We study the robustness verification problem of tree based models, including random forest (RF) and gradient boosted decision tree (GBDT). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches cast this verification problem into a mixed integer linear programming (MILP) problem, which finds the minimal adversarial distortion in exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles the verification problem can be cast as a max-clique problem on a multi-partite boxicity graph. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we devise an efficient verification algorithm that can give tight lower bounds on robustness of decision tree ensembles, and allows iterative improvement and any-time termination. On RF/GBDT models trained on a variety of datasets, we significantly outperform the lower bounds obtained by relaxing the MILP formulation into a linear program (LP), and are hundreds times faster than solving MILPs to get the exact minimal adversarial distortion. Our proposed method is capable of giving tight robustness verification bounds on large GBDTs with hundreds of deep trees.

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. To address both points simultaneously, we propose using the kernel interpretation of tree ensembles as a Gaussian Process prior to obtain model variance estimates, and we develop a compatible optimization formulation for the acquisition function. The latter further allows us to seamlessly integrate known constraints to improve sampling efficiency by considering domain-knowledge in engineering settings and modeling search space symmetries, e.g., hierarchical relationships in neural architecture search. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.

We develop a simple and unified framework for nonlinear variable importance estimation that incorporates uncertainty in the prediction function and is compatible with a wide range of machine learning models (e.g., tree ensembles, kernel methods, neural networks, etc).

Tree ensembles are one of the most widely used model classes. However, these models are susceptible to adversarial examples, i.e., slightly perturbed examples that elicit a misprediction. There has been significant research on designing approaches to construct such examples for tree ensembles. But this is a computationally challenging problem that often must be solved a large number of times (e.g., for all examples in a training set). This is compounded by the fact that current approaches attempt to find such examples from scratch. In contrast, we exploit the fact that multiple similar problems are being solved. Specifically, our approach exploits the insight that adversarial examples for tree ensembles tend to perturb a consistent but relatively small set of features. We show that we can quickly identify this set of features and use this knowledge to speedup constructing adversarial examples.

Feature and Interaction Importance (FII) methods are essential in supervised learning for assessing the relevance of input variables and their interactions in complex prediction models. In many domains, such as personalized medicine, local interpretations for individual predictions are often required, rather than global scores summarizing overall feature importance. Random Forests (RFs) are widely used in these settings, and existing interpretability methods typically exploit tree structures and split statistics to provide model-specific insights. However, theoretical understanding of local FII methods for RF remains limited, making it unclear how to interpret high importance scores for individual predictions. We propose a novel, local, model-specific FII method that identifies frequent co-occurrences of features along decision paths, combining global patterns with those observed on paths specific to a given test point. We prove that our method consistently recovers the true local signal features and their interactions under a Locally Spike Sparse (LSS) model and also identifies whether large or small feature values drive a prediction. We illustrate the usefulness of our method and theoretical results through simulation studies and a real-world data example.

New York City reports over one hundred thousand motor vehicle collisions each year, creating substantial injury and public health burden. We present RaX-Crash, a resource efficient and explainable small model pipeline for structured injury severity prediction on the official NYC Motor Vehicle Collisions dataset. RaX-Crash integrates three linked tables with tens of millions of records, builds a unified feature schema in partitioned storage, and trains compact tree based ensembles (Random Forest and XGBoost) on engineered tabular features, which are compared against locally deployed small language models (SLMs) prompted with textual summaries. On a temporally held out test set, XGBoost and Random Forest achieve accuracies of 0.7828 and 0.7794, clearly outperforming SLMs (0.594 and 0.496); class imbalance analysis shows that simple class weighting improves fatal recall with modest accuracy trade offs, and SHAP attribution highlights human vulnerability factors, timing, and location as dominant drivers of predicted severity. Overall, RaX-Crash indicates that interpretable small model ensembles remain strong baselines for city scale injury analytics, while hybrid pipelines that pair tabular predictors with SLM generated narratives improve communication without sacrificing scalability.

Axis-aligned decision trees are fast and stable but struggle on datasets with rotated or interaction-dependent decision boundaries, where informative splits require linear combinations of features rather than single-feature thresholds. Oblique forests address this with per-node hyperplane splits, but at added computational cost and implementation complexity. We propose a simple alternative: JARF, Jacobian-Aligned Random Forests. Concretely, we first fit an axis-aligned forest to estimate class probabilities or regression outputs, compute finite-difference gradients of these predictions with respect to each feature, aggregate them into an expected Jacobian outer product that generalizes the expected gradient outer product (EGOP), and use it as a single global linear preconditioner for all inputs. This supervised preconditioner applies a single global rotation of the feature space, then hands the transformed data back to a standard axis-aligned forest, preserving off-the-shelf training pipelines while capturing oblique boundaries and feature interactions that would otherwise require many axis-aligned splits to approximate. The same construction applies to any model that provides gradients, though we focus on random forests and gradient-boosted trees in this work. On tabular classification and regression benchmarks, this preconditioning consistently improves axis-aligned forests and often matches or surpasses oblique baselines while improving training time. Our experimental results and theoretical analysis together indicate that supervised preconditioning can recover much of the accuracy of oblique forests while retaining the simplicity and robustness of axis-aligned trees.

Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized regression trees. In this paper, we develop a theoretical framework for analyzing such methods through Reproducing Kernel Hilbert Spaces (RKHSs) constructed on tree ensembles--more precisely, on the random partitions generated by randomized regression trees. We establish fundamental analytical properties of the resulting Random Forest kernel, including boundedness, continuity, and universality, and show that a Random Forest predictor can be characterized as the unique minimizer of a penalized empirical risk functional in this RKHS, providing a variational interpretation of ensemble learning. We further extend this perspective to the continuous-time formulation of Gradient Boosting introduced by Dombry and Duchamps (2024a,b), and demonstrate that it corresponds to a gradient flow on a Hilbert manifold induced by the Random Forest RKHS. A key feature of this framework is that both the kernel and the RKHS geometry are data-dependent, offering a theoretical explanation for the strong empirical performance of tree-based ensembles. Finally, we illustrate the practical potential of this approach by introducing a kernel principal component analysis built on the Random Forest kernel, which enhances the interpretability of ensemble models, as well as GVI, a new geometric variable importance criterion.

Multi-layered distributed representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision.