This paper proposes a new algorithm for learning gradient boosted decision trees while ensuring the existence of recourse actions. Algorithmic recourse aims to provide a recourse action for altering the undesired prediction result given by a model. While existing studies often focus on extracting valid and executable actions from a given learned model, such reasonable actions do not always exist for models optimized solely for predictive accuracy. To address this issue, recent studies proposed a framework for learning a model while guaranteeing the existence of reasonable actions with high probability. However, these methods can not be applied to gradient boosted decision trees, which are renowned as one of the most popular models for tabular datasets. We propose an efficient gradient boosting algorithm that takes recourse guarantee into account, while maintaining the same time complexity as the standard ones. We also propose a post-processing method for refining a learned model under the constraint of a recourse guarantee and provide a PAC-style analysis of the refined model. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifoldvalued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fréchet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and realworld applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.

Tree ensembles have demonstrated state-of-the-art predictive performance across a wide range of problems involving tabular data. Nevertheless, the black-box nature of tree ensembles is a strong limitation, especially for applications with critical decisions at stake. The Hoeffding or ANOVA functional decomposition is a powerful explainability method, as it breaks down black-box models into a unique sum of lower-dimensional functions, provided that input variables are independent. In standard learning settings, input variables are often dependent, and the Hoeffding decomposition is generalized through hierarchical orthogonality constraints. Such generalization leads to unique and sparse decompositions with well-defined main effects and interactions. However, the practical estimation of this decomposition from a data sample is still an open problem. Therefore, we introduce the TreeHFD algorithm to estimate the Hoeffding decomposition of a tree ensemble from a data sample. We show the convergence of TreeHFD, along with the main properties of orthogonality, sparsity, and causal variable selection.

Class-imbalanced learning (CIL) on tabular data is important in many realworld applications where the minority class holds the critical but rare outcomes.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure called Boulevard that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance in only O(nd2) time with the Nystr om method. Numerical experiments verify the asymptotic normality and demonstrate that our algorithms perform well, do not require early stopping, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

Since the seminal work of TabPFN [16], research on tabular foundation models (TFMs) based on in-context learning (ICL) has challenged long-standing paradigms in machine learning. Without seeing any real-world data, models pretrained on purely synthetic datasets generalize remarkably well across diverse datasets, often using only a moderate number of in-context examples. This shifts the focus in tabular machine learning from model architecture design to the design of synthetic datasets, or, more precisely, to the prior distributions that generate them. Yet the guiding principles for prior design remain poorly understood. This work marks the first attempt to address the gap. We systematically investigate and identify key properties of synthetic priors that allow pretrained TFMs to generalize well. Based on these insights, we introduce MITRA 1, a TFM trained on a curated mixture of synthetic priors selected for their diversity, distinctiveness, and performance on real-world tabular data. MITRA consistently outperforms state-of-the-art TFMs, such as TabPFNv2 [17] and TabICL [29], across both classification and regression benchmarks, with better sample efficiency.

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on ensembling. By selecting the most frequently generated model from the base learner when repeatedly applied to subsamples, we can attain exponentially decaying tails for the excess risk, even if the base learner suffers from slow (i.e., polynomial) decay rates. This tail enhancement power of ensembling applies to base learners that have reasonable predictive power to begin with and is stronger than variance reduction in the sense of exhibiting rate improvement. We demonstrate how our ensemble methods can substantially improve out-of-sample performances in a range of numerical examples involving heavy-tailed data or intrinsically slow rates.

This paper proposes a new algorithm for learning gradient boosted decision trees while ensuring the existence of recourse actions. Algorithmic recourse aims to provide a recourse action for altering the undesired prediction result given by a model. While existing studies often focus on extracting valid and executable actions from a given learned model, such reasonable actions do not always exist for models optimized solely for predictive accuracy. To address this issue, recent studies proposed a framework for learning a model while guaranteeing the existence of reasonable actions with high probability. However, these methods can not be applied to gradient boosted decision trees, which are renowned as one of the most popular models for tabular datasets. We propose an efficient gradient boosting algorithm that takes recourse guarantee into account, while maintaining the same time complexity as the standard ones. We also propose a post-processing method for refining a learned model under the constraint of a recourse guarantee and provide a PAC-style analysis of the refined model. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure called Boulevard that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that \textit{increasing} the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance in only $O(nd^2)$ time with the Nyström method. Numerical experiments verify the asymptotic normality and demonstrate that our algorithms perform well, do not require early stopping, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

The global uniform aggregation of random forests leaves conditional bias along the decision boundary uncorrected. To correct this locally, we propose exploiting the structural pattern of each tree's decision path. At inference, a random forest reaches its prediction through the root-to-leaf path the sample traverses in each tree, so path-level reliability offers a finer granularity than tree-level weighting can access. We show that reliability varies meaningfully across path patterns in the boundary region identified by the forest itself, and that using this signal yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks (Wilcoxon p < 0.0001). We further devise a way to measure the sufficiency of residual information in the fitted RF's decision boundary, providing an estimate of the expected gain before the method is applied; on the qualifying group identified this way, the method delivers a mean +0.99 pp accuracy improvement with strict wins on every dataset (7/0/0). Class-recall regression -- the typical failure mode of RF correction methods -- is measured: zero minority-recall regressions and a single majority-recall regression at the 0.2 pp threshold, indicating that the correction operates in the direction of bias reduction rather than class trade-off. Our work suggests that the structural information of decision paths, previously overlooked in random forest research, can contribute to RF performance improvement.