Boosting (machine learning)

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Boosting is a machine learning ensemble meta-algorithm for primarily reducing bias, and also variance^[1] in supervised learning, and a family of machine learning algorithms which convert weak learners to strong ones.^[2] Boosting is based on the question posed by Kearns and Valiant (1988, 1989):^[3][4] Can a set of weak learners create a single strong learner? A weak learner is defined to be a classifier which is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification.

Robert Schapire's affirmative answer in a 1990 paper^[5] to the question of Kearns and Valiant has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting.^[6]

When first introduced, the hypothesis boosting problem simply referred to the process of turning a weak learner into a strong learner. "Informally, [the hypothesis boosting] problem asks whether an efficient learning algorithm […] that outputs a hypothesis whose performance is only slightly better than random guessing [i.e. a weak learner] implies the existence of an efficient algorithm that outputs a hypothesis of arbitrary accuracy [i.e. a strong learner]."^[3] Algorithms that achieve hypothesis boosting quickly became simply known as "boosting". Freund and Schapire's arcing (Adapt[at]ive Resampling and Combining),^[7] as a general technique, is more or less synonymous with boosting.^[8]

Boosting algorithms

While boosting is not algorithmically constrained, most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they are typically weighted in some way that is usually related to the weak learners' accuracy. After a weak learner is added, the data are reweighted: examples that are misclassified gain weight and examples that are classified correctly lose weight (some boosting algorithms actually decrease the weight of repeatedly misclassified examples, e.g., boost by majority and BrownBoost). Thus, future weak learners focus more on the examples that previous weak learners misclassified.

There are many boosting algorithms. The original ones, proposed by Robert Schapire (a recursive majority gate formulation^[5]) and Yoav Freund (boost by majority^[9]), were not adaptive and could not take full advantage of the weak learners. However, Schapire and Freund then developed AdaBoost, an adaptive boosting algorithm that won the prestigious Gödel Prize.

Only algorithms that are provable boosting algorithms in the probably approximately correct learning formulation can accurately be called boosting algorithms. Other algorithms that are similar in spirit to boosting algorithms are sometimes called "leveraging algorithms", although they are also sometimes incorrectly called boosting algorithms.^[9]

The main variation between many boosting algorithms is their method of weighting training data points and hypotheses. AdaBoost is very popular and perhaps the most significant historically as it was the first algorithm that could adapt to the weak learners. However, there are many more recent algorithms such as LPBoost, TotalBoost, BrownBoost, xgboost, MadaBoost, LogitBoost, and others. Many boosting algorithms fit into the AnyBoost framework,^[9] which shows that boosting performs gradient descent in function space using a convex cost function.

Object categorization

Given images containing various known objects in the world, a classifier can be learned from them to automatically categorize the objects in future images. Simple classifiers built based on some image feature of the object tend to be weak in categorization performance. Using boosting methods for object categorization is a way to unify the weak classifiers in a special way to boost the overall ability of categorization.

Problem of object categorization

Object categorization is a typical task of computer vision which involves determining whether or not an image contains some specific category of object. The idea is closely related with recognition, identification, and detection. Appearance based object categorization typically contains feature extraction, learning a classifier, and applying the classifier to new examples. There are many ways to represent a category of objects, e.g. from shape analysis, bag of words models, or local descriptors such as SIFT, etc. Examples of supervised classifiers are Naive Bayes classifier, SVM, mixtures of Gaussians, neural network, etc. However, research has shown that object categories and their locations in images can be discovered in an unsupervised manner as well.^[10]

Status quo for object categorization

The recognition of object categories in images is a challenging problem in computer vision, especially when the number of categories is large. This is due to high intra class variability and the need for generalization across variations of objects within the same category. Objects within one category may look quite different. Even the same object may appear unalike under different viewpoint, scale, and illumination. Background clutter and partial occlusion add difficulties to recognition as well.^[11] Humans are able to recognize thousands of object types, whereas most of the existing object recognition systems are trained to recognize only a few, e.g., human face, car, simple objects, etc.^[12] Research has been very active on dealing with more categories and enabling incremental additions of new categories, and although the general problem remains unsolved, several multi-category objects detectors (number of categories around 20) for clustered scenes have been developed. One means is by feature sharing and boosting.

Boosting for binary categorization

We use AdaBoost for face detection as an example of binary categorization. The two categories are faces versus background. The general algorithm is as follows:

1. Form a large set of simple features
2. Initialize weights for training images
3. for T rounds
   1. Normalize the weights
   2. For available features from the set, train a classifier using a single feature and evaluate the training error
   3. Choose the classifier with the lowest error
   4. Update the weights of the training images: increase if classified wrongly by this classifier, decrease if correctly
4. Form the final strong classifier as the linear combination of the T classifiers (coefficient larger if training error is small)

After boosting, a classifier constructed from 200 features could yield a 95% detection rate under a false positive rate.^[13]

Another application of boosting for binary categorization is a system which detects pedestrians using patterns of motion and appearance.^[14] This work is the first to combine both motion information and appearance information as features to detect a walking person. It takes a similar approach as the face detection work of Viola and Jones.

Boosting for multi-class categorization

Compared with binary categorization, multi-class categorization looks for common features that can be shared across the categories at the same time. They turn to be more generic edge like features. During learning, the detectors for each category can be trained jointly. Compared with training separately, it generalizes better, needs less training data, and requires less number of features to achieve same performance.

The main flow of the algorithm is similar to the binary case. What is different is that a measure of the joint training error shall be defined in advance. During each iteration the algorithm chooses a classifier of a single feature (features which can be shared by more categories shall be encouraged). This can be done via converting multi-class classification into a binary one (a set of categories versus the rest),^[15] or by introducing a penalty error from the categories which do not have the feature of the classifier.^[16]

In the paper "Sharing visual features for multiclass and multiview object detection", A. Torralba et al. used GentleBoost for boosting and showed that when training data is limited, learning via sharing features does a much better job than no sharing, given same boosting rounds. Also, for a given performance level, the total number of features required (and therefore the run time cost of the classifier) for the feature sharing detectors, is observed to scale approximately logarithmically with the number of class, i.e., slower than linear growth in the non-sharing case. Similar results are shown in the paper "Incremental learning of object detectors using a visual shape alphabet", yet the authors used AdaBoost for boosting.

Criticism

In 2008 Phillip Long (at Google) and Rocco A. Servedio (Columbia University) published a paper^[17] at the 25th International Conference for Machine Learning suggesting that many of these algorithms are probably flawed. They conclude that "convex potential boosters cannot withstand random classification noise," thus making the applicability of such algorithms for real world, noisy data sets questionable. The paper shows that if any fraction of the training data is mis-labeled, the boosting algorithm tries extremely hard to correctly classify these training examples, and fails to produce a model with accuracy better than 1/2. This result does not apply to branching program based boosters but does apply to AdaBoost, LogitBoost, and others.^[17]

See also

Implementations

• Scikit-learn, an open source machine learning library for python
• Orange, a free data mining software suite, module Orange.ensemble
• Weka is a machine learning set of tools that offers variate implementations of boosting algorithms like AdaBoost and LogitBoost
• R package GBM (Generalized Boosted Regression Models) implements extensions to Freund and Schapire's AdaBoost algorithm and Friedman's gradient boosting machine.
• jboost; AdaBoost, LogitBoost, RobustBoost, Boostexter and alternating decision trees
• R package adabag: Applies Multiclass AdaBoost.M1, AdaBoost-SAMME and Bagging

References

Footnotes

Notations

• Yoav Freund and Robert E. Schapire (1997); A Decision-Theoretic Generalization of On-line Learning and an Application to Boosting, Journal of Computer and System Sciences, 55(1):119-139
• Robert E. Schapire and Yoram Singer (1999); Improved Boosting Algorithms Using Confidence-Rated Predictors, Machine Learning, 37(3):297-336

External links

• Robert E. Schapire (2003); The Boosting Approach to Machine Learning: An Overview, MSRI (Mathematical Sciences Research Institute) Workshop on Nonlinear Estimation and Classification
• Zhou Zhi-Hua (2014) Boosting 25 years, CCL 2014 Keynote.
• Zhou, Zhihua (2008). "On the margin explanation of boosting algorithm." (PDF). In: Proceedings of the 21st Annual Conference on Learning Theory (COLT'08): 479–490.  On the margin explanation of boosting algorithm.
• Zhou, Zhihua (2013). "On the doubt about margin explanation of boosting." (PDF). Artificial Intelligence. 203: 1–18.  On the doubt about margin explanation of boosting.