Class imbalance poses a major challenge in different classification tasks, which is a frequently occurring scenario in many real-world applications. Data resampling is considered to be the standard approach to address this issue. The goal of the technique is to balance the class distribution by generating new samples or eliminating samples from the data. A wide variety of sampling techniques have been proposed over the years to tackle this challenging problem. Sampling techniques can also be incorporated into the ensemble learning framework to obtain more generalized prediction performance. Balanced Random Forest (BRF) and SMOTE-Bagging are some of the popular ensemble approaches. In this study, we propose a modification to the BRF classifier to enhance the prediction performance. In the original algorithm, the Random Undersampling (RUS) technique was utilized to balance the bootstrap samples. However, randomly eliminating too many samples from the data leads to significant data loss, resulting in a major decline in performance. We propose to alleviate the scenario by incorporating a novel hybrid sampling approach to balance the uneven class distribution in each bootstrap sub-sample. Our proposed hybrid sampling technique, when incorporated into the framework of the Random Forest classifier, termed as iBRF: improved Balanced Random Forest classifier, achieves better prediction performance than other sampling techniques used in imbalanced classification tasks. Experiments were carried out on 44 imbalanced datasets on which the original BRF classifier produced an average MCC score of 47.03% and an F1 score of 49.09%. Our proposed algorithm outperformed the approach by producing a far better MCC score of 53.04% and an F1 score of 55%. The results obtained signify the superiority of the iBRF algorithm and its potential to be an effective sampling technique in imbalanced learning.

We derive Gaussian approximation bounds for random forest predictions based on a set of training points given by a Poisson process, under fairly mild regularity assumptions on the data generating process. Our approach is based on the key observation that the random forest predictions satisfy a certain geometric property called region-based stabilization. In the process of developing our results for the random forest, we also establish a probabilistic result, which might be of independent interest, on multivariate Gaussian approximation bounds for general functionals of Poisson process that are region-based stabilizing. This general result makes use of the Malliavin-Stein method, and is potentially applicable to various related statistical problems.

Summary of the paper: This paper revisits the idea of decision DAGs for classification. Unlike a decision tree, a decision DAG is able to merge nodes at each layer, preventing the tree from growing exponentially with depth. This represents an alternative to decision-trees utilizing pruning methods as a means of controlling model size and preventing overfitting. The paper casts learning with this model as an empirical risk minimization problem, where the idea is to learn both the DAG structure along with the split parameters of each node. Two algorithms are presented to learn the structure and parameters in a greedy layer-wise manner using an information-gain based objective.

Randomized decision trees and forests have a rich history in machine learning and have seen considerable success in application, perhaps particularly so for computer vision. However, they face a fundamental limitation: given enough data, the number of nodes in decision trees will grow exponentially with depth. For certain applications, for example on mobile or embedded processors, memory is a limited resource, and so the exponential growth of trees limits their depth, and thus their potential accuracy. This paper proposes decision jungles, revisiting the idea of ensembles of rooted decision directed acyclic graphs (DAGs), and shows these to be compact and powerful discriminative models for classification. Unlike conventional decision trees that only allow one path to every node, a DAG in a decision jungle allows multiple paths from the root to each leaf. We present and compare two new node merging algorithms that jointly optimize both the features and the structure of the DAGs efficiently. During training, node splitting and node merging are driven by the minimization of exactly the same objective function, here the weighted sum of entropies at the leaves. Results on varied datasets show that, compared to decision forests and several other baselines, decision jungles require dramatically less memory while considerably improving generalization.

We consider the problem of maintaining the data-structures of a partition-based regression procedure in a setting where the training data arrives sequentially over time.

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 retrained 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 study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing logarithmic depth trees. On the theoretical front, we formulate a new objective function, which is optimized at each node of the tree and creates dynamic partitions of the data which are both pure (in terms of class labels) and balanced. We demonstrate that under favorable conditions, we can construct logarithmic depth trees that have leaves with low label entropy. However, the objective function at the nodes is challenging to optimize computationally. We address the empirical problem with a new online decision tree construction procedure. Experiments demonstrate that this online algorithm quickly achieves improvement in test error compared to more common logarithmic training time approaches, which makes it a plausible method in computationally constrained large-k applications.

Decision trees and randomized forests are widely used in computer vision and machine learning.

Deep distributed decision trees and tree ensembles have grown in importance due to the need to model increasingly large datasets.