BART Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression method, introduced by Chipman, George, and McCulloch (2006, 2010). It defines a prior distribution over the space of functions by representing them as a sum of binary decision trees, and then specifying a stochastic tree generation process. The posterior is then obtained with Metropolis-Gibbs sampling over the trees. See Hill, Linero, and Murray (2020) for a review, and Daniels, Linero, and Roy (2023, ch. 5) for a textbook treatment. BART's success BART has proven empirically effective, and is gaining popularity (consider, e.g., Tan and Roy 2019). The Atlantic Causal Inference Conference (ACIC) Data Challenge has confirmed BART as one of the best regression methods for causal inference (Dorie et al. 2019; Gruber et al. 2019; Hahn, Dorie, and Murray 2019; Thal and Finucane 2023). Many BART variants have been developed throughout the years, adding features such as variable selection (Linero 2018).

Traditional decision trees are limited by axis-orthogonal splits, which can perform poorly when true decision boundaries are oblique. While oblique decision tree methods address this limitation, they often face high computational costs, difficulties with multi-class classification, and a lack of effective feature selection. In this paper, we introduce LDATree and FoLDTree, two novel frameworks that integrate Uncorrelated Linear Discriminant Analysis (ULDA) and Forward ULDA into a decision tree structure. These methods enable efficient oblique splits, handle missing values, support feature selection, and provide both class labels and probabilities as model outputs. Through evaluations on simulated and real-world datasets, LDATree and FoLDTree consistently outperform axis-orthogonal and other oblique decision tree methods, achieving accuracy levels comparable to the random forest.

Many agencies have adopted the FHWA-recommended systemic approach to traffic safety, an essential supplement to the traditional hotspot crash analysis which develops region-wide safety projects based on identified risk factors. However, this approach narrows analysis to specific crash and facility types. This specification causes inefficient use of crash and inventory data as well as non-comprehensive risk evaluation and countermeasure selection for each location. To improve the comprehensiveness of the systemic approach to safety, we develop an enhanced process, ROADFIRST, that allows users to identify potential crash types and contributing factors at any location. As the knowledge base for such a process, crash types and contributing factors are analyzed with respect to features of interest, including both dynamic and static traffic-related features, using Random Forest and analyzed with the SHapley Additive exPlanations (SHAP) analysis. We identify and rank features impacting the likelihood of three sample contributing factors, namely alcohol-impaired driving, distracted driving, and speeding, according to crash and road inventory data from North Carolina, and quantify state-wide road segment risk for each contributing factor. The introduced models and methods serve as a sample for the further development of ROADFIRST by state and local agencies, which benefits the planning of more comprehensive region-wide safety improvement projects.

The sports betting industry has experienced rapid growth, driven largely by technological advancements and the proliferation of online platforms. Machine learning (ML) has played a pivotal role in the transformation of this sector by enabling more accurate predictions, dynamic odds-setting, and enhanced risk management for both bookmakers and bettors. This systematic review explores various ML techniques, including support vector machines, random forests, and neural networks, as applied in different sports such as soccer, basketball, tennis, and cricket. These models utilize historical data, in-game statistics, and real-time information to optimize betting strategies and identify value bets, ultimately improving profitability. For bookmakers, ML facilitates dynamic odds adjustment and effective risk management, while bettors leverage data-driven insights to exploit market inefficiencies. This review also underscores the role of ML in fraud detection, where anomaly detection models are used to identify suspicious betting patterns. Despite these advancements, challenges such as data quality, real-time decision-making, and the inherent unpredictability of sports outcomes remain. Ethical concerns related to transparency and fairness are also of significant importance. Future research should focus on developing adaptive models that integrate multimodal data and manage risk in a manner akin to financial portfolios. This review provides a comprehensive examination of the current applications of ML in sports betting, and highlights both the potential and the limitations of these technologies.

Decision Trees have remained a popular machine learning method for tabular datasets, mainly due to their interpretability. However, they lack the expressiveness needed to handle highly nonlinear or unstructured datasets. Motivated by recent advances in tree-based machine learning (ML) techniques and first-order optimization methods, we introduce Generalized Soft Trees (GSTs), which extend soft decision trees (STs) and are capable of processing images directly. We demonstrate their advantages with respect to tractability, performance, and interpretability. We develop a tractable approach to growing GSTs, given by the DeepTree algorithm, which, in addition to new regularization terms, produces high-quality models with far fewer nodes and greater interpretability than traditional soft trees. We test the performance of our GSTs on benchmark tabular and image datasets, including MIMIC-IV, MNIST, Fashion MNIST, CIFAR-10 and Celeb-A. We show that our approach outperforms other popular tree methods (CART, Random Forests, XGBoost) in almost all of the datasets, with Convolutional Trees having a significant edge in the hardest CIFAR-10 and Fashion MNIST datasets. Finally, we explore the interpretability of our GSTs and find that even the most complex GSTs are considerably more interpretable than deep neural networks. Overall, our approach of Generalized Soft Trees provides a tractable method that is high-performing on (un)structured datasets and preserves interpretability more than traditional deep learning methods.

Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression technique of rising fame. It is a sum-of-decision-trees model, and is in some sense the Bayesian version of boosting. In the limit of infinite trees, it becomes equivalent to Gaussian process (GP) regression. This limit is known but has not yet led to any useful analysis or application. For the first time, I derive and compute the exact BART prior covariance function. With it I implement the infinite trees limit of BART as GP regression. Through empirical tests, I show that this limit is worse than standard BART in a fixed configuration, but also that tuning the hyperparameters in the natural GP way yields a competitive method, although a properly tuned BART is still superior. The advantage of using a GP surrogate of BART is the analytical likelihood, which simplifies model building and sidesteps the complex BART MCMC. More generally, this study opens new ways to understand and develop BART and GP regression. The implementation of BART as GP is available in the Python package https://github.com/Gattocrucco/lsqfitgp .

Data stream learning is a very relevant paradigm because of the increasing real-world scenarios generating data at high velocities and in unbounded sequences. Stream learning aims at developing models that can process instances as they arrive, so models constantly adapt to new concepts and the temporal evolution in the stream. In multi-label data stream environments where instances have the peculiarity of belonging simultaneously to more than one class, the problem becomes even more complex and poses unique challenges such as different concept drifts impacting different labels at simultaneous or distinct times, higher class imbalance, or new labels emerging in the stream. This paper proposes a novel approach to multi-label data stream classification called Multi-Label Hoeffding Adaptive Tree (MLHAT). MLHAT leverages the Hoeffding adaptive tree to address these challenges by considering possible relations and label co-occurrences in the partitioning process of the decision tree, dynamically adapting the learner in each leaf node of the tree, and implementing a concept drift detector that can quickly detect and replace tree branches that are no longer performing well. The proposed approach is compared with other 18 online multi-label classifiers on 41 datasets. The results, validated with statistical analysis, show that MLHAT outperforms other state-of-the-art approaches in 12 well-known multi-label metrics.

Random Forests have been one of the most popular bagging methods in the past few decades, especially due to their success at handling tabular datasets. They have been extensively studied and compared to boosting models, like XGBoost, which are generally considered more performant. Random Forests adopt several simplistic assumptions, such that all samples and all trees that form the forest are equally important for building the final model. We introduce Enhanced Random Forests, an extension of vanilla Random Forests with extra functionalities and adaptive sample and model weighting. We develop an iterative algorithm for adapting the training sample weights, by favoring the hardest examples, and an approach for finding personalized tree weighting schemes for each new sample. Our method significantly improves upon regular Random Forests across 15 different binary classification datasets and considerably outperforms other tree methods, including XGBoost, when run with default hyperparameters, which indicates the robustness of our approach across datasets, without the need for extensive hyperparameter tuning. Our tree-weighting methodology results in enhanced or comparable performance to the uniformly weighted ensemble, and is, more importantly, leveraged to define importance scores for trees based on their contributions to classifying each new sample. This enables us to only focus on a small number of trees as the main models that define the outcome of a new sample and, thus, to partially recover interpretability, which is critically missing from both bagging and boosting methods. In binary classification problems, the proposed extensions and the corresponding results suggest the equivalence of bagging and boosting methods in performance, and the edge of bagging in interpretability by leveraging a few learners of the ensemble, which is not an option in the less explainable boosting methods.

Tree ensemble models like random forests and gradient boosting machines are widely used in machine learning due to their excellent predictive performance. However, a high-performance ensemble consisting of a large number of decision trees lacks sufficient transparency and explainability. In this paper, we demonstrate that when shallow decision trees are used as base learners, the ensemble learning algorithms can not only become inherently interpretable subject to an equivalent representation as the generalized additive models but also sometimes lead to better generalization performance. First, an interpretation algorithm is developed that converts the tree ensemble into the functional ANOVA representation with inherent interpretability. Second, two strategies are proposed to further enhance the model interpretability, i.e., by adding constraints in the model training stage and post-hoc effect pruning. Experiments on simulations and real-world datasets show that our proposed methods offer a better trade-off between model interpretation and predictive performance, compared with its counterpart benchmarks.

Random forest (RF) stands out as a highly favored machine learning approach for classification problems. The effectiveness of RF hinges on two key factors: the accuracy of individual trees and the diversity among them. In this study, we introduce a novel approach called heterogeneous RF (HRF), designed to enhance tree diversity in a meaningful way. This diversification is achieved by deliberately introducing heterogeneity during the tree construction. Specifically, features used for splitting near the root node of previous trees are assigned lower weights when constructing the feature sub-space of the subsequent trees. As a result, dominant features in the prior trees are less likely to be employed in the next iteration, leading to a more diverse set of splitting features at the nodes. Through simulation studies, it was confirmed that the HRF method effectively mitigates the selection bias of trees within the ensemble, increases the diversity of the ensemble, and demonstrates superior performance on datasets with fewer noise features. To assess the comparative performance of HRF against other widely adopted ensemble methods, we conducted tests on 52 datasets, comprising both real-world and synthetic data. HRF consistently outperformed other ensemble methods in terms of accuracy across the majority of datasets.