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

Robust Decision Trees Against Adversarial Examples

Although adversarial examples and model robustness have been extensively studied in the context of linear models and neural networks, research on this issue in tree-based models and how to make tree-based models robust against adversarial examples is still limited. In this paper, we show that tree based models are also vulnerable to adversarial examples and develop a novel algorithm to learn robust trees. At its core, our method aims to optimize the performance under the worst-case perturbation of input features, which leads to a max-min saddle point problem. Incorporating this saddle point objective into the decision tree building procedure is non-trivial due to the discrete nature of trees --- a naive approach to finding the best split according to this saddle point objective will take exponential time. To make our approach practical and scalable, we propose efficient tree building algorithms by approximating the inner minimizer in this saddle point problem, and present efficient implementations for classical information gain based trees as well as state-of-the-art tree boosting models such as XGBoost. Experimental results on real world datasets demonstrate that the proposed algorithms can substantially improve the robustness of tree-based models against adversarial examples

Cascading Randomized Weighted Majority: A New Online Ensemble Learning Algorithm

With the increasing volume of data in the world, the best approach for learning from this data is to exploit an online learning algorithm. Online ensemble methods are online algorithms which take advantage of an ensemble of classifiers to predict labels of data. Prediction with expert advice is a well-studied problem in the online ensemble learning literature. The Weighted Majority algorithm and the randomized weighted majority (RWM) are the most well-known solutions to this problem, aiming to converge to the best expert. Since among some expert, the best one does not necessarily have the minimum error in all regions of data space, defining specific regions and converging to the best expert in each of these regions will lead to a better result. In this paper, we aim to resolve this defect of RWM algorithms by proposing a novel online ensemble algorithm to the problem of prediction with expert advice. We propose a cascading version of RWM to achieve not only better experimental results but also a better error bound for sufficiently large datasets.Comment: 15 pages, 3 figure

Predicting diabetes-related hospitalizations based on electronic health records

OBJECTIVE: To derive a predictive model to identify patients likely to be hospitalized during the following year due to complications attributed to Type II diabetes. METHODS: A variety of supervised machine learning classification methods were tested and a new method that discovers hidden patient clusters in the positive class (hospitalized) was developed while, at the same time, sparse linear support vector machine classifiers were derived to separate positive samples from the negative ones (non-hospitalized). The convergence of the new method was established and theoretical guarantees were proved on how the classifiers it produces generalize to a test set not seen during training. RESULTS: The methods were tested on a large set of patients from the Boston Medical Center - the largest safety net hospital in New England. It is found that our new joint clustering/classification method achieves an accuracy of 89% (measured in terms of area under the ROC Curve) and yields informative clusters which can help interpret the classification results, thus increasing the trust of physicians to the algorithmic output and providing some guidance towards preventive measures. While it is possible to increase accuracy to 92% with other methods, this comes with increased computational cost and lack of interpretability. The analysis shows that even a modest probability of preventive actions being effective (more than 19%) suffices to generate significant hospital care savings. CONCLUSIONS: Predictive models are proposed that can help avert hospitalizations, improve health outcomes and drastically reduce hospital expenditures. The scope for savings is significant as it has been estimated that in the USA alone, about $5.8 billion are spent each year on diabetes-related hospitalizations that could be prevented.Accepted manuscrip

Boosting as a Product of Experts

In this paper, we derive a novel probabilistic model of boosting as a Product of Experts. We re-derive the boosting algorithm as a greedy incremental model selection procedure which ensures that addition of new experts to the ensemble does not decrease the likelihood of the data. These learning rules lead to a generic boosting algorithm - POE- Boost which turns out to be similar to the AdaBoost algorithm under certain assumptions on the expert probabilities. The paper then extends the POEBoost algorithm to POEBoost.CS which handles hypothesis that produce probabilistic predictions. This new algorithm is shown to have better generalization performance compared to other state of the art algorithms