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

RandomBoost: Simplified Multi-class Boosting through Randomization

We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.Comment: 15 page

Active Learning Strategies for Technology Assisted Sensitivity Review

Government documents must be reviewed to identify and protect any sensitive information, such as personal information, before the documents can be released to the public. However, in the era of digital government documents, such as e-mail, traditional sensitivity review procedures are no longer practical, for example due to the volume of documents to be reviewed. Therefore, there is a need for new technology assisted review protocols to integrate automatic sensitivity classification into the sensitivity review process. Moreover, to effectively assist sensitivity review, such assistive technologies must incorporate reviewer feedback to enable sensitivity classifiers to quickly learn and adapt to the sensitivities within a collection, when the types of sensitivity are not known a priori. In this work, we present a thorough evaluation of active learning strategies for sensitivity review. Moreover, we present an active learning strategy that integrates reviewer feedback, from sensitive text annotations, to identify features of sensitivity that enable us to learn an effective sensitivity classifier (0.7 Balanced Accuracy) using significantly less reviewer effort, according to the sign test (p < 0.01 ). Moreover, this approach results in a 51% reduction in the number of documents required to be reviewed to achieve the same level of classification accuracy, compared to when the approach is deployed without annotation features