Bayesian Additive Regression Trees (BART) are a powerful semiparametric ensemble learning technique for modeling nonlinear regression functions. Although initially BART was proposed for predicting only continuous and binary response variables, over the years multiple extensions have emerged that are suitable for estimating a wider class of response variables (e.g. categorical and count data) in a multitude of application areas. In this paper we describe a Generalized framework for Bayesian trees and their additive ensembles where the response variable comes from an exponential family distribution and hence encompasses a majority of these variants of BART. We derive sufficient conditions on the response distribution, under which the posterior concentrates at a minimax rate, up to a logarithmic factor. In this regard our results provide theoretical justification for the empirical success of BART and its variants.

We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees, making HE-BART a non-parametric alternative to mixed effects models which avoids the need for the user to specify the structure of the random effects in the model, whilst maintaining the prediction and uncertainty calibration properties of standard BART. Using simulated and real-world examples, we demonstrate that this new extension yields superior predictions for many of the standard mixed effects models' example data sets, and yet still provides consistent estimates of the random effect variances. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.

We address a task of estimating sparse coefficients in linear regression when the covariates are drawn from an $L$-subexponential random vector, which belongs to a class of distributions having heavier tails than a Gaussian random vector. Prior works have tackled this issue by assuming that the covariates are drawn from an $L$-subexponential random vector and have established error bounds that resemble those derived for Gaussian random vectors. However, these previous methods require stronger conditions to derive error bounds than those employed for Gaussian random vectors. In the present paper, we present an error bound identical to that obtained for Gaussian random vectors, up to constant factors, without requiring stronger conditions, even when the covariates are drawn from an $L$-subexponential random vector. Somewhat interestingly, we utilize an $\ell_1$-penalized Huber regression, that is recognized for its robustness to heavy-tailed random noises, not covariates. We believe that the present paper reveals a new aspect of the $\ell_1$-penalized Huber regression.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

Algorithmic stability--that is, how perturbing training data influences a learned model--is fundamental to modern data analysis. In learning theory, certain forms of stability are necessary and sufficient for generalization (Bousquet and Elisseeff, 2002; Poggio et al., 2004; Shalev-Shwartz et al., 2010). In model selection, stability measures can reliably identify important features (Meinshausen and Bühlmann, 2010; Shah and Samworth, 2013; Ren et al., 2021). In scientific applications, stable methods promote reproducibility, a prerequisite for meaningful inference (Yu, 2013). In distribution-free prediction, stability is a key assumption for the validity of jackknife prediction intervals (Barber et al., 2021; Steinberger and Leeb, 2023). Anticipating various benefits of stability, Breiman (1996a,b) proposed bagging as an ensemble metaalgorithm to stabilize any base learning algorithm. Bagging, short for bootstrap aggregating, refits the base algorithm to many perturbations of the training data and averages the resulting predictions. Breiman's vision of bagging as off-the-shelf stabilizer motivates our main question: How stable is bagging on an arbitrary base algorithm, placing no assumptions on the data generating distribution? In this paper, we first answer this question for the case of base algorithms with bounded outputs and then show extensions to the unbounded case.

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem. Several iterative methods have been developed for tackling this class of problems. Alas, their convergence guarantees are either asymptotic for the upper-level objective, or the convergence rates are slow and sub-optimal. To address this issue, in this paper, we introduce a novel bilevel optimization method that locally approximates the solution set of the lower-level problem via a cutting plane, and then runs a conditional gradient update to decrease the upper-level objective. When the upper-level objective is convex, we show that our method requires ${\mathcal{O}}(\max\{1/\epsilon_f,1/\epsilon_g\})$ iterations to find a solution that is $\epsilon_f$-optimal for the upper-level objective and $\epsilon_g$-optimal for the lower-level objective. Moreover, when the upper-level objective is non-convex, our method requires ${\mathcal{O}}(\max\{1/\epsilon_f^2,1/(\epsilon_f\epsilon_g)\})$ iterations to find an $(\epsilon_f,\epsilon_g)$-optimal solution. We also prove stronger convergence guarantees under the H\"olderian error bound assumption on the lower-level problem. To the best of our knowledge, our method achieves the best-known iteration complexity for the considered class of bilevel problems.

This article presents a dataset of 10,917 news articles with hierarchical news categories collected between 1 January 2019 and 31 December 2019. We manually labeled the articles based on a hierarchical taxonomy with 17 first-level and 109 second-level categories. This dataset can be used to train machine learning models for automatically classifying news articles by topic. This dataset can be helpful for researchers working on news structuring, classification, and predicting future events based on released news.

As the availability, size and complexity of data have increased in recent years, machine learning (ML) techniques have become popular for modeling. Predictions resulting from applying ML models are often used for inference, decision-making, and downstream applications. A crucial yet often overlooked aspect of ML is uncertainty quantification, which can significantly impact how predictions from models are used and interpreted. Extreme Gradient Boosting (XGBoost) is one of the most popular ML methods given its simple implementation, fast computation, and sequential learning, which make its predictions highly accurate compared to other methods. However, techniques for uncertainty determination in ML models such as XGBoost have not yet been universally agreed among its varying applications. We propose enhancements to XGBoost whereby a modified quantile regression is used as the objective function to estimate uncertainty (QXGBoost). Specifically, we included the Huber norm in the quantile regression model to construct a differentiable approximation to the quantile regression error function. This key step allows XGBoost, which uses a gradient-based optimization algorithm, to make probabilistic predictions efficiently. QXGBoost was applied to create 90\% prediction intervals for one simulated dataset and one real-world environmental dataset of measured traffic noise. Our proposed method had comparable or better performance than the uncertainty estimates generated for regular and quantile light gradient boosting. For both the simulated and traffic noise datasets, the overall performance of the prediction intervals from QXGBoost were better than other models based on coverage width-based criterion.

Traffic congestion caused by non-recurring incidents such as vehicle crashes and debris is a key issue for Traffic Management Centers (TMCs). Clearing incidents in a timely manner is essential for improving safety and reducing delays and emissions for the traveling public. However, TMCs and other responders face a challenge in predicting the duration of incidents (until the roadway is clear), making decisions of what resources to deploy difficult. To address this problem, this research developed an analytical framework and end-to-end machine-learning solution for predicting incident duration based on information available as soon as an incident report is received. Quality predictions of incident duration can help TMCs and other responders take a proactive approach in deploying responder services such as tow trucks, maintenance crews or activating alternative routes. The predictions use a combination of classification and regression machine learning modules. The performance of the developed solution has been evaluated based on the Mean Absolute Error (MAE), or deviation from the actual incident duration as well as Area Under the Curve (AUC) and Mean Absolute Percentage Error (MAPE). The results showed that the framework significantly improved incident duration prediction compared to methods from previous research.

The principle of DEPENDENCY LENGTH MINIMIZATION, which seeks to keep syntactically related words close in a sentence, is thought to universally shape the structure of human languages for effective communication. However, the extent to which dependency length minimization is applied in human language systems is not yet fully understood. Preverbally, the placement of long-before-short constituents and postverbally, short-before-long constituents are known to minimize overall dependency length of a sentence. In this study, we test the hypothesis that placing only the shortest preverbal constituent next to the main-verb explains word order preferences in Hindi (a SOV language) as opposed to the global minimization of dependency length. We characterize this approach as a least-effort strategy because it is a cost-effective way to shorten all dependencies between the verb and its preverbal dependencies. As such, this approach is consistent with the bounded-rationality perspective according to which decision making is governed by "fast but frugal" heuristics rather than by a search for optimal solutions. Consistent with this idea, our results indicate that actual corpus sentences in the Hindi-Urdu Treebank corpus are better explained by the least effort strategy than by global minimization of dependency lengths. Additionally, for the task of distinguishing corpus sentences from counterfactual variants, we find that the dependency length and constituent length of the constituent closest to the main verb are much better predictors of whether a sentence appeared in the corpus than total dependency length. Overall, our findings suggest that cognitive resource constraints play a crucial role in shaping natural languages.