A decision tree is a binary tree (tree where each non-leaf node has two child nodes). It can be used either for classification or for regression. For classification, each tree leaf is marked with a class label; multiple leaves may have the same label. For regression, a constant is also assigned to each tree leaf, so the approximation function is piecewise constant.
**Ordered variables.** The variable value is compared with a threshold that is also stored in the node. If the value is less than the threshold, the procedure goes to the left. Otherwise, it goes to the right. For example, if the weight is less than 1 kilogram, the procedure goes to the left, else to the right.
**Categorical variables.** A discrete variable value is tested to see whether it belongs to a certain subset of values (also stored in the node) from a limited set of values the variable could take. If it does, the procedure goes to the left. Otherwise, it goes to the right. For example, if the color is green or red, go to the left, else to the right.
So, in each node, a pair of entities (``variable_index`` , ``decision_rule
(threshold/subset)`` ) is used. This pair is called a *split* (split on
the variable ``variable_index`` ). Once a leaf node is reached, the value
assigned to this node is used as the output of the prediction procedure.
Sometimes, certain features of the input vector are missed (for example, in the darkness it is difficult to determine the object color), and the prediction procedure may get stuck in the certain node (in the mentioned example, if the node is split by color). To avoid such situations, decision trees use so-called *surrogate splits*. That is, in addition to the best "primary" split, every tree node may also be split to one or more other variables with nearly the same results.
The tree is built recursively, starting from the root node. All training data (feature vectors and responses) is used to split the root node. In each node the optimum decision rule (the best "primary" split) is found based on some criteria. In machine learning, ``gini`` "purity" criteria are used for classification, and sum of squared errors is used for regression. Then, if necessary, the surrogate splits are found. They resemble the results of the primary split on the training data. All the data is divided using the primary and the surrogate splits (like it is done in the prediction procedure) between the left and the right child node. Then, the procedure recursively splits both left and right nodes. At each node the recursive procedure may stop (that is, stop splitting the node further) in one of the following cases:
When the tree is built, it may be pruned using a cross-validation procedure, if necessary. That is, some branches of the tree that may lead to the model overfitting are cut off. Normally, this procedure is only applied to standalone decision trees. Usually tree ensembles build trees that are small enough and use their own protection schemes against overfitting.
Besides the prediction that is an obvious use of decision trees, the tree can be also used for various data analyses. One of the key properties of the constructed decision tree algorithms is an ability to compute the importance (relative decisive power) of each variable. For example, in a spam filter that uses a set of words occurred in the message as a feature vector, the variable importance rating can be used to determine the most "spam-indicating" words and thus help keep the dictionary size reasonable.
Importance of each variable is computed over all the splits on this variable in the tree, primary and surrogate ones. Thus, to compute variable importance correctly, the surrogate splits must be enabled in the training parameters, even if there is no missing data.
The structure contains all the decision tree training parameters. You can initialize it by default constructor and then override any parameters directly before training, or the structure may be fully initialized using the advanced variant of the constructor.
:param maxDepth:The maximum possible depth of the tree. That is the training algorithms attempts to split a node while its depth is less than ``maxDepth``. The root node has zero depth. The actual depth may be smaller if the other termination criteria are met (see the outline of the training procedure in the beginning of the section), and/or if the tree is pruned.
:param regressionAccuracy:Termination criteria for regression trees. If all absolute differences between an estimated value in a node and values of train samples in this node are less than this parameter then the node will not be split further.
:param useSurrogates:If true then surrogate splits will be built. These splits allow to work with missing data and compute variable importance correctly. .. note:: currently it's not implemented.
:param maxCategories:Cluster possible values of a categorical variable into ``K<=maxCategories`` clusters to find a suboptimal split. If a discrete variable, on which the training procedure tries to make a split, takes more than ``maxCategories`` values, the precise best subset estimation may take a very long time because the algorithm is exponential. Instead, many decision trees engines (including our implementation) try to find sub-optimal split in this case by clustering all the samples into ``maxCategories`` clusters that is some categories are merged together. The clustering is applied only in ``n > 2``-class classification problems for categorical variables with ``N > max_categories`` possible values. In case of regression and 2-class classification the optimal split can be found efficiently without employing clustering, thus the parameter is not used in these cases.
:param CVFolds:If ``CVFolds > 1`` then algorithms prunes the built decision tree using ``K``-fold cross-validation procedure where ``K`` is equal to ``CVFolds``.
:param use1SERule:If true then a pruning will be harsher. This will make a tree more compact and more resistant to the training data noise but a bit less accurate.
:param truncatePrunedTree:If true then pruned branches are physically removed from the tree. Otherwise they are retained and it is possible to get results from the original unpruned (or pruned less aggressively) tree.
:param priors:The array of a priori class probabilities, sorted by the class label value. The parameter can be used to tune the decision tree preferences toward a certain class. For example, if you want to detect some rare anomaly occurrence, the training base will likely contain much more normal cases than anomalies, so a very good classification performance will be achieved just by considering every case as normal. To avoid this, the priors can be specified, where the anomaly probability is artificially increased (up to 0.5 or even greater), so the weight of the misclassified anomalies becomes much bigger, and the tree is adjusted properly. You can also think about this parameter as weights of prediction categories which determine relative weights that you give to misclassification. That is, if the weight of the first category is 1 and the weight of the second category is 10, then each mistake in predicting the second category is equivalent to making 10 mistakes in predicting the first category.
The class represents a single decision tree or a collection of decision trees. The current public interface of the class allows user to train only a single decision tree, however the class is capable of storing multiple decision trees and using them for prediction (by summing responses or using a voting schemes), and the derived from DTrees classes (such as ``RTrees`` and ``Boost``) use this capability to implement decision tree ensembles.
The static method creates empty decision tree with the specified parameters. It should be then trained using ``train`` method (see ``StatModel::train``). Alternatively, you can load the model from file using ``StatModel::load<DTrees>(filename)``.
