ensemble-methods-notebooks-master/Ch3.2-combining-predictions-by-weighting.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains code and comments from Section 3.2 of the book [Ensemble Methods for Machine Learning](https://www.manning.com/books/ensemble-methods-for-machine-learning). Please see the book for additional details on this topic. This notebook and code are released under the [MIT license](https://github.com/gkunapuli/ensemble-methods-notebooks/blob/master/LICENSE)._\n",
    "\n",
    "---\n",
    "\n",
    "## 3.2 Combining predictions by weighting\n",
    "\n",
    "First, we copy over the data generation stuff and the functions ``fit`` and ``predict_individual`` exactly as is from Section 3.1. (An alternate way to do this would be to import the functions from the notebook using the ``ipynb`` package)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X, y = make_moons(600, noise=0.25, random_state=13)\n",
    "X, Xval, y, yval = train_test_split(X, y, test_size=0.25)        # Set aside 25% of data for validation\n",
    "Xtrn, Xtst, ytrn, ytst = train_test_split(X, y, test_size=0.25)  # Set aside a further 25% of data for hold-out test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --- Some code to suppress warnings generated due to versioning changes in sklearn and scipy\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.dtype size changed\")\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.ufunc size changed\")\n",
    "# --- Can be removed at a future date\n",
    "\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.gaussian_process import GaussianProcessClassifier\n",
    "from sklearn.gaussian_process.kernels import RBF\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "estimators = [('dt', DecisionTreeClassifier(max_depth=5)),\n",
    "              ('svm', SVC(gamma=1.0, C=1.0, probability=True)),\n",
    "              ('gp', GaussianProcessClassifier(RBF(1.0))),\n",
    "           \t  ('3nn', KNeighborsClassifier(n_neighbors=3)),\n",
    "              ('rf',RandomForestClassifier(max_depth=3, n_estimators=25)),\n",
    "              ('gnb', GaussianNB())]\n",
    "\n",
    "def fit(estimators, X, y):\n",
    "    for model, estimator in estimators:\n",
    "        estimator.fit(X, y)\n",
    "    return estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def predict_individual(X, estimators, proba=False):\n",
    "    n_estimators = len(estimators)\n",
    "    n_samples = X.shape[0] \n",
    "\n",
    "    y = np.zeros((n_samples, n_estimators))\n",
    "    for i, (model, estimator) in enumerate(estimators):\n",
    "        if proba:\n",
    "            y[:, i] = estimator.predict_proba(X)[:, 1]  \n",
    "        else:\n",
    "            y[:, i] = estimator.predict(X)              \n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the estimators to the synthetic data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimators = fit(estimators, Xtrn, ytrn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 3.2.1\tMajority Vote\n",
    "\n",
    "**Listing 3.3**: Combine predictions using majority vote. \n",
    "The listing below combines the individual predictions y_individual from a heterogeneous set of base estimators using majority voting. Note that since the weights of the base estimators are all equal, we do not explicitly compute them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import mode\n",
    "\n",
    "def combine_using_majority_vote(X, estimators):\n",
    "    y_individual = predict_individual(X, estimators, proba=False)\n",
    "    y_final = mode(y_individual, axis=1)\n",
    "    return y_final[0].reshape(-1, )"
   ]
  },
  {
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   "execution_count": 6,
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      ]
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "ypred = combine_using_majority_vote(Xtst, estimators)\n",
    "tst_err = 1 - accuracy_score(ytst, ypred)\n",
    "tst_err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### 3.2.2 Accuracy weighting\n",
    "\n",
    "**Listing 3.4**: Combine using accuracy weighting\n",
    "\n",
    "Accuracy weighting is a performance-based weighting strategy, where higher-performing base estimators in the ensemble are assigned higher weights, so that they contribute more to the final prediction.\n",
    "\n",
    "Once we have trained each base classifier, we evaluate its performance on a validation set. Let $\\alpha_t$ be the validation accuracy of the $t$-th classifier, $H_t$. The weight of each base classifier is then computed as $w_t =  \\frac{\\alpha_t}{\\sum_{t=1}^m \\, \\alpha_t}$.\n",
    "\n",
    "The denominator is a normalization term: the sum of all the individual validation accuracies. This computation ensures that a classifier’s weight is proportional to its accuracy and all the weights sum to 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def combine_using_accuracy_weighting(X, estimators, Xval, yval):\n",
    "    n_estimators = len(estimators)\n",
    "    yval_individual = predict_individual(Xval, estimators, proba=False)\n",
    "    \n",
    "    wts = [accuracy_score(yval, yval_individual[:, i]) \n",
    "       for i in range(n_estimators)] \n",
    "    wts /= np.sum(wts)\n",
    "\n",
    "    ypred_individual = predict_individual(X, estimators, proba=False)\n",
    "    y_final = np.dot(ypred_individual, wts) \n",
    "\n",
    "    return np.round(y_final)"
   ]
  },
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   "execution_count": 8,
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     "execution_count": 8,
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   "source": [
    "ypred = combine_using_accuracy_weighting(Xtst, estimators, Xval, yval)\n",
    "tst_err = 1 - accuracy_score(ytst, ypred)\n",
    "tst_err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 3.2.3 Entropy weighting\n",
    "\n",
    "The entropy weighting approach is another performance-based weighting approach, except that it uses entropy as the evaluation metric to judge the value of each base estimator. [Entropy](https://en.wikipedia.org/wiki/Entropy_(information_theory)) is a measure of uncertainty or impurity in a set; a more disorderly set will have higher entropy. \n",
    "\n",
    "**Listing 3.5** Computing entropy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(y):\n",
    "    _, counts = np.unique(y, return_counts=True) \n",
    "    p = np.array(counts.astype('float') / len(y))\n",
    "    ent = -p.T @ np.log2(p) \n",
    "\n",
    "    return ent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Listing 3.6**: Combine using entropy weighting\n",
    "\n",
    "Let $E_t$ be the validation entropy of the $t$-th classifier, $H_t$. The weight of each base classifier is then computed as \\frac{(1/E_t)}{\\sum_{t=1}^m \\, (1/E_t)}$. Contrast this with accuracy weighting, and observe that the entropies are inverted. This is because lower entropies are desirable, much like higher accuracies are desirable in a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def combine_using_entropy_weighting(X, estimators, Xval, yval):\n",
    "    n_estimators = len(estimators)\n",
    "    yval_individual = predict_individual(Xval, estimators, proba=False)\n",
    "    \n",
    "    wts = [1/entropy(yval_individual[:, i]) \n",
    "           for i in range(n_estimators)]\n",
    "    wts /= np.sum(wts)\n",
    "\n",
    "    ypred_individual = predict_individual(X, estimators, proba=False)\n",
    "    y_final = np.dot(ypred_individual, wts)\n",
    "    \n",
    "    return np.round(y_final)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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     "execution_count": 11,
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   ],
   "source": [
    "ypred = combine_using_entropy_weighting(Xtst, estimators, Xval, yval)\n",
    "tst_err = 1 - accuracy_score(ytst, ypred)\n",
    "tst_err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--- \n",
    "### 3.2.4\tDempster-Shafer combination\n",
    "\n",
    "[Dempster-Shafer Theory](https://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory) is a generalization of probability theory that supports reasoning under uncertainty and with incomplete knowledge. While the foundations of DST are beyond the scope of this book, the theory itself provides a way to fuse beliefs and evidence from multiple sources into one single belief. \n",
    "\n",
    "DST uses a number between 0 and 1 to indicate belief in a proposition, such as “the test example x belongs to Class 1”.  This number is known as a basic probability assignment (BPA) and expresses the certainty that the text example x belongs to Class 1. BPA values closer to 1 characterize decisions made with more certainty. The BPA allows us to translate an estimator’s confidence to a belief over what the true label is.\n",
    "\n",
    "**Listing 3.7**: Combining using Dempster-Shafer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def combine_using_Dempster_Schafer(X, estimators):\n",
    "    p_individual = predict_individual(X, estimators, proba=True)\n",
    "    bpa0 = 1.0 - np.prod(p_individual, axis=1) - 1e-6\n",
    "    bpa1 = 1.0 - np.prod(1.0 - p_individual, axis=1) - 1e-6\n",
    "\n",
    "    belief = np.vstack([bpa0 / (1 - bpa0), bpa1 / (1 - bpa1)]).T\n",
    "    y_final = np.argmax(belief, axis=1)\n",
    "    return y_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "0.03539823008849563"
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     "execution_count": 13,
     "metadata": {},
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    }
   ],
   "source": [
    "ypred = combine_using_Dempster_Schafer(Xtst, estimators)\n",
    "tst_err = 1 - accuracy_score(ytst, ypred)\n",
    "tst_err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Unlisted**: Logarithmic opinion pooling (LOP), first described in [Heskes98](https://papers.nips.cc/paper/1413-selecting-weighting-factors-in-logarithmic-opinion-pools.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def combine_using_LOP(X, estimators, Xval, yval):\n",
    "    n_estimators = len(estimators)\n",
    "    yval_individual = predict_individual(Xval, estimators, proba=False)\n",
    "    wts = [1 - accuracy_score(yval, yval_individual[:, i]) for i in range(n_estimators)]\n",
    "    wts /= np.sum(wts)\n",
    "\n",
    "    p_individual = predict_individual(X, estimators, proba=True)\n",
    "    p_LOP = np.exp(np.dot(np.log(p_individual), wts))\n",
    "    return np.round(p_LOP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Visualizing the decision boundaries of all 4 weighting methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from visualization import plot_2d_classifier, get_colors\n",
    "\n",
    "\n",
    "combination_methods = [('Majority Vote', combine_using_majority_vote),\n",
    "                       ('Dempster-Shafer', combine_using_Dempster_Schafer),\n",
    "                       ('Accuracy Weighting', combine_using_accuracy_weighting),\n",
    "                       ('Entropy Weighting', combine_using_entropy_weighting)]\n",
    "# ('Logarithmic Opinion Pool', combine_using_LOP)]\n",
    "\n",
    "nrows, ncols = 2, 2\n",
    "cm = get_colors(colormap='RdBu')\n",
    "\n",
    "# Init plotting\n",
    "xMin, xMax = Xtrn[:, 0].min() - 0.25, Xtrn[:, 0].max() + 0.25\n",
    "yMin, yMax = Xtrn[:, 1].min() - 0.25, Xtrn[:, 1].max() + 0.25\n",
    "xMesh, yMesh = np.meshgrid(np.arange(xMin, xMax, 0.05),\n",
    "                           np.arange(yMin, yMax, 0.05))\n",
    "fig, ax = plt.subplots(nrows=nrows, ncols=ncols, figsize=(6, 6))\n",
    "\n",
    "for i, (method, combiner) in enumerate(combination_methods):\n",
    "    c, r = divmod(i, 2)\n",
    "    if i < 2:\n",
    "        zMesh = combiner(np.c_[xMesh.ravel(), yMesh.ravel()], estimators)\n",
    "        ypred = combiner(Xtst, estimators)\n",
    "    else:\n",
    "        zMesh = combiner(np.c_[xMesh.ravel(), yMesh.ravel()], estimators, Xval, yval)\n",
    "        ypred = combiner(Xtst, estimators, Xval, yval)\n",
    "    zMesh = zMesh.reshape(xMesh.shape)\n",
    "\n",
    "    ax[r, c].contourf(xMesh, yMesh, zMesh, cmap='RdBu', alpha=0.65)\n",
    "    ax[r, c].contour(xMesh, yMesh, zMesh, [0.5], colors='k', linewidths=2.5)\n",
    "    ax[r, c].scatter(Xtrn[ytrn == 0, 0], Xtrn[ytrn == 0, 1], marker='o', c=cm[0], edgecolors='k')\n",
    "    ax[r, c].scatter(Xtrn[ytrn == 1, 0], Xtrn[ytrn == 1, 1], marker='s', c=cm[1], edgecolors='k')\n",
    "\n",
    "    # tst_err = 1 - accuracy_score(ytst, ypred)\n",
    "    # title = '{0} (err = {1:4.2f}%)'.format(method, tst_err*100) \n",
    "    title = '{0}'.format(method) \n",
    "\n",
    "    ax[r, c].set_xticks([])\n",
    "    ax[r, c].set_yticks([])\n",
    "    ax[r, c].set_title(title)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig('./figures/CH03_F10_Kunapuli.png', dpi=300, bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}