Expanding Data-Agnostic Pivotal Instances Selection Models with Proximity Trees and Ensemble Learning

As decision-making processes grow more complex, machine learning tools have become essential for tackling business and societal challenges. However, many existing methods rely on decision-making procedures that are difficult to interpret. Since humans naturally make decisions by comparing new cases with a few representative examples, we aim to design an approach that selects such pivots to construct an interpretable predictive model. Inspired by decision trees, we propose a hierarchical, interpretable-by-design pivot selection model based on the similarity between pivots and input instances. Our method functions both as a pivot selection technique and a standalone predictive model. Extending beyond single pivots, we incorporate pairs of pivots that are used by proximity and oblique trees, as well as ensembles, which enhance the versatility and effectiveness of our proposal. Additionally, our approach is data modality-agnostic, leveraging pre-trained networks for data transformation. Experiments across diverse datasets, including tabular data, text, images, and time series, demonstrate the effectiveness of our approach, outperforming alternative instance selection strategies and achieving competitive results against state-of-the-art interpretable models while maintaining a minimal number of pivots.

Twoblock clustering trees with coskewness-based dimension reduction: recovering piecewise multivariate linear regimes

The twoblock clustering tree (\tbtree) is introduced as a highly interpretable regression tree for multivariate responses. Twoblock trees are deterministic decision trees that have local multivariate linear models as their leaves and use dense or sparse twoblock dimension reduction as local leaf models and in the impurity. The resulting models are both computationally efficient and can be highly interpretable. Beyond proposing the decision tree estimator itself, this paper also introduces an estimator for the twoblock dimension reduced space based on maximizing coskewness, which facilitates identification of non-normal clusters in the data. The tree inherently produces a set of local linear models and is therefore apt to recover peicewise linear regimes, which is illustrated in a simulation. However, two real world data examples illustrate that twoblock trees are also capable of modeling more complexly nonlinear dependencies and can perform on par with black box modeling techniques, such as random forests. At each point, both the twoblock models that generate the splits, as well as the ones in the leaves, can be inspected and interpreted.

DeepPySR -- A Symbolic Regression Framework with Dynamic Pruning, Pareto Selection, and Hierarchical Composition for Real-World Scientific Discovery

Symbolic regression (SR) discovers analytical equations from data, yielding glass-box models with directly interpretable formulas, unlike black-box methods that rely on unstable post-hoc tools such as SHAP or LIME. This transparency is crucial in clinical medicine and social science, but SR faces three challenges: high-dimensional inputs, principled selection of Pareto-front formulae, and data irregularities such as multicollinearity and class imbalance. We introduce DeepPySR, which addresses these issues with a dynamic variable-pruning schedule to remove irrelevant features during search, an exponential Pareto selection criterion that eliminates trade-offs between accuracy and complexity, and a multi-layer architecture for hierarchical symbolic composition. On four Feynman physics benchmarks and seven biomedical and social-science datasets, DeepPySR outperforms PySR and baselines on body fat (R$^2$: 0.794 vs.\ 0.702), heart disease (F1: 0.898 vs.\ 0.787), student performance (R$^2$: 0.964 vs.\ 0.948), and Raine BMI (R$^2$: 0.525 vs.\ 0.370), producing interpretable formulas aligned with domain risk factors.

CLARITree: Cholesky and Lookahead Accelerations for Regression with Interpretable Piecewise Linear Trees

Regression trees are among the most interpretable yet expressive model classes in machine learning. Historically, greedy induction has been the dominant approach for constructing well-performing regression trees. While optimal methods based on dynamic programming and branch-and-bound exist, they are computationally prohibitive for general linear regression trees, despite often achieving substantially better performance than greedy approaches. Recent work has shown that specialized lookahead strategies can dramatically improve runtime while maintaining near-optimal performance, primarily in classification settings. In this work, we develop a novel algorithm for near-optimal, sparse, piecewise linear regression trees that combines a lookahead-style search strategy with efficient rank-one Cholesky updates of the Gram matrix. We demonstrate, both theoretically and empirically, that our method achieves a favorable trade-off between computational efficiency, predictive accuracy, and sparsity, and scales significantly better than the current state of the art.

NOVA: Symbolic Regression Discovery of Interpretable Car-Following and Lane-Change Models with Driver Heterogeneity

We present NOVA, an autonomous symbolic regression framework that identifies interpretable car-following and lane-change structures from raw trajectory data with minimal behavioral priors. Applied to 4,765,788 active driving observations from the NGSIM I-80 and US-101 datasets, NOVA's deterministic Rust-powered search engine evaluates over 10,000 candidate algebraic structures and identifies a compact two-term acceleration model under a forward-shifted rolling-mean prediction target. Evaluated under two complementary preprocessing pipelines, NOVA achieves $RMSE = 1.376 m/s^2$ ($R^2 = 15.57\%$) on the intent-forecasting benchmark, outperforming the best recalibrated symbolic-regression baseline (SR-LLM, PNAS~2025) by 0.135 m/s$^2$ in RMSE under an identical evaluation protocol. Across eight independent experiments, a single dominant nonlinear term emerges as a robust backbone of human car-following; a residual-guided extension further links the selected structure to an established psychophysical theory of collision avoidance. The discovered feature operators transfer zero-shot between freeway sites with under 3 pp $R^2$ loss. Extended to lane-change modelling within a multinomial logit framework, NOVA achieves 67.4\% balanced accuracy under strict vehicle-ID holdout on 502 unseen drivers, surpassing existing lane-changing baselines by +29.8 percentage points on a three-class problem.

Gradient Boosted Risk Scores

Risk scores are an interpretable and actionable class of machine learning models with applications in medicine, insurance, and risk management. Unlike most computational methods, risk scores are designed to be computed by a human by attributing points to a data sample based on a limited set of criteria. The most common approaches for generating risk scores use linear regressions to estimate the effect of selected variables. We propose a simple and effective approach towards building compact and predictive risk scores. We provide an algorithm based on gradient boosting that is capable of modeling nonlinear effects, along with a C++ implementation with Python and R bindings. Through extensive empirical evaluation on twelve tabular datasets spanning regression, classification, and time-to-event tasks, we show that our method achieves competitive predictive performance while producing substantially more compact scores than regression-based alternatives, with 60% fewer rules for classification tasks and 16% fewer rules for time-to-event tasks on average, compared to AutoScore.