Boosting

A common machine learning task is supervised learning. In supervised learning, the goal is to learn the functional relationship F: y = F(x) between the input x and the output y . 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 N training examples {(x_i,y_i)}1N with x_i \in{R^K} and y_i \in{-1, +1} . x_i is a K -component vector. Each component encodes a feature relevant to the learning task at hand. The desired two-class 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 two-class Discrete AdaBoost algorithm, outlined below. Initially the same weight is assigned to each sample (step 2). Then, a weak classifier f_{m(x)} is trained on the weighted training data (step 3a). Its weighted training error and scaling factor c_m 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 M -1 times. The final classifier F(x) is the sign of the weighted sum over the individual weak classifiers (step 4).

Two-class Discrete AdaBoost Algorithm

1. Set N examples {(x_i,y_i)}1N with x_i \in{R^K}, y_i \in{-1, +1} .

2. Assign weights as w_i = 1/N, i = 1,...,N .

3. Repeat for m = 1,2,...,M :

   3.1. Fit the classifier f_m(x) \in{-1,1} , using weights w_i on the training data.

   3.2. Compute err_m = E_w [1_{(y \neq f_m(x))}], c_m = log((1 - err_m)/err_m) .

   3.3. Set w_i \Leftarrow w_i exp[c_m 1_{(y_i \neq f_m(x_i))}], i = 1,2,...,N, and renormalize so that \Sigma i w_i = 1 .

4. Classify new samples x using the formula: \textrm{sign} (\Sigma m = 1M c_m f_m(x)) .

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.

CvBoostParams

The structure is derived from :ocv:class:`CvDTreeParams` but not all of the decision tree parameters are supported. In particular, cross-validation is not supported.

All parameters are public. You can initialize them by a constructor and then override some of them directly if you want.

CvBoostParams::CvBoostParams

The constructors.

See :ocv:func:`CvDTreeParams::CvDTreeParams` for description of other parameters.

Default parameters are:

CvBoostParams::CvBoostParams()
{
    boost_type = CvBoost::REAL;
    weak_count = 100;
    weight_trim_rate = 0.95;
    cv_folds = 0;
    max_depth = 1;
}

CvBoostTree

The weak tree classifier, a component of the boosted tree classifier :ocv:class:`CvBoost`, is a derivative of :ocv:class:`CvDTree`. Normally, there is no need to use the weak classifiers directly. However, they can be accessed as elements of the sequence :ocv:member:`CvBoost::weak`, retrieved by :ocv:func:`CvBoost::get_weak_predictors`.

CvBoost

Boosted tree classifier derived from :ocv:class:`CvStatModel`.

CvBoost::CvBoost

Default and training constructors.

The constructors follow conventions of :ocv:func:`CvStatModel::CvStatModel`. See :ocv:func:`CvStatModel::train` for parameters descriptions.

CvBoost::train

Trains a boosted tree classifier.

The train method follows the common template of :ocv:func:`CvStatModel::train`. The responses must be categorical, which means that boosted trees cannot be built for regression, and there should be two classes.

CvBoost::predict

Predicts a response for an input sample.

The method runs the sample through the trees in the ensemble and returns the output class label based on the weighted voting.

CvBoost::prune

Removes the specified weak classifiers.

The method removes the specified weak classifiers from the sequence.

CvBoost::calc_error

Returns error of the boosted tree classifier.

The method is identical to :ocv:func:`CvDTree::calc_error` but uses the boosted tree classifier as predictor.

CvBoost::get_weak_predictors

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 :ocv:class:`CvBoostTree` class or to some of its derivatives.

CvBoost::get_params

Returns current parameters of the boosted tree classifier.

CvBoost::get_data

Returns used train data of the boosted tree classifier.