{
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    {
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      "source": [
        "\n# SGD: convex loss functions\n\nA plot that compares the various convex loss functions supported by\n:class:`~sklearn.linear_model.SGDClassifier` .\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Authors: The scikit-learn developers\n# SPDX-License-Identifier: BSD-3-Clause\n\nimport matplotlib.pyplot as plt\nimport numpy as np\n\n\ndef modified_huber_loss(y_true, y_pred):\n    z = y_pred * y_true\n    loss = -4 * z\n    loss[z >= -1] = (1 - z[z >= -1]) ** 2\n    loss[z >= 1.0] = 0\n    return loss\n\n\nxmin, xmax = -4, 4\nxx = np.linspace(xmin, xmax, 100)\nlw = 2\nplt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color=\"gold\", lw=lw, label=\"Zero-one loss\")\nplt.plot(xx, np.where(xx < 1, 1 - xx, 0), color=\"teal\", lw=lw, label=\"Hinge loss\")\nplt.plot(xx, -np.minimum(xx, 0), color=\"yellowgreen\", lw=lw, label=\"Perceptron loss\")\nplt.plot(xx, np.log2(1 + np.exp(-xx)), color=\"cornflowerblue\", lw=lw, label=\"Log loss\")\nplt.plot(\n    xx,\n    np.where(xx < 1, 1 - xx, 0) ** 2,\n    color=\"orange\",\n    lw=lw,\n    label=\"Squared hinge loss\",\n)\nplt.plot(\n    xx,\n    modified_huber_loss(xx, 1),\n    color=\"darkorchid\",\n    lw=lw,\n    linestyle=\"--\",\n    label=\"Modified Huber loss\",\n)\nplt.ylim((0, 8))\nplt.legend(loc=\"upper right\")\nplt.xlabel(r\"Decision function $f(x)$\")\nplt.ylabel(\"$L(y=1, f(x))$\")\nplt.show()"
      ]
    }
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