A common machine learning task is supervised learning. In supervised learning, the goal is to learn the functional relationship between the input and the output . Predicting the qualitative output is called classification, while predicting the quantitative output is called regression.
Boosting is a powerful learning concept that provides a solution to the supervised classification learning task. It combines the performance of many “weak” classifiers to produce a powerful committee [HTF01]. A weak classifier is only required to be better than chance, and thus can be very simple and computationally inexpensive. However, many of them smartly combine results to a strong classifier that often outperforms most “monolithic” strong classifiers such as SVMs and Neural Networks.
Decision trees are the most popular weak classifiers used in boosting schemes. Often the simplest decision trees with only a single split node per tree (called stumps ) are sufficient.
The boosted model is based on training examples with and . is a component vector. Each component encodes a feature relevant to the learning task at hand. The desired twoclass output is encoded as 1 and +1.
Different variants of boosting are known as Discrete Adaboost, Real AdaBoost, LogitBoost, and Gentle AdaBoost [FHT98]. All of them are very similar in their overall structure. Therefore, this chapter focuses only on the standard twoclass Discrete AdaBoost algorithm, outlined below. Initially the same weight is assigned to each sample (step 2). Then, a weak classifier is trained on the weighted training data (step 3a). Its weighted training error and scaling factor is computed (step 3b). The weights are increased for training samples that have been misclassified (step 3c). All weights are then normalized, and the process of finding the next weak classifier continues for another 1 times. The final classifier is the sign of the weighted sum over the individual weak classifiers (step 4).
Twoclass Discrete AdaBoost Algorithm
Set examples with .
Assign weights as .
Repeat for :
3.1. Fit the classifier , using weights on the training data.
3.2. Compute .
3.3. Set and renormalize so that .
Classify new samples x using the formula: .
Note
Similar to the classical boosting methods, the current implementation supports twoclass classifiers only. For M > 2 classes, there is the AdaBoost.MH algorithm (described in [FHT98]) that reduces the problem to the twoclass problem, yet with a much larger training set.
To reduce computation time for boosted models without substantially losing accuracy, the influence trimming technique can be employed. As the training algorithm proceeds and the number of trees in the ensemble is increased, a larger number of the training samples are classified correctly and with increasing confidence, thereby those samples receive smaller weights on the subsequent iterations. Examples with a very low relative weight have a small impact on the weak classifier training. Thus, such examples may be excluded during the weak classifier training without having much effect on the induced classifier. This process is controlled with the weight_trim_rate parameter. Only examples with the summary fraction weight_trim_rate of the total weight mass are used in the weak classifier training. Note that the weights for all training examples are recomputed at each training iteration. Examples deleted at a particular iteration may be used again for learning some of the weak classifiers further [FHT98].
[HTF01]  Hastie, T., Tibshirani, R., Friedman, J. H. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. 2001. 
[FHT98]  (1, 2, 3) Friedman, J. H., Hastie, T. and Tibshirani, R. Additive Logistic Regression: a Statistical View of Boosting. Technical Report, Dept. of Statistics*, Stanford University, 1998. 
Boosting training parameters.
The structure is derived from CvDTreeParams but not all of the decision tree parameters are supported. In particular, crossvalidation is not supported.
All parameters are public. You can initialize them by a constructor and then override some of them directly if you want.
The constructors.
Parameters: 


See CvDTreeParams::CvDTreeParams() for description of other parameters.
Also there is one structure member that you can set directly:
Splitting criteria used to choose optimal splits during a weak tree construction. Possible values are:
 CvBoost::DEFAULT Use the default for the particular boosting method, see below.
 CvBoost::GINI Use Gini index. This is default option for Real AdaBoost; may be also used for Discrete AdaBoost.
 CvBoost::MISCLASS Use misclassification rate. This is default option for Discrete AdaBoost; may be also used for Real AdaBoost.
 CvBoost::SQERR Use least squares criteria. This is default and the only option for LogitBoost and Gentle AdaBoost.
Default parameters are:
CvBoostParams::CvBoostParams()
{
boost_type = CvBoost::REAL;
weak_count = 100;
weight_trim_rate = 0.95;
cv_folds = 0;
max_depth = 1;
}
The weak tree classifier, a component of the boosted tree classifier CvBoost, is a derivative of CvDTree. Normally, there is no need to use the weak classifiers directly. However, they can be accessed as elements of the sequence CvBoost::weak, retrieved by CvBoost::get_weak_predictors().
Note
In case of LogitBoost and Gentle AdaBoost, each weak predictor is a regression tree, rather than a classification tree. Even in case of Discrete AdaBoost and Real AdaBoost, the CvBoostTree::predict return value (CvDTreeNode::value) is not an output class label. A negative value “votes” for class #0, a positive value  for class #1. The votes are weighted. The weight of each individual tree may be increased or decreased using the method CvBoostTree::scale.
Default and training constructors.
The constructors follow conventions of CvStatModel::CvStatModel(). See CvStatModel::train() for parameters descriptions.
Trains a boosted tree classifier.
Parameters:  update – Specifies whether the classifier needs to be updated (true, the new weak tree classifiers added to the existing ensemble) or the classifier needs to be rebuilt from scratch (false). 

The train method follows the common template of CvStatModel::train(). The responses must be categorical, which means that boosted trees cannot be built for regression, and there should be two classes.
Predicts a response for an input sample.
Parameters: 


The method runs the sample through the trees in the ensemble and returns the output class label based on the weighted voting.
Removes the specified weak classifiers.
Parameters:  slice – Continuous subset of the sequence of weak classifiers to be removed. 

The method removes the specified weak classifiers from the sequence.
Note
Do not confuse this method with the pruning of individual decision trees, which is currently not supported.
Returns error of the boosted tree classifier.
The method is identical to CvDTree::calc_error() but uses the boosted tree classifier as predictor.
Returns the sequence of weak tree classifiers.
The method returns the sequence of weak classifiers. Each element of the sequence is a pointer to the CvBoostTree class or to some of its derivatives.