The success of boosted classifiers is most often attributed to improvements in margins.

Tree-boosting is a widely used machine learning technique for tabular data. However, its out-of-sample accuracy is critically dependent on multiple hyperparameters. In this article, we empirically compare several popular methods for hyperparameter optimization for tree-boosting including random grid search, the tree-structured Parzen estimator (TPE), Gaussian-process-based Bayesian optimization (GP-BO), Hyperband, the sequential model-based algorithm configuration (SMAC) method, and deterministic full grid search using $59$ regression and classification data sets. We find that the SMAC method clearly outperforms all the other considered methods. We further observe that (i) a relatively large number of trials larger than $100$ is required for accurate tuning, (ii) using default values for hyperparameters yields very inaccurate models, (iii) all considered hyperparameters can have a material effect on the accuracy of tree-boosting, i.e., there is no small set of hyperparameters that is more important than others, and (iv) choosing the number of boosting iterations using early stopping yields more accurate results compared to including it in the search space for regression tasks.

We propose Partition Trees, a tree-based framework for conditional density estimation over general outcome spaces, supporting both continuous and categorical variables within a unified formulation. Our approach models conditional distributions as piecewise-constant densities on data adaptive partitions and learns trees by directly minimizing conditional negative log-likelihood. This yields a scalable, nonparametric alternative to existing probabilistic trees that does not make parametric assumptions about the target distribution. We further introduce Partition Forests, an ensemble extension obtained by averaging conditional densities. Empirically, we demonstrate improved probabilistic prediction over CART-style trees and competitive or superior performance compared to state-of-the-art probabilistic tree methods and Random Forests, along with robustness to redundant features and heteroscedastic noise.

Random Forests (RF) are among the most powerful and widely used predictive models for centralized tabular data, yet few methods exist to adapt them to the federated learning setting. Unlike most federated learning approaches, the piecewise-constant nature of RF prevents exact gradient-based optimization. As a result, existing federated RF implementations rely on unprincipled heuristics: for instance, aggregating decision trees trained independently on clients fails to optimize the global impurity criterion, even under simple distribution shifts. We propose FedForest, a new federated RF algorithm for horizontally partitioned data that naturally accommodates diverse forms of client data heterogeneity, from covariate shift to more complex outcome shift mechanisms. We prove that our splitting procedure, based on aggregating carefully chosen client statistics, closely approximates the split selected by a centralized algorithm. Moreover, FedForest allows splits on client indicators, enabling a non-parametric form of personalization that is absent from prior federated random forest methods. Empirically, we demonstrate that the resulting federated forests closely match centralized performance across heterogeneous benchmarks while remaining communication-efficient.

The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the paired sampling heuristic to reduce estimation error, the theoretical mechanism driving this improvement has remained opaque. In this work, we provide an elegant and fundamental justification for paired sampling: we prove that the Shapley value depends exclusively on the odd component of the set function, and that paired sampling orthogonalizes the regression objective to filter out the irrelevant even component. Leveraging this insight, we propose OddSHAP, a novel consistent estimator that performs polynomial regression solely on the odd subspace. By utilizing the Fourier basis to isolate this subspace and employing a proxy model to identify high-impact interactions, OddSHAP overcomes the combinatorial explosion of higher-order approximations. Through an extensive benchmark evaluation, we find that OddSHAP achieves state-of-the-art estimation accuracy.

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal mean squared error for fitting Lipschitz GAMs with $p$ features at rate $O(pn^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs.

Estimating Heterogeneous Treatment Effects (HTE) in industrial applications such as AdTech and healthcare presents a dual challenge: extreme class imbalance and heavy-tailed outcome distributions. While the X-Learner framework effectively addresses imbalance through cross-imputation, we demonstrate that it is fundamentally vulnerable to "Outlier Smearing" when reliant on Mean Squared Error (MSE) minimization. In this failure mode, the bias from a few extreme observations ("whales") in the minority group is propagated to the entire majority group during the imputation step, corrupting the estimated treatment effect structure. To resolve this, we propose the Robust X-Learner (RX-Learner). This framework integrates a redescending γ-divergence objective -- structurally equivalent to the Welsch loss under Gaussian assumptions -- into the gradient boosting machinery. We further stabilize the non-convex optimization using a Proxy Hessian strategy grounded in Majorization-Minimization (MM) principles. Empirical evaluation on a semi-synthetic Criteo Uplift dataset demonstrates that the RX-Learner reduces the Precision in Estimation of Heterogeneous Effect (PEHE) metric by 98.6% compared to the standard X-Learner, effectively decoupling the stable "Core" population from the volatile "Periphery".

This paper establishes a rigorous theoretical foundation for the function class implicitly learned by XGBoost, bridging the gap between its empirical success and our theoretical understanding. We introduce an infinite-dimensional function class $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ that extends finite ensembles of bounded-depth regression trees, together with a complexity measure $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ that generalizes the $L^1$ regularization penalty used in XGBoost. We show that every optimizer of the XGBoost objective is also an optimizer of an equivalent penalized regression problem over $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ with penalty $V^{d, s}_{\infty-\text{XGB}}(\cdot)$, providing an interpretation of XGBoost as implicitly targeting a broader function class. We also develop a smoothness-based interpretation of $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ and $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ in terms of Hardy--Krause variation. We prove that the least squares estimator over $\{f \in \mathcal{F}^{d, s}_{\infty-\text{ST}}: V^{d, s}_{\infty-\text{XGB}}(f) \le V\}$ achieves a nearly minimax-optimal rate of convergence $n^{-2/3} (\log n)^{4(\min(s, d) - 1)/3}$, thereby avoiding the curse of dimensionality. Our results provide the first rigorous characterization of the function space underlying XGBoost, clarify its connection to classical notions of variation, and identify an important open problem: whether the XGBoost algorithm itself achieves minimax optimality over this class.