{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Balance model complexity and cross-validated score\n\nThis example balances model complexity and cross-validated score by\nfinding a decent accuracy within 1 standard deviation of the best accuracy\nscore while minimising the number of PCA components [1].\n\nThe figure shows the trade-off between cross-validated score and the number\nof PCA components. The balanced case is when n_components=10 and accuracy=0.88,\nwhich falls into the range within 1 standard deviation of the best accuracy\nscore.\n\n[1] Hastie, T., Tibshirani, R.,, Friedman, J. (2001). Model Assessment and\nSelection. The Elements of Statistical Learning (pp. 219-260). New York,\nNY, USA: Springer New York Inc..\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\nfrom sklearn.datasets import load_digits\nfrom sklearn.decomposition import PCA\nfrom sklearn.model_selection import GridSearchCV\nfrom sklearn.pipeline import Pipeline\nfrom sklearn.svm import LinearSVC\n\n\ndef lower_bound(cv_results):\n    \"\"\"\n    Calculate the lower bound within 1 standard deviation\n    of the best `mean_test_scores`.\n\n    Parameters\n    ----------\n    cv_results : dict of numpy(masked) ndarrays\n        See attribute cv_results_ of `GridSearchCV`\n\n    Returns\n    -------\n    float\n        Lower bound within 1 standard deviation of the\n        best `mean_test_score`.\n    \"\"\"\n    best_score_idx = np.argmax(cv_results[\"mean_test_score\"])\n\n    return (\n        cv_results[\"mean_test_score\"][best_score_idx]\n        - cv_results[\"std_test_score\"][best_score_idx]\n    )\n\n\ndef best_low_complexity(cv_results):\n    \"\"\"\n    Balance model complexity with cross-validated score.\n\n    Parameters\n    ----------\n    cv_results : dict of numpy(masked) ndarrays\n        See attribute cv_results_ of `GridSearchCV`.\n\n    Return\n    ------\n    int\n        Index of a model that has the fewest PCA components\n        while has its test score within 1 standard deviation of the best\n        `mean_test_score`.\n    \"\"\"\n    threshold = lower_bound(cv_results)\n    candidate_idx = np.flatnonzero(cv_results[\"mean_test_score\"] >= threshold)\n    best_idx = candidate_idx[\n        cv_results[\"param_reduce_dim__n_components\"][candidate_idx].argmin()\n    ]\n    return best_idx\n\n\npipe = Pipeline(\n    [\n        (\"reduce_dim\", PCA(random_state=42)),\n        (\"classify\", LinearSVC(random_state=42, C=0.01)),\n    ]\n)\n\nparam_grid = {\"reduce_dim__n_components\": [6, 8, 10, 12, 14]}\n\ngrid = GridSearchCV(\n    pipe,\n    cv=10,\n    n_jobs=1,\n    param_grid=param_grid,\n    scoring=\"accuracy\",\n    refit=best_low_complexity,\n)\nX, y = load_digits(return_X_y=True)\ngrid.fit(X, y)\n\nn_components = grid.cv_results_[\"param_reduce_dim__n_components\"]\ntest_scores = grid.cv_results_[\"mean_test_score\"]\n\nplt.figure()\nplt.bar(n_components, test_scores, width=1.3, color=\"b\")\n\nlower = lower_bound(grid.cv_results_)\nplt.axhline(np.max(test_scores), linestyle=\"--\", color=\"y\", label=\"Best score\")\nplt.axhline(lower, linestyle=\"--\", color=\".5\", label=\"Best score - 1 std\")\n\nplt.title(\"Balance model complexity and cross-validated score\")\nplt.xlabel(\"Number of PCA components used\")\nplt.ylabel(\"Digit classification accuracy\")\nplt.xticks(n_components.tolist())\nplt.ylim((0, 1.0))\nplt.legend(loc=\"upper left\")\n\nbest_index_ = grid.best_index_\n\nprint(\"The best_index_ is %d\" % best_index_)\nprint(\"The n_components selected is %d\" % n_components[best_index_])\nprint(\n    \"The corresponding accuracy score is %.2f\"\n    % grid.cv_results_[\"mean_test_score\"][best_index_]\n)\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.21"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}