Tree Ensembles

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Sep 16, 2026econ.EM

Stable Policy Learning

In evidence-based policymaking, typically one experimental sample is observed, then a learned policy recommendation is implemented at scale. Policies learned from the experimental data can perform well in expected welfare, yet random sampling in the experiment can produce recommendations with poor welfare outcomes. In this paper, we ask: how should policy learning algorithms balance expected welfare against sampling risk? Our main contribution is to show that algorithmic stability plays a central role in characterizing and navigating the tradeoff. Intuitively, if a policy learning algorithm's recommendation remains stable when one experimental unit is replaced, then that algorithm has limited sampling risk. We propose a method for policy learning called policy-vote bagging, which learns treatment decisions on many subsamples then averages their votes into treatment probabilities. Relative to using one subsample, averaging across subsamples preserves expected welfare and improves expected utility for a risk-averse researcher. We derive sharp bounds linking estimation accuracy, subsample size, and welfare variation, including an exact guarantee under CARA utility.

Harvey Barnhard, Giacomo Opocher, Rahul Singh

Harvard University · University of Mannheim

Welfare Tree Ensembles

Aug 13, 2026stat.ML

Bagging Robustly Learns VC Classes with Linear Sample Complexity

We revisit the problem of learning predictors robust to adversarial examples at test-time. We prove that VC classes are adversarially robustly learnable with sample complexity linear in the VC dimension

d

, providing an exponential improvement over the previous upper bound of Montasser, Hanneke, and Srebro (2019). Remarkably, this result is achieved with a simple improper algorithm that combines the classic heuristic bagging (bootstrap aggregation) of Breiman (1996) with robust empirical risk minimization (RERM). Our algorithm computes RERMs on

O(d^\star)

independent bootstrap samples and outputs their majority vote, where

d^\star

denotes the dual VC dimension. We complement this result with a lower bound showing that this is unavoidable: in general, any learner in this oracle model requires

Ω(d^\star)

calls to an RERM oracle, even when given arbitrarily many training examples.

Omar Montasser

Yale University

Empirical Risk Minimization Tree Ensembles Adversarial Examples Sample Complexity Model-Based Bootstrap Voice Conversion

Jul 29, 2026stat.ML

Feature Bagging Provides Stability

We study feature bagging through the lens of algorithmic stability. Feature bagging is an ensemble strategy that aggregates base learners trained on randomly subsampled feature subsets, possibly in a data-dependent manner. We introduce feature instability (FI), the feature-axis analogue of instance instability (II), which measures sensitivity to removing a single feature. Smaller values of II or FI correspond to stronger stability, and our experiments show that FI captures generalization-relevant information complementary to II. Within this framework, we analyze feature bagging in both a parametric linear model and a model-free setting inspired by recursive feature subsampling in random forests. In both settings, we establish formal guarantees showing that feature bagging improves the relevant stability relative to its non-bagged counterpart, with larger improvements under more aggressive subsampling. We further show that a modest number of bagging rounds is sufficient to approach the infinite-bagging stability level.

Yuheng Ma, Qiang Sun

School of Statistics, East China Normal University · University of Toronto · MBZUAI

Tree Ensembles Random Forest Subsampling Instability

Jun 30, 2026cs.LG

Multistage Defer Trees for Hybrid Interpretability: If at First You Can't Succeed, Tree Again

Recent work has shown that well-optimized individual decision trees can match complex black box models in some settings, primarily in noisy domains. For the remaining settings, however, complex ensembled compositions of trees often achieve higher accuracy at the cost of interpretability, leaving practitioners with difficult modeling decisions along an accuracy-interpretability tradeoff. Ideally, we would like to classify as much of the data as possible with one or a small number of trees, achieving interpretability for most samples while maintaining state-of-the-art accuracy. We introduce Multistage Defer Trees: a sequence of sparse decision trees that each make predictions for most samples, while deferring a small proportion to the next tree in the sequence or, ultimately, to a black box. We demonstrate that we can train this model class to match the performance of complex tree-based ensembles while routing most samples through only one or a small number of sparse decision trees. We discuss a range of techniques for training these models while maintaining simplicity. Our method expands the accuracy--interpretability frontier in settings where single-tree methods remain insufficient, demonstrating that even when complex models are necessary, they need not be fully opaque.

Zakk Heile, Hayden McTavish, Margo Seltzer +1

Department of Computer Science · Duke University · Durham, USA +2

Decision Trees Tree Ensembles Interpretability Trees

Jun 29, 2026cs.LG

The Hidden Cost of Resampling: How Imbalance Correction Degrades Probability Calibration in Tree Ensembles

Resampling methods such as SMOTE and random under/over-sampling are standard tools for class-imbalanced classification, almost always evaluated by minority-class accuracy or F1. Prior work has established that undersampling degrades probability calibration by distorting the training prior [1]. We extend this lens to synthetic oversampling (SMOTE) and provide a practical, evidence-based guide to when calibration damage matters and how to fix it. Across five public datasets (imbalance ratio 1.9-70) and two ensemble models (random forest, gradient boosting), with ten seeds and paired statistics, we find: (1) SMOTE's calibration cost is real but small (ECE +0.009; Cliff's delta = +0.27, small-to-moderate) across the studied imbalance range (IR 1.9-70) and its discrimination gains typically outweigh the calibration penalty; (2) random undersampling is the genuine danger -- its damage grows sharply with imbalance, inflating ECE from 0.008 to 0.395 on a dataset with ratio 70, largely because the resulting training sets are too small to estimate probabilities reliably; (3) a single post-hoc recalibration step (Platt or isotonic) eliminates the damage, reducing ECE by up to 66% at a negligible ranking-power cost (AUC -0.002, Cliff's delta = -0.07); and (4) the analytic prior-shift correction that repairs undersampling does not transfer to SMOTE, because SMOTE distorts the class-conditional density rather than only the prior -- so data-driven recalibration remains necessary. We recommend that imbalanced-learning studies report calibration alongside discrimination, and that practitioners recalibrate after resampling whenever predicted probabilities drive decisions.

Zewen Liu

Qilu Institute of Technology · Tai’an, Shandong, China

Oversampling Imbalanced Classification Class Imbalance Tree Ensembles Resampling

Jun 27, 2026cs.LG

A Kernel Fisher Discriminant Analysis-Based Tree Ensemble Classifier: KFDA Forest

In general, an ensemble classifier is more accurate than a single classifier. In this study, we propose an ensemble classifier called the kernel Fisher discriminant analysis forest (KFDA Forest), which is a tree-based ensemble method that applies KFDA. To promote diversity, bootstrap is used, and variable sets are randomly divided into K subsets. KFDA is performed on each subset to increase classification accuracy. KFDA maximizes the distance between classes while minimizing the distance within classes. KFDA can also be applied to classification problems in a nonlinear data structure using the kernel trick because it can transform the input space into a kernel feature space, commonly named a rotation, rather than performing a dimensionality reduction. Because new feature axes and KFDA projections are parallel, decision trees are used as a base classifier. To compare the proposed method with existing ensemble methods, we apply these to real datasets from the UCI and KEEL repositories.

Donghwan Kim, Seung Hwan Park, Jun-Geol Baek

School of Industrial Management Engineering, Korea University Seoul, Korea · School of Mechanical Engineering, Chungnam National University Daejeon, Korea

Tree Ensembles Kernel Method Forests

Jun 17, 2026stat.ML

Kernel of Partition Paths: A Unified Representation for Tree Ensembles

A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and feature-importance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. The present paper studies that object. KPP indexes the feature map by the nodes of the forest, weighted by a path metric that turns each coordinate into a component of a squared-Euclidean path-isometric embedding. KPP unifies four pillars under a single node-indexed representation whose Gram is non-diagonal and carries a metric: prediction, exact additive attribution, deterministic Lipschitz robust radius in the KPP metric, and uniform Rademacher risk bounds for regression and classification under fixed, honest, or cross-fit conditioning. All probabilistic guarantees are conditional on the representation and are stated under three explicit conditioning regimes; the robust-radius guarantee is deterministic in the KPP metric rather than in a norm on the raw input. Conjectured fast-rate refinements for both regression and classification are stated as open problems and are not claimed as theorems.

Nicolas Mahler

Datapred SAS 23 rue Mirabeau 94300 Vincennes, France · Datapred SA EPFL Innovation Park – Bâtiment A 1015 Lausanne, Switzerland

Tree Ensembles Decision Trees Kernel Method Partitioning Concentration Bounds Spherical Latent Space+3

Jun 11, 2026cs.LG

Simplex-Constrained Sparse Bagging: Transitioning from Uniform Priors to Sparse Posteriors in Ensemble Learning

We present Simplex-Constrained Sparse Bagging (SCSB), a mathematically rigorous framework for post-training compression and probability calibration of bootstrap-based bagging ensembles. Standard bagging ensembles (such as Random Forests, Bagged SVMs, and Bagged Neural Networks) assign uniform voting power to all constituent estimators. However, this naive uniform prior ignores the varying local competence of base estimators and contributes to model overconfidence. We formulate ensemble pruning and calibration as a joint optimization problem over the probability simplex by minimizing the Out-Of-Bag (OOB) loss. To induce sparsity, we address the theoretical "L1-simplex paradox" - the mathematical reality that the L1 norm is constant on the simplex and fails to prune - by introducing a concave quadratic penalty. SCSB is model-agnostic and achieves up to 96% ensemble compression, yielding linear inference speedups and superior probability calibration (lowered Expected Calibration Error) while preserving or enhancing generalization accuracy.

Meher Sai Preetam Madiraju, Meher Bhaskar Madiraju

Tree Ensembles Ensemble Support Vector Machines Empirical Risk Minimization Posterior Prior Knowledge Integration

May 27, 2026cs.LG

PINE: Pruning Boosted Tree Ensembles with Conformal In-Distribution Prediction Equivalence

Tree ensembles are machine learning models with strong predictive performance and interpretability, and remain widely used for tabular data. Standard pruning methods for tree ensembles typically optimize an accuracy-compression trade-off and may change a subset of predictions, potentially compromising decision consistency. Faithful pruning methods address this issue by preserving prediction equivalence over the entire input space, but this requirement leads to lower compression ratios. We propose PINE, a pruning method that provides strong guarantees within an in-distribution region. PINE preserves prediction equivalence within this region and controls the region size using a single parameter

α

via conformal calibration. Experiments on 12 public tabular datasets show that PINE improves the compression ratio by up to 30% while preserving predictions at a comparable level to existing faithful pruning methods.

Haruki Yajima, Yusuke Matsui

The University of Tokyo.

Tree Ensembles Structured Pruning Online Conformal Prediction In-Distribution Tabular Data

May 21, 2026cs.LG

Proxy-Based Approximation of Shapley and Banzhaf Interactions

Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this limitation, we introduce ProxySHAP. ProxySHAP reconciles the high sample efficiency of tree-based proxy models with a principled path to consistency via residual correction. On a theoretical level, we derive a polynomial-time generalization of interventional TreeSHAP to compute exact interaction indices for tree ensembles, successfully bypassing exponential tree-depth dependencies in prior methods. Furthermore, we formally analyze the residual adjustment strategy, characterizing the specific conditions under which Maximum Sample Reuse (MSR) corrects proxy bias without its variance scaling exponentially with interaction size. Extensive benchmarking demonstrates that ProxySHAP sets a new state-of-the-art standard for approximation quality, including in large-scale applications with thousands of features. By achieving the lowest error in both small- and large-budget regimes, ProxySHAP significantly outperforms the prior best estimators ProxySPEX and KernelSHAP-IQ, while also delivering superior performance on downstream explainability tasks.

Santo M. A. R. Thies, Hubert Baniecki, R. Teal Witter +3

LMU Munich · MCML · DFKI +4

Shapley Value Tree Ensembles Influence Function Approximation

May 19, 2026cs.LG

A Family of Divergence Measures for Evaluating the Reconstruction Quality of Explainable Ensemble Trees

Validating interpretable surrogate models for ensemble learners requires measuring agreement between the ensemble's internal representation and its surrogate approximation, rather than mere association. Correlation-based approaches are scale-invariant and fail to detect systematic discrepancies in co-occurrence structure. We propose a statistical framework grounded in the agreement-association distinction, centered on the normalized Loss of Interpretability (nLoI). Rooted in the Cressie-Read power divergence family with lambda equal to 2, the nLoI admits a closed-form decomposition into within-node and between-node components, providing a unique diagnostic capability to identify precisely where and why reconstruction fails. The framework incorporates four complementary measures capturing distinct structural facets of approximation quality. A unified permutation testing procedure delivers valid inference for all measures within a single resampling pass. Theoretical properties, including boundedness and symmetry, are established for each metric. Monte Carlo simulations and empirical evaluations confirm exact Type I error control and demonstrate that these measures detect reconstruction fidelity gradients invisible to correlation-based alternatives. The framework is developed and illustrated in the context of Explainable Ensemble Trees (E2Tree), and empirical evaluation on three benchmark datasets illustrates the practical utility of the framework.

Massimo Aria, Agostino Gnasso, Carmela Iorio

Department of Economics and Statistics, University of Naples2026 Federico II, Naples, Italy

Tree Ensembles Ensemble Evaluation Metrics Interpretability Divergence Surrogate Models+2

May 14, 2026cs.LG

Woodelf++: A Fast and Unified Partial Dependence Plot Algorithm for Decision Tree Ensembles

Partial Dependence Plots (PDPs) visualize how changes in a single feature affect the average model prediction. They are widely used in practice to interpret decision tree ensembles and other machine learning models. Joint-PDPs extend this idea to pairs of features, revealing their combined effect. Partial Dependence Interaction Values (PDIVs) measure feature interactions. The Any-Order-PDIVs task computes these interactions for every feature subset across all rows of the dataset. We introduce Woodelf++, a unified and efficient approach for computing all these useful explainability tools on decision tree ensembles, building on Woodelf, an algorithm for efficient SHAP computation. By deriving suitable metrics over pseudo-Boolean functions, Woodelf++ can compute PDPs (exact and approximate), Joint-PDPs, and Any-Order-PDIVs in a unified framework. Our method delivers substantial complexity improvements over the state of the art, including an exponential gain for Any-Order-PDIVs. Additionally, we introduce and efficiently compute Full PDPs, which leverage the model's split thresholds to faithfully capture its behavior across all possible feature values. Woodelf++ is implemented in pure Python and supports GPU acceleration. On a dataset with 400,000 rows, Woodelf++ computes PDP and Joint-PDP up to 6x faster than the state of the art and up to five orders of magnitude faster than scikit-learn. For Any-Order-PDIVs, the gap is even larger: Woodelf++ computes all interaction values in 5 minutes, while the state of the art is estimated to require over 1,000,000 years.

Ron Wettenstein, Alexander Nadel, Udi Boker

Reichman University, Herzliya, Israel · Faculty of Data and Decision Sciences, Technion, Haifa, Israel

Tree Ensembles Explainability

May 13, 2026cs.AI

Quantifying Sensitivity for Tree Ensembles: A symbolic and compositional approach

Decision tree ensembles (DTE) are a popular model for a wide range of AI classification tasks, used in multiple safety critical domains, and hence verifying properties on these models has been an active topic of study over the last decade. One such verification question is the problem of sensitivity, which asks, given a DTE, whether a small change in subset of features can lead to misclassification of the input. In this work, our focus is to build a quantitative notion of sensitivity, tailored to DTEs, by discretizing the input space of the model and enumerating the regions which are susceptible to sensitivity. We propose a novel algorithmic technique that can perform this computation efficiently, within a certified error and confidence bound. Our approach is based on encoding the problem as an algebraic decision diagram (ADD), and further splitting it into subproblems that can be solved efficiently and make the computation compositional and scalable. We evaluate the performance of our technique over benchmarks of varying size in terms of number of trees and depth, comparing it against the performance of model counters over the same problem encoding. Experimental results show that our tool XCount achieves significant speedup over other approaches and can scale well with the increasing sizes of the ensembles.

Ajinkya Naik, Chaitanya Garg, S. Akshay +2

Indian Institute of Technology Bombay, India · University of Toronto, Canada

Tree Ensembles Ensemble Trees

May 12, 2026cs.LG

Pitfalls of Unlabeled Disagreement-Based Drift Detection in Streaming Tree Ensembles

Detecting concept drift in high-speed data streams remains challenging, particularly when models must operate on unlabeled data and avoid false alarms caused by benign shifts. While disagreement-based uncertainty has shown promise in neural networks, its adaptation to ensembles of incremental decision trees (IDTs) remains largely unexplored. We investigate this approach by constructing batch-specific disagreement measures via label flipping in ensemble members and evaluating their effectiveness for drift detection in tabular data streams. Our experiments show that, although this method performs well in ensembles of multi-layer perceptrons (MLPs), it consistently underperforms loss-based detectors when applied to IDTs. We attribute this behavior to the intrinsic rigidity of IDTs: learning primarily through structural expansion, with limited parameter adaptation, restricts model plasticity and prevents disagreement from reliably reflecting learning potential. Recent work on restructuring IDTs using their intrinsic decomposition into non-overlapping rules offers a promising direction for improving adaptability.

Lara Sá Neves, Afonso Lourenço, Lizy K. John +1

GECAD, ISEP, Polytechnic of Porto, Portugal · The University of Texas at Austin, USA

Tree Ensembles Unlabeled Data Decision Trees Ensemble Disagreement Flips

May 12, 2026stat.ML

Minimax Rates and Spectral Distillation for Tree Ensembles

Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these algorithms, with two main contributions. First, we derive minimax-optimal convergence for RF regression, showing that, under mild regularity conditions on tree growth, the eigenvalue decay of the induced kernel operator governs the statistical rate. Second, we exploit this spectral viewpoint to develop compression schemes for tree ensembles. For RFs, leading eigenfunctions of the kernel operator capture the dominant predictive directions; for GBMs, leading singular vectors of the smoother matrix play an analogous role. Learning nonlinear maps for these spectral representations yields distilled models that are orders of magnitude smaller than the originals while maintaining competitive predictive performance. Our methods compare favorably to state of the art algorithms for forest pruning and rule extraction, with applications to resource constrained computing.

Binh Duc Vu, David S. Watson

King’s College London

Tree Ensembles Random Forest Minimax Rate Semi-Supervised Learning Convergence Dataset Distillation

May 7, 2026cs.LG

Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigms

Trust in counterfactual explanations depends critically on whether their recommended changes are truly minimal: suboptimal explanations may vastly overshoot the actual changes needed to alter a decision, and heuristic errors can affect individuals unevenly, giving some users relevant recourse while assigning others unnecessarily costly recommendations. Consequently, we study the problem of computing optimal counterfactual explanations for tree ensembles under plausibility and actionability constraints. This is a combinatorial problem: for a fixed model, counterfactual search boils down to selecting consistent branching decisions and threshold-defined regions under a distance objective. We exploit this structure through CPCF, a constraint programming (CP) formulation in which numerical features are encoded as interval domains induced by split thresholds, while discrete features retain native finite-domain representations. This yields a compact finite-domain formulation that supports multiple distance objectives without continuous split-boundary search. We then place CPCF in a broader comparison across mathematical programming paradigms: we extend a maximum Boolean satisfiability (MaxSAT) formulation, originally designed for hard-voting random forests, to soft-voting ensembles, and compare against the current state-of-the-art mixed-integer linear programming (MILP) optimal approach. Across ten datasets and three types of tree ensembles, we analyze scalability, anytime performance, and sensitivity to distance metrics. We observe that CP achieves the best overall performance. More importantly, our results identify regimes in which the specific strengths of each paradigm make it best suited: CP is most versatile overall, MaxSAT handles hard-voting ensembles particularly well, and MILP remains competitive in amortized inference settings with a moderate number of split levels.

Awa Khouna, Youssouf Emine, Julien Ferry +1

Polytechnique Montréal · Ivey Business School

Tree Ensembles Counterfactual Explanation Satisfiability

May 6, 2026cs.LG

Quadrature-TreeSHAP: Depth-Independent TreeSHAP and Shapley Interactions

Shapley values are a standard tool for explaining predictions of tree ensembles, with Path-Dependent SHAP being the most widely used variant. Despite substantial progress, existing methods still exhibit trade-offs between depth-dependent runtime, numerical stability, and support for higher-order interactions. To address these challenges, we introduce Quadrature-TreeSHAP, a quadrature-based reformulation of Path-Dependent TreeSHAP that is numerically stable, naturally extends to any-order Shapley interaction values and is practically insensitive to tree depth. Our implementation supports both CPU and GPU and is integrated into XGBoost. Our method is based on a weighted-Banzhaf interaction polynomial, which expresses Banzhaf interaction values as expectations under a feature participation probability

p

. Shapley values and any-order interaction values are then recovered by integrating these polynomials over

p

from 0 to 1. We evaluate these integrals using Gauss-Legendre quadrature, and show that, in practice, only 8 fixed quadrature points are sufficient to reach machine precision. In fact, Quadrature-TreeSHAP with 8 fixed points achieves greater numerical stability than TreeSHAP. This fixed-point formulation removes depth dependence from the inner computation and enables efficient SIMD execution. We confirm these advantages empirically. On 12 XGBoost benchmarks, Quadrature-TreeSHAP computes Shapley values 1.06x-10.59x faster than TreeSHAP on CPU and 1.84x-6.95x faster than GPUTreeSHAP on GPU. Shapley pairwise interactions are 3.80x-58.11x faster on CPU, with higher-order interactions achieving speedups of up to 1200x compared to TreeSHAP-IQ.

Ron Wettenstein, Rory Mitchell, Peng Yu

Reichman University, Herzliya, Israel · Nvidia Corporation · Shopify

Shapley Additive Explanations Tree Ensembles Shaping

Apr 28, 2026cs.LG

RCProb: Probabilistic rule extraction from classification tree ensembles

Tree ensembles provide strong classification performance but usually behave as black-box models. Post-hoc interpretability techniques such as RuleCOSI+ extract a small ruleset that approximates the ensemble, but this simplification can leave the probabilities attached to the extracted rules unreliable. In particular, RuleCOSI+ assigns empirical class probabilities to the extracted rules and repeatedly uses those rule statistics during its greedy combination and simplification procedure. We present RCProb, a probabilistic extension that uses smoothed atomic class-conditional evidence for the expensive search stages and a support-adaptive mixture with an ensemble-informed m-estimate for the final rule probabilities. The method is evaluated on 18 binary and 5 multiclass datasets using random forest (RF) and gradient boosting machine (GBM) ensembles. Relative to RuleCOSI+, the median paired log-loss reduction is 71.9% for RF and 62.5% for GBM, with both differences remaining significant after Holm correction. The number of rules decreases by 38.7% for RF and 38.5% for GBM, while the primary tests do not detect a macro-F1 difference. Confidence-ECE also decreases for both ensembles, with statistical support for RF after correction. A separate controlled experiment with dedicated calibration data shows that native RCProb probabilities are competitive with RuleCOSI+ followed by temperature scaling, although additional post-hoc calibration can still improve RCProb. The results show that probability estimation is an important part of rule extraction and not only a post-processing step.

Josue Obregon

Department of Industrial Engineering, Seoul National University of Science and Technology (SeoulTech), Seoul, 01811, Republic of Korea

Tree Ensembles Probabilistic Model Simplification Random

Mar 27, 2025stat.AP

Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance

With the rapid development of machine learning and deep learning techniques, actuaries and the broader insurance industry face a persistent trade-off between predictive accuracy and interpretability. This paper provides a comprehensive applied assessment of Explainable Boosting Machines (EBM) in a car insurance framework, focusing on claim frequency and severity modeling. EBM combines the additive structure of generalized additive models (GAM) with a cyclic gradient boosting algorithm, resulting in a glass-box model whose predictions are interpretable by design. Using real-world data, we empirically illustrate its practical relevance and compare EBM with modern benchmark models used in non-life insurance pricing. The evaluation considers (i) out-of-sample predictive accuracy, including Murphy diagrams and Bregman dominance tests, and (ii) calibration assessment using T-reliability diagrams and Murphy's score decomposition. Finally, we highlight the link between EBM predictions and Shapley values, showing how predictions can be transparently decomposed into exact main and pairwise interaction effects, providing actionable insights beyond predictive performance.

Markéta Krúpová, Nabil Rachdi, Quentin Guibert

CEREMADE · 1ADDACTIS France, 46 bis Chemin du Vieux Moulin, 69160 Tassin-la-Demi-Lune, France · 2CEREMADE, Universit´e Paris-Dauphine, PSL University, CNRS, 75016 Paris, France

Insurance Tree Ensembles Severity Generalized Linear Model Frequency