Albert Dorador

Albert Dorador

Piecewise-constant regression trees remain popular for their interpretability, yet often lag behind black-box models like Random Forest in predictive accuracy. In this work, we introduce TRUST (Transparent, Robust, and Ultra-Sparse Trees), a novel regression tree model that combines the accuracy of Random Forests with the interpretability of shallow decision trees and sparse linear models. TRUST further enhances transparency by leveraging Large Language Models to generate tailored, user-friendly explanations. Extensive validation on synthetic and real-world benchmark datasets demonstrates that TRUST consistently outperforms other interpretable models -- including CART, Lasso, and Node Harvest -- in predictive accuracy, while matching the accuracy of Random Forest and offering substantial gains in both accuracy and interpretability over M5', a well-established model that is conceptually related.

Albert Dorador

Regression forests have long delivered state-of-the-art accuracy, often outperforming regression trees and even neural networks, but they suffer from limited interpretability as ensemble methods. In this work, we revisit forest pruning, an approach that aims to have the best of both worlds: the accuracy of regression forests and the interpretability of regression trees. This pursuit, whose foundation lies at the core of random forest theory, has seen vast success in empirical studies. In this paper, we contribute theoretical results that support and qualify those empirical findings; namely, we prove the asymptotic advantage of a Lasso-pruned forest over its unpruned counterpart under weak assumptions, as well as high-probability finite-sample generalization bounds for regression forests pruned according to the main methods, which we then validate by way of simulation. Then, we test the accuracy of pruned regression forests against their unpruned counterparts on 19 different datasets (16 synthetic, 3 real). We find that in the vast majority of scenarios tested, there is at least one forest-pruning method that yields equal or better accuracy than the original full forest (in expectation), while just using a small fraction of the trees. We show that, in some cases, the reduction in the size of the forest is so dramatic that the resulting sub-forest can be meaningfully merged into a single tree, obtaining a level of interpretability that is qualitatively superior to that of the original regression forest, which remains a black box.

Albert Dorador

Reliable estimation of feature contributions in machine learning models is essential for trust, transparency and regulatory compliance, especially when models are proprietary or otherwise operate as black boxes. While permutation-based methods are a standard tool for this task, classical implementations rely on repeated random permutations, introducing computational overhead and stochastic instability. In this paper, we show that by replacing multiple random permutations with a single, deterministic, and optimal permutation, we achieve a method that retains the core principles of permutation-based importance while being non-random, faster, and more stable. We validate this approach across nearly 200 scenarios, including real-world household finance and credit risk applications, demonstrating improved bias-variance tradeoffs and accuracy in challenging regimes such as small sample sizes, high dimensionality, and low signal-to-noise ratios. Finally, we introduce Systemic Variable Importance, a natural extension designed for model stress-testing that explicitly accounts for feature correlations. This framework provides a transparent way to quantify how shocks or perturbations propagate through correlated inputs, revealing dependencies that standard variable importance measures miss. Two real-world case studies demonstrate how this metric can be used to audit models for hidden reliance on protected attributes (e.g., gender or race), enabling regulators and practitioners to assess fairness and systemic risk in a principled and computationally efficient manner.

Albert Dorador

We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators. While, on the one hand, $\ell_1$-regularization is a standard tool for variable selection in high-dimensional regimes and, on the other hand, the $\ell_2$ penalty provides stability and solution uniqueness through strict convexity, the standard Elastic Net nevertheless suffers from shrinkage bias that frequently yields suboptimal prediction accuracy. We propose to address this limitation through a framework called \textit{relaxation}. Existing relaxation implementations rely on naive linear interpolations of penalized and unpenalized solutions, which ignore the non-linear geometry that characterizes the entire regularization path and risk violating the Karush-Kuhn-Tucker conditions. Renet addresses these limitations by enforcing sign consistency through an adaptive relaxation procedure that dynamically dispatches between convex blending and efficient sub-path refitting. Furthermore, we identify and formalize a unique synergy between relaxation and the ``One-Standard-Error'' rule: relaxation serves as a robust debiasing mechanism, allowing practitioners to leverage the parsimony of the 1-SE rule without the traditional loss in predictive fidelity. Our theoretical framework incorporates automated stability safeguards for ultra-high dimensional regimes and is supported by a comprehensive benchmarking suite across 20 synthetic and real-world datasets, demonstrating that Renet consistently outperforms the standard Elastic Net and provides a more robust alternative to the Adaptive Elastic Net in high-dimensional, low signal-to-noise ratio and high-multicollinearity regimes. By leveraging an adaptive solver backend, Renet delivers these statistical gains while offering a computational profile that remains competitive with state-of-the-art coordinate descent implementations.