Popular Ensemble Methods: An Empirical Study

An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund and Shapire, 1996; Shapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier -- especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble's performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees

Vote-boosting ensembles

Vote-boosting is a sequential ensemble learning method in which the individual classifiers are built on different weighted versions of the training data. To build a new classifier, the weight of each training instance is determined in terms of the degree of disagreement among the current ensemble predictions for that instance. For low class-label noise levels, especially when simple base learners are used, emphasis should be made on instances for which the disagreement rate is high. When more flexible classifiers are used and as the noise level increases, the emphasis on these uncertain instances should be reduced. In fact, at sufficiently high levels of class-label noise, the focus should be on instances on which the ensemble classifiers agree. The optimal type of emphasis can be automatically determined using cross-validation. An extensive empirical analysis using the beta distribution as emphasis function illustrates that vote-boosting is an effective method to generate ensembles that are both accurate and robust

On PAC-Bayesian Bounds for Random Forests

Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various PAC-Bayesian approaches to derive such bounds. The bounds do not require additional hold-out data, because the out-of-bag samples from the bagging in the training process can be exploited. A random forest predicts by taking a majority vote of an ensemble of decision trees. The first approach is to bound the error of the vote by twice the error of the corresponding Gibbs classifier (classifying with a single member of the ensemble selected at random). However, this approach does not take into account the effect of averaging out of errors of individual classifiers when taking the majority vote. This effect provides a significant boost in performance when the errors are independent or negatively correlated, but when the correlations are strong the advantage from taking the majority vote is small. The second approach based on PAC-Bayesian C-bounds takes dependencies between ensemble members into account, but it requires estimating correlations between the errors of the individual classifiers. When the correlations are high or the estimation is poor, the bounds degrade. In our experiments, we compute generalization bounds for random forests on various benchmark data sets. Because the individual decision trees already perform well, their predictions are highly correlated and the C-bounds do not lead to satisfactory results. For the same reason, the bounds based on the analysis of Gibbs classifiers are typically superior and often reasonably tight. Bounds based on a validation set coming at the cost of a smaller training set gave better performance guarantees, but worse performance in most experiments

Two-Stage Bagging Pruning for Reducing the Ensemble Size and Improving the Classification Performance

Ensemble methods, such as the traditional bagging algorithm, can usually improve the performance of a single classifier. However, they usually require large storage space as well as relatively time-consuming predictions. Many approaches were developed to reduce the ensemble size and improve the classification performance by pruning the traditional bagging algorithms. In this article, we proposed a two-stage strategy to prune the traditional bagging algorithm by combining two simple approaches: accuracy-based pruning (AP) and distance-based pruning (DP). These two methods, as well as their two combinations, “AP+DP” and “DP+AP” as the two-stage pruning strategy, were all examined. Comparing with the single pruning methods, we found that the two-stage pruning methods can furthermore reduce the ensemble size and improve the classification. “AP+DP” method generally performs better than the “DP+AP” method when using four base classifiers: decision tree, Gaussian naive Bayes, K-nearest neighbor, and logistic regression. Moreover, as compared to the traditional bagging, the two-stage method “AP+DP” improved the classification accuracy by 0.88%, 4.06%, 1.26%, and 0.96%, respectively, averaged over 28 datasets under the four base classifiers. It was also observed that “AP+DP” outperformed other three existing algorithms Brag, Nice, and TB assessed on 8 common datasets. In summary, the proposed two-stage pruning methods are simple and promising approaches, which can both reduce the ensemble size and improve the classification accuracy

Bagging ensemble selection

Ensemble selection has recently appeared as a popular ensemble learning method, not only because its implementation is fairly straightforward, but also due to its excellent predictive performance on practical problems. The method has been highlighted in winning solutions of many data mining competitions, such as the Netix competition, the KDD Cup 2009 and 2010, the UCSD FICO contest 2010, and a number of data mining competitions on the Kaggle platform. In this paper we present a novel variant: bagging ensemble selection. Three variations of the proposed algorithm are compared to the original ensemble selection algorithm and other ensemble algorithms. Experiments with ten real world problems from diverse domains demonstrate the benefit of the bagging ensemble selection algorithm

Ensembles of probability estimation trees for customer churn prediction

Customer churn prediction is one of the most, important elements tents of a company's Customer Relationship Management, (CRM) strategy In tins study, two strategies are investigated to increase the lift. performance of ensemble classification models, i.e (1) using probability estimation trees (PETs) instead of standard decision trees as base classifiers; and (n) implementing alternative fusion rules based on lift weights lot the combination of ensemble member's outputs Experiments ale conducted lot font popular ensemble strategics on five real-life chin n data sets In general, the results demonstrate how lift performance can be substantially improved by using alternative base classifiers and fusion tides However: the effect vanes lot the (Idol cut ensemble strategies lit particular, the results indicate an increase of lift performance of (1) Bagging by implementing C4 4 base classifiets. (n) the Random Subspace Method (RSM) by using lift-weighted fusion rules, and (in) AdaBoost, by implementing both

An empirical evaluation of imbalanced data strategies from a practitioner's point of view

This research tested the following well known strategies to deal with binary imbalanced data on 82 different real life data sets (sampled to imbalance rates of 5%, 3%, 1%, and 0.1%): class weight, SMOTE, Underbagging, and a baseline (just the base classifier). As base classifiers we used SVM with RBF kernel, random forests, and gradient boosting machines and we measured the quality of the resulting classifier using 6 different metrics (Area under the curve, Accuracy, F-measure, G-mean, Matthew's correlation coefficient and Balanced accuracy). The best strategy strongly depends on the metric used to measure the quality of the classifier. For AUC and accuracy class weight and the baseline perform better; for F-measure and MCC, SMOTE performs better; and for G-mean and balanced accuracy, underbagging