
        "outputId": "82d75574-2c21-4ed3-903f-1d43111da3e5"
      },
      "source": [
        "cl_a, cl_b = 3, 5\n",
        "X_aa = X_train[(y_train == cl_a) & (y_train_pred == cl_a)]\n",
        "X_ab = X_train[(y_train == cl_a) & (y_train_pred == cl_b)]\n",
        "X_ba = X_train[(y_train == cl_b) & (y_train_pred == cl_a)]\n",
        "X_bb = X_train[(y_train == cl_b) & (y_train_pred == cl_b)]\n",
        "\n",
        "plt.figure(figsize=(8,8))\n",
        "plt.subplot(221); plot_digits(X_aa[:25], images_per_row=5)\n",
        "plt.subplot(222); plot_digits(X_ab[:25], images_per_row=5)\n",
        "plt.subplot(223); plot_digits(X_ba[:25], images_per_row=5)\n",
        "plt.subplot(224); plot_digits(X_bb[:25], images_per_row=5)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NgaO90nCzWe2"
      },
      "source": [
        "The two blocks on the left show digits classified as 3s, and the two blocks on the right show images classified as 5s. Some of the digits that the classifier gets wrong (i.e., in the bottom-left and top-right blocks) are so badly written that even a human would have trouble classifying them\n",
        "\n",
        "However, most misclassified images seem like obvious errors to us, and it’s hard to understand why the classifier made the mistakes it did. 3 The reason is that we used a simple SGDClassifier, which is a linear model. All it does is assign a weight per class to each pixel, and when it sees a new image it just sums up the weighted pixel intensities to get a score for each class. So since 3s and 5s differ only by a few pixels, this model will easily confuse them\n",
        "\n",
        "The main difference between 3s and 5s is the position of the small line that joins the top line to the bottom arc. If you draw a 3 with the junction slightly shifted to the left, the classifier might classify it as a 5, and vice versa. In other words, this classifier is quite sensitive to image shifting and rotation. So one way to reduce the 3/5 confusion would be to preprocess the images to ensure that they are well centered and not too rotated. This will probably help reduce other errors as well"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ecO-qj-00guJ"
      },
      "source": [
        "# Multilabel Classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q_TcZW4c1iVh"
      },
      "source": [
        "Until now each instance has always been assigned to just one class. In some cases you may want your classifier to output multiple classes for each instance\n",
        "\n",
        "For example, consider a face-recognition classifier: what should it do if it recognizes several people on the same picture? Of course it should attach one tag per person it recognizes. Say the classifier has been trained to recognize three faces, Alice, Bob, and Charlie; then when it is shown a picture of Alice and Charlie, it should output [1, 0, 1] (meaning “Alice yes, Bob no, Charlie yes”\n",
        "\n",
        "Such a classification system that outputs multiple binary tags is called a multilabel classification system"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DFnmCRey2LcA"
      },
      "source": [
        "We won’t go into face recognition just yet, but let’s look at a simpler example, just for illustration purposes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M0-lLdl6zQrW",
        "outputId": "5dee5fe3-3080-426e-a636-dbd602965a9f"
      },
      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "\n",
        "y_train_large = (y_train >= 7)\n",
        "y_train_odd = (y_train % 2 == 1)\n",
        "y_multilabel = np.c_[y_train_large, y_train_odd]\n",
        "\n",
        "knn_clf = KNeighborsClassifier()\n",
        "knn_clf.fit(X_train, y_multilabel)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
              "                     metric_params=None, n_jobs=None, n_neighbors=5, p=2,\n",
              "                     weights='uniform')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A0Dd4QSnVI75"
      },
      "source": [
        "This code creates a y_multilabel array containing two target labels for each digit image: the first indicates whether or not the digit is large (7, 8, or 9) and the second indicates whether or not it is odd\n",
        "\n",
        "The next lines create a KNeighborsClassifier instance (which supports multilabel classification, but not all classifiers do) and we train it using the multiple targets array. Now you can make a prediction, and notice that it outputs two labels"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nTKEYmAjVaiA",
        "outputId": "0058053b-ffbb-42fa-c08a-38d562b99a3c"
      },
      "source": [
        "knn_clf.predict([some_digit])"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False,  True]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a9ejzQrWViph"
      },
      "source": [
        "And it gets it right! The digit 5 is indeed not large (False) and odd (True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V33TZlV5VqQR"
      },
      "source": [
        "There are many ways to evaluate a multilabel classifier, and selecting the right metric really depends on your project. For example, one approach is to measure the F1 score for each individual label (or any other binary classifier metric discussed earlier), then simply compute the average score\n",
        "\n",
        "This code computes the average F1 score across all labels"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gq6XbSc6VeXp",
        "outputId": "554a0ea2-221d-4af2-b1f3-8695396668d6"
      },
      "source": [
        "y_train_knn_pred = cross_val_predict(knn_clf, X_train, y_multilabel, cv=3)\n",
        "f1_score(y_multilabel, y_train_knn_pred, average='macro')"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9769332033574774"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cip3FEWbXBKp"
      },
      "source": [
        "This assumes that all labels are equally important, which may not be the case. In par ticular, if you have many more pictures of Alice than of Bob or Charlie, you may want to give more weight to the classifier’s score on pictures of Alice. One simple option is to give each label a weight equal to its support (i.e., the number of instances with that target label). To do this, simply set average=\"weighted\" in the preceding code "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R64ExLlQXOyo"
      },
      "source": [
        "# Multioutput Classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zPavIuzEXShA"
      },
      "source": [
        "The last type of classification task we are going to discuss here is called multioutput multiclass classification (or simply multioutput classification). It is simply a generalization of multilabel classification where each label can be multiclass (i.e., it can have more than two possible values)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lht2SpmaXkd7"
      },
      "source": [
        "To illustrate this, let’s build a system that removes noise from images. It will take as input a noisy digit image, and it will (hopefully) output a clean digit image, repre sented as an array of pixel intensities, just like the MNIST images\n",
        "\n",
        "Notice that the classifier’s output is multilabel (one label per pixel) and each label can have multiple values (pixel intensity ranges from 0 to 255). It is thus an example of a multioutput classification system"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E_0R6mRKXuzH"
      },
      "source": [
        "Let’s start by creating the training and test sets by taking the MNIST images and adding noise to their pixel intensities using NumPy’s function. The target randint() images will be the original images"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7EJ6KtLX3AP"
      },
      "source": [
        "noise = np.random.randint(0, 100, (len(X_train), 784))\n",
        "X_train_mod = X_train + noise\n",
        "noise = np.random.randint(0, 100, (len(X_test), 784))\n",
        "X_test_mod = X_test + noise\n",
        "y_train_mod = X_train\n",
        "y_test_mod = X_test"
      ],
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cA0eJ7JaZ_Gn"
      },
      "source": [
        "Let’s take a peek at an image from the test set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jHtJr5OvaOAX"
      },
      "source": [
        "def plot_digit(data):\n",
        "    image = data.reshape(28, 28)\n",
        "    plt.imshow(image, cmap = mpl.cm.binary,\n",
        "               interpolation=\"nearest\")\n",
        "    plt.axis(\"off\")"
      ],
      "execution_count": 76,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 183
        },
        "id": "4FIJinedaCoW",
        "outputId": "40e4ad4f-d92a-4a41-a1f5-e3393be057c0"
      },
      "source": [
        "some_index = 0\n",
        "plt.subplot(121); plot_digit(X_test_mod[some_index])\n",
        "plt.subplot(122); plot_digit(y_test_mod[some_index])"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zyg-r-RHaQXA"
      },
      "source": [
        "On the left is the noisy input image, and on the right is the clean target image. Now let’s train the classifier and make it clean this image"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "cXqobGX_aP_v",
        "outputId": "b30b3771-9a31-4e09-cf8d-3c7d29e70821"
      },
      "source": [
        "knn_clf.fit(X_train_mod, y_train_mod)\n",
        "clean_digit = knn_clf.predict([X_test_mod[some_index]])\n",
        "plot_digit(clean_digit)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b3Iibr34kYEb"
      },
      "source": [
        "Looks close enough to the target! This concludes our tour of classification. Hopefully you should now know how to select good metrics for classification tasks, pick the appropriate precision/recall tradeoff, compare classifiers, and more generally build good classification systems for a variety of tasks"
      ]
    }
  ]
}