{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston, load_iris\n",
    "from sklearn.externals.six import StringIO \n",
    "import pydot\n",
    "\n",
    "from sklearn.tree import DecisionTreeRegressor, DecisionTreeClassifier, export_graphviz\n",
    "from sklearn.cross_validation import train_test_split, cross_val_score\n",
    "%matplotlib inline\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook I'm reviewing heuristics for ranking features in decision trees and random forests, and their implementation in sklearn. In the text I sometimes use variable as a synonym of feature.\n",
    "Feature selection is a step embedded in the process of growing decision trees. An attractive side effect is that once model is built, we can retrive the relative importance of each feature in the decision making procees. This not only increases the general interpretability of the model, but can help both in exploratory data analysis as well as in feature engineering piepelines. A nice example of how tree based models can be used to improve feature engineering can be found in the winner recap notes of the Criteo Kaggle competition (http://machine-learning-notes.blogspot.nl/2014/12/kaggle-criteo-winner-method-recap.html). \n",
    "\n",
    "Tree based models, and ensambles of trees, are very powerful and well understood methods for supervised learning. Ensamles such as Random Forests are roboust and stable methods for both classification and regression, while decision trees allow for conceptually simple and easilly interpretable models. For an overview of tree models in classification and regression in sklean, there is an excellent talk from \n",
    "Gilles Louppe at PyData Paris 2015 (http://www.slideshare.net/glouppe/slides-46767187). A well regarded paper from the same author that provides a thorough analysis of the mathematics of feature selection in  tree ensamles is \"Understanding variable importances in forests of randomized trees\" (Louppe et al. 2014). With this notebook I'm attempting to fill some gaps and bridge literature review to implementation (sklearn)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll be using the Boston dataset (http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_boston.html) for regression and the Iris dataset (http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html) for classification examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "boston = load_boston()\n",
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tree models for regression and classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tree based models are non parametric methods that recursively partition the feature space into rectangular disjoint subsets, and fit a model in each of them. Assuming the space is partitioned in *M* regions, a *regression tree* would predict a response $Y$ given inputs $X = \\{x_1, x_2, .. x_n\\}$ as $$f(x_i) = \\sum\\limits_{m=1}^M c_mI(x_i\\in R_m)$$ \n",
    "where $I$ is the indicator function and $c_m$ a constant that models $Y$ in region $R_m$.  This model can be represented by a tree that has $R_1..R_m$ as its terminal nodes. In both the regression and classification cases, the algorithm decides the splitting variables and split points, and tree topology. Essentially, at each split point, the algorithm performs a feature selection step using an heuristic to estimate information gain; this is represented by a numerical value known as the *Gini importance* of a feature (not to be confused with the Gini index!).\n",
    "We can exploit this very same process to rank features (features engineering) and to explain their imporance with regards to the models we want to learn from data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main difference between the regression and classification case is the criterion employed to evaluate the quality of a split when growing a tree. Regardless of this aspect, in sklearn, the importance of a variable is calculated as the Gini Importance or \"mean decreased impurity\" (http://stackoverflow.com/questions/15810339/how-are-feature-importances-in-randomforestclassifier-determined). See\n",
    "\"Classification and regression trees\" (Breiman, Friedman, 1984)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gini importance (MDI) of a variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gini importance, or *mean decreased impurity* is defined as the total decrease in node impurity $i(s, n)$, at split $s$ for some impurity function $i(n)$ . That is\n",
    "$$ \\Delta i(s, n) = i(n) - p_L i(t_L) -  p_R i(t_R) $$\n",
    "Where $p_L$ and $p_R$ are the proportion of $N_L$ and $N_R$ samples in the left and right splits, over the total number of samples $N_n$ for node $n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Under the hood](https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/tree/_tree.pyx#L3340), sklearn calculates MDI as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "cdef class Tree:\n",
    "    [...]\n",
    "    cpdef compute_feature_importances(self, normalize=True):\n",
    "           [...]\n",
    "           while node != end_node:\n",
    "                if node.left_child != _TREE_LEAF:\n",
    "                    # ... and node.right_child != _TREE_LEAF:\n",
    "                    left = &nodes[node.left_child]\n",
    "                    right = &nodes[node.right_child]\n",
    "\n",
    "                    importance_data[node.feature] += (\n",
    "                        node.weighted_n_node_samples * node.impurity -\n",
    "                        left.weighted_n_node_samples * left.impurity -\n",
    "                        right.weighted_n_node_samples * right.impurity)\n",
    "                node += 1\n",
    "\n",
    "        importances /= nodes[0].weighted_n_node_samples\n",
    "        [...]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This method looks at a node and its left, right children. A list of split variables (*node.feature* objects) and the associated importance score is kept in *importance_data*. The node impurity is weighted by the probability of reaching that node,  approximated by the proportion of samples (*weighted_n_node_samples*) reaching that node."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "node.weighted_n_node_samples * node.impurity -\n",
    "left.weighted_n_node_samples * left.impurity -\n",
    "right.weighted_n_node_samples * right.impurity\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *impurity* criteria are defined by implementations of the *Criterion* interface. For classification trees, impurity criteria are *Entropy* - cross entropy - and *Gini*, the Gini index. For regression trees the impurity criteria is *MSE* (mean squared error)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As said, *sklearn.tree.DecisionTreeRegressor* uses mean squared error (MSE) to determine the quality of a split; that is, an estimate $\\hat{c}_m$ for $c_m$ is calcuated so to minimize the sum of squares $\\sum (y_i - \\hat{f}(x_i))^2$ with $y_i$ being the target variable and $\\hat{f}(x_i)$ its predicted value. The best (*proof!*) estimator is obtained by taking  $\\hat{f}({x_i}) = avg(y_i | x_i \\in R_m)$. By bias variance decompostion of the squared error , we have $Var[\\hat{f}(x_i)] = E[(\\hat{f}(x_i) - E[\\hat{f}(x_i)])^2]$. So, for a split node, the mean squared error can then be calculated as the sum of variance of the left and right split: $MSE = Var_{left} + Var_{right}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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QAAmQQHQCEGLWrFkTUPDoo49W4SQg85+T+++/XyAYZDdFqgcBCB+YUoZKH3/8sZoenn/+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ejfhI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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To keep the diagram tractable, restrict the tree to at most 5 leaf nodes\n",
    "reg = DecisionTreeRegressor(max_leaf_nodes=5)\n",
    "reg.fit(boston.data, boston.target)\n",
    "dot_data = StringIO()\n",
    "export_graphviz(reg, out_file=\"/tmp/tree.dot\", \n",
    "                feature_names=boston.feature_names) \n",
    "# pydot.graph_from_dot_data is broken in my env\n",
    "!dot -Tpng /tmp/tree.dot -o /tmp/tree.png\n",
    "from IPython.display import Image\n",
    "Image(filename='/tmp/tree.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the example above, with 5 terminal nodes, we identify three split variables: RM, DIS and LSTAT. For each non terminal node, the diagram shows the split variables and split value, the MSE and the number of datapoints (samples) contained in the resulting partitioned region. Terminal nodes, on the other hand, report the value for the response we want to predict.\n",
    "We can retrieve the Gini importance of each feature in the fitted model with the *feature\\_importances_* property. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5GQ4ODtXeoYsQQgj/lAZ5fn4+xGIx97rsBusaGhrIzc1FTEwMvv32WzRv3hyB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f54a310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor(max_leaf_nodes=5)\n",
    "reg.fit(boston.data, boston.target)\n",
    "plt = pd.DataFrame(zip(boston.feature_names, reg.feature_importances_),\n",
    "             columns=['feature', 'Gini importance']).plot(kind='bar', x='feature')\n",
    "_ = plt.set_title('Regression tree on the Boston dataset (5 leaf nodes)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Things become a bit more interesting when we grow larger trees."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OQK1WIygoCAMHDkRoaKg0T6PRYOPGjZgyZQqCgoKwd+9ePHnyRO8NJiKi/9F5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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd6a950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor()\n",
    "reg.fit(boston.data, boston.target)\n",
    "plt = pd.DataFrame(zip(boston.feature_names, reg.feature_importances_), \n",
    "             columns=['feature', 'Gini importance']).plot(kind='bar', x='feature')\n",
    "_ = plt.set_title('Regression tree on the Boston dataset')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume a  classification task where the target $k$ classes take  values in $0,1,...,K−1$. If node $m$ represents a region $R_m$ with $N_m$ observations, then let $p_{mk} = \\frac{1}{N_m} \\sum_{x_i \\in R_m} I(y_i = k)$ be the proportion of class $k$ observations in node $m$. \n",
    "$sklearn.DecisionTreeClassifier$ allows two impurity criteria for determining splits in such a setting. On the Iris dataset the two criteria agree on which features are important. Experimental results suggest that for tree induction purposes both impurity measures generally lead to similar results (Tan et. al, Introduction to Data Mining). This is not entirely surprising given that both mesaures are particular cases of Tsallis entropy  $H_\\beta = \\frac{1}{\\beta-1}(1 - \\sum_{k=0}^{K-1} p^{\\beta}_{mk})$. For Gini index $\\beta=2$, while cross entroy is recovered by taking $\\beta \\rightarrow 1$.\n",
    "\n",
    "Cross *entropy* might give higher scores to balanced partitions when there are many classes though. See \"Technical Note: Some Properties of Splitting Criteria\" (Breiman , 1996). On the other hand working in log scale *might* introduce computational overhead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gini Index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gini Index is defined as $\\sum_{k=0}^{K-1} p_{mk} (1 - p_{mk}) = 1 - \\sum_{k=0}^{K-1} p_{mk}^2$. It is a measure of statistical dispersion commonly used to measure inequality among values of frequency distributions. An interpretation of the Gini index is popular in social sciences as a way to represent levels of income http://en.wikipedia.org/wiki/Gini_coefficient of a nation's residents. In other words, it is the area under the Lorentz curve (http://en.wikipedia.org/wiki/Lorenz_curve). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JjCFORCQxhjgRkcQY4kREEmOIExFJjCFORCQxhjgRkcQY4kREEmOIExFJjCFO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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f154b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cls = DecisionTreeClassifier(criterion='gini', splitter='best')\n",
    "est = cls.fit(iris.data, iris.target)\n",
    "zip(iris.feature_names, cls.feature_importances_)\n",
    "plt = pd.DataFrame(zip(iris.feature_names, cls.feature_importances_), \n",
    "             columns=['feature', 'Gini importance']).plot(kind='bar', x='feature')\n",
    "_ = plt.set_title('Classification tree on the Iris dataset (criterion=gini)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross-entropy is defined as $- \\sum_{k=0}^{K-1} p_{mk} \\log(p_{mk})$. Intutively it tells us the amount of information contained at each split node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NjY3UlpeXByMjI9SoUQNGRkaoV68eMjMzK5yhtbV11at+DgylTkPB/tSu6tif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\noy/EcWXtWbt2Ld5++238/vvv6NmzJ3b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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef85f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cls = DecisionTreeClassifier(criterion='entropy', splitter='best')\n",
    "est = cls.fit(iris.data, iris.target)\n",
    "zip(iris.feature_names, cls.feature_importances_)\n",
    "plt = pd.DataFrame(zip(iris.feature_names, cls.feature_importances_), \n",
    "             columns=['feature', 'Gini importance']).plot(kind='bar', x='feature')\n",
    "_ = plt.set_title('Classification tree on the Iris dataset (criterion=entropy)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both DecistionTreeRegressor and DecisionTreeClassifier accept parameters that influence the shape of a tree, hence the topology of the partitioned feature space. These parameters allow to set thresholds to the number of features per split and tree depth. Once the process for growing trees is understood, sklean documentation should be pretty much straightforward. A parameter worth mentionign is *random_state*, that controls the randomization of sampling at each split. If we set this parameter to a constant, we are guaranteed to produce the same splits for each run of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensable methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trees lead to very interpretable moodels, which are trivial to visualize. On the one hand this property makes them very attractive as a mean of \"communicating\" predictive models to a non technical audience. On the other end, they usually result in low bias high variance models. To control variance, we can combine the predictions of several trees into a single model.\n",
    "At the time of writing sklean ships with two tree ensemble methods: Random Forest (Breiman, 2001) and Extremely Randomized Trees (Geurts et al., 2006).\n",
    "Both methods extend the ideas of bootstrap aggregation or \"bagging\" (Breiman 1996), that is sampling a training set with replacement to obtain $m$ datasets (bootstrap sets) and combine the output $m$ models fit on each sampled set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random Forest brings bagging to the feature selection step. $N$ trees are grown on a boostrapped dataset than,\n",
    "before each split, the algorithm randomly picks $m \\leq p$ variables as candidates for splitting. The best candidate is picked according to an heuristic, and the node is split in left/right children. After $N$ such trees are grown, the algorithm combines their predictions. In case of regression trees, this means averaging the output of the ensamlbe of $f$ models as:\n",
    "$f_{rf}(x) = \\frac{1}{N} \\sum_{n=1}^{N} f_n (x)$. For classification forests, a common combination strategy is majority voting.\n",
    "A common value for $m$ is $\\sqrt{p}$, the intuition being that small values of $m$ reduce the correlation between pair of trees, hence reduce the variance of the ensemble."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression and classification with Random Forests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*sklearn.ensemble.RandomForestRegressor* and *sklearn.ensemble.RandomForestClassifier* are interaces for building ensembles of DecisionTreeRegressor and  DecisionTreeClassifier respectively. The criteria for determining node impurity are the same as we've seen before: *mse* for regression trees and *gini* or *entropy* for classification trees. The logic for growing and combining the ensemble output is implemented in *sklearn.ensemble.ForestRegressor* and *sklearn.ensemble.ForstClassifier*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### oob_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random Forest is known to be a robust classifier that does not overfit; the authors claim no need for cross-validation or even using a test set for model selection (https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm#features). An estimate of the generalization error can be obtains as  part of the algorithm run, by leaving out a portion of the bootstrap dataset used for fitting each tree and use it to build a test dataset across the $N$ trees with all data points left out by all trees. That is, but building an out-of-bag test set on the go. This behaviour is controlled by the boolean *oob_score* parameter. On a fitted model, the *oob_score*  argument will then report the error estimate for the ensemble.\n",
    "\n",
    "In sklearn the out-of-bag error is calculated in *_set_oob_score* in [ForestRegressor](https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/ensemble/forest.py#L647) and [ForestClassifier](https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/ensemble/forest.py#L362). For regression trees, the oob score is expressed as the sum of the $R^2$ of each predictor on the oob dataset, averaged over the number of predictors. For classification trees, it is the vote given by each predictors *oob_decision_function* that for a forest of $k$ trees is a list of "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "decision = (predictions[k] /\n",
    "                        predictions[k].sum(axis=1)[:, np.newaxis])\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where *predictions[k]* is the sum of class probabilities predicted by the *predict_proba(X)* method, for some test input $X$, that for a singe tree $k$ is the fraction of samples of the same class in a leaf."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intepretability of random forest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With Random Forest we lose the capability visualizing the model as a decision tree diagram. However, we can still  access the feature importance vector for the whole fitted esemble with the *feature\\_importances\\_* property. This is [computed as](https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/ensemble/forest.py#L309)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "sum(all_importances) / len(self.estimators_)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extra trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sklearn allows for Extremely Randomized Trees to be used instead of Decision Trees to compose an ensemble. I won't cover the working of ExtraTree in this notebook. For a very concise comparison see http://stackoverflow.com/questions/22409855/randomforestclassifier-vs-extratreesclassifier-in-scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Categorical features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the toy examples above, I've dealt only with numerical features. Fitting models with categorical variables might be a bit confusing if you come from evirnoment like R, where the most common implementations are either able to handle categorical variables natively, or take care of encoding them. In sklearn, a bit more work is necessary to encode categorical variables using eg. Hashing Trick (sklearn.feature_extraction.FeatureHasher) and One-Hot-Encoding (). Alternatively, Pandas provides the convenient DataFrame.get_dummies() method. \n",
    "\n",
    "Suprisingly, to me at least, when growing trees on large datasets sklearn behaves well even with integer enconding of categorical features. See https://stackoverflow.com/questions/15821751/how-to-use-dummy-variable-to-represent-categorical-data-in-python-scikit-learn-r and https://github.com/szilard/benchm-ml/issues/1"
   ]
  }
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