It is assumed that Si are sorted in increasing order of s(Si). Non-linearities of four trees are shown in Figure 6. Ti is absolutely linear; thus its non-linearity measure is zero. T2 is very close to being a balanced tree: non-linearity one. T3 is preferred to T4, i.e. this function is sensitive to the location of non-linearity within a tree (the lower a non-linearity occurs in a tree the lower (better) its measure).

Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for real-world prediction tasks. The most popular random forest variants (such as Breiman's random forest and extremely randomized trees) operate on batches of training data. Online methods are now in greater demand. Existing online random forests, however, require more training data than their batch counterpart to achieve comparable predictive performance. In this work, we use Mondrian processes (Roy and Teh, 2009) to construct ensembles of random decision trees we call Mondrian forests. Mondrian forests can be grown in an incremental/online fashion and remarkably, the distribution of online Mondrian forests is the same as that of batch Mondrian forests. Mondrian forests achieve competitive predictive performance comparable with existing online random forests and periodically re-trained batch random forests, while being more than an order of magnitude faster, thus representing a better computation vs accuracy tradeoff.

Even with the advent of more sophisticated, data-hungry methods, boosted decision trees remain extraordinarily successful for fast rigid object detection, achieving top accuracy on numerous datasets. While effective, most boosted detectors use decision trees with orthogonal (single feature) splits, and the topology of the resulting decision boundary may not be well matched to the natural topology of the data. Given highly correlated data, decision trees with oblique (multiple feature) splits can be effective. Use of oblique splits, however, comes at considerable computational expense. Inspired by recent work on discriminative decorrelation of HOG features, we instead propose an efficient feature transform that removes correlations in local neighborhoods. The result is an overcomplete but locally decorrelated representation ideally suited for use with orthogonal decision trees. In fact, orthogonal trees with our locally decorrelated features outperform oblique trees trained over the original features at a fraction of the computational cost. The overall improvement in accuracy is dramatic: on the Caltech Pedestrian Dataset, we reduce false positives nearly tenfold over the previous state-of-the-art.

We present new ensemble learning algorithms for multi-class classification. Our algorithms can use as a base classifier set a family of deep decision trees or other rich or complex families and yet benefit from strong generalization guarantees. We give new data-dependent learning bounds for convex ensembles in the multi-class classification setting expressed in terms of the Rademacher complexities of the sub-families composing the base classifier set, and the mixture weight assigned to each sub-family. These bounds are finer than existing ones both thanks to an improved dependency on the number of classes and, more crucially, by virtue of a more favorable complexity term expressed as an average of the Rademacher complexities based on the ensemble’s mixture weights. We introduce and discuss several new multi-class ensemble algorithms benefiting from these guarantees, prove positive results for the H-consistency of several of them, and report the results of experiments showing that their performance compares favorably with that of multi-class versions of AdaBoost and Logistic Regression and their L1-regularized counterparts.

Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity allows it to be used in hierarchical representation learning, the learned representations are local: Activation makes a soft selection among all root-to-leaf paths in a tree. In this work we extend the budding tree and propose the distributed tree where the children use different and independent splits and hence multiple paths in a tree can be traversed at the same time. This ability to combine multiple paths gives the power of a distributed representation, as in a traditional perceptron layer. We show that distributed trees perform comparably or better than budding and traditional hard trees on classification and regression tasks.

We present a new package in R implementing Bayesian additive regression trees (BART). The package introduces many new features for data analysis using BART such as variable selection, interaction detection, model diagnostic plots, incorporation of missing data and the ability to save trees for future prediction. It is significantly faster than the current R implementation, parallelized, and capable of handling both large sample sizes and high-dimensional data.

Random ferns is a machine learning algorithm proposed by [11] for matching same elements between two images of the same scene, allowing one to recognise certain objects or trace them on videos. The original motivation behind this method was to create a simple and efficient algorithm by extending the Naïve Bayes classifier; still the authors acknowledged its strong connection to the decision tree ensembles like the Random forest [2] algorithm. Since introduction, Random ferns have been applied in numerous computer vision application, like image recognition [1], action recognition [10] or augmented reality [14]. However, it has not gathered attention outside this field; thus, this work aims to bring this algorithm to a much wider spectrum of applications. In order to do that, I propose a generalised version of the algorithm, implemented as an R [13] package rFerns. The paper is organised as follows. Section 2 briefly recalls the Bayesian derivation of the original version of Random ferns, presents the decision tree ensemble interpretation of the algorithm and lists modifications leading to the rFerns variant.

With the increasing demand for personalization in clinical decision support system, one of the most challenging tasks is effective patient preferences elicitation. In the context of the MobiGuide project, within a medical application related to atrial fibrillation, a decision support system has been developed for both doctors and patients. In particular, we support shared decision-making, by integrating decision tree models with a dedicated tool for utility coefficients elicitation. In this paper we focus on the decision problem regarding the choice of anticoagulant therapy for low risk non-valvular atrial fibrillation patients. In addition to the traditional methods, such as time trade-off and standard gamble, an alternative way for preferences elicitation is proposed, exploiting patients’ self-reported data in health-related social media as the main source of information.

When digitizing a print bilingual dictionary, whether via optical character recognition or manual entry, it is inevitable that errors are introduced into the electronic version that is created. We investigate automating the process of detecting errors in an XML representation of a digitized print dictionary using a hybrid approach that combines rule-based, feature-based, and language model-based methods. We investigate combining methods and show that using random forests is a promising approach. We find that in isolation, unsupervised methods rival the performance of supervised methods. Random forests typically require training data so we investigate how we can apply random forests to combine individual base methods that are themselves unsupervised without requiring large amounts of training data. Experiments reveal empirically that a relatively small amount of data is sufficient and can potentially be further reduced through specific selection criteria.

We adapt the idea of random projections applied to the output space, so as to enhance tree-based ensemble methods in the context of multi-label classification. We show how learning time complexity can be reduced without affecting computational complexity and accuracy of predictions. We also show that random output space projections may be used in order to reach different bias-variance tradeoffs, over a broad panel of benchmark problems, and that this may lead to improved accuracy while reducing significantly the computational burden of the learning stage.