Many human tasks benefit from prior experience when that experience is related to the task at hand. This phenomenon, whereby knowledge from previous tasks is transferred to new ones, has motivated the machine learning technique known as transfer learning. From a statistical perspective, consider the problem of analyzing a regression relationship when the available data are limited. Transfer learning (Torrey and Shavlik (2010)), one of the most widely used techniques in machine learning, can provide a solution. In this framework, one typically leverages related estimates obtained from large but non-identically distributed auxiliary samples, and then refines these estimates to obtain improved estimators from the smaller target sample. Transfer learning has been shown to be effective in a wide range of real-world applications, including computer vision (Kolesnikov et al. (2020); Bu et al. (2021)), natural language processing (Lee et al. (2020); Yuan et al. (2020)), and bioinformatics (Vorontsov et al. (2024); Gao and Cui (2020)), among others. Recently, the theoretical properties of transfer-learned estimators have been extensively investigated across a range of statistical problems.

Machine learning models and libraries can train datasets of different sizes and perform prediction and classification operations, but machine learning models and libraries cause slow and long training times on large datasets. This article introduces EmbeddedML, a training-time-optimized and mathematically enhanced machine learning library. The speed was increased by approximately times compared to scikit-learn without any loss in terms of accuracy in regression models such as Multiple Linear Regression. Logistic Regression and Support Vector Machines (SVM) algorithms have been mathematically rewritten to reduce training time and increase accuracy in classification models. With the applied mathematical improvements, training time has been reduced by approximately 2 times for SVM on small datasets and by around 800 times on large datasets, and by approximately 4 times for Logistic Regression, compared to the scikit-learn implementation. In summary, the EmbeddedML library offers regression, classification, clustering, and dimensionality reduction algorithms that are mathematically rewritten and optimized to reduce training time.

Recursive decision trees have emerged as a leading methodology for heterogeneous causal treatment effect estimation and inference in experimental and observational settings. These procedures are fitted using the celebrated CART (Classification And Regression Tree) algorithm [Breiman et al., 1984], or custom variants thereof, and hence are believed to be "adaptive" to high-dimensional data, sparsity, or other specific features of the underlying data generating process. Athey and Imbens [2016] proposed several "honest" causal decision tree estimators, which have become the standard in both academia and industry. We study their estimators, and variants thereof, and establish lower bounds on their estimation error. We demonstrate that these popular heterogeneous treatment effect estimators cannot achieve a polynomial-in-$n$ convergence rate under basic conditions, where $n$ denotes the sample size. Contrary to common belief, honesty does not resolve these limitations and at best delivers negligible logarithmic improvements in sample size or dimension. As a result, these commonly used estimators can exhibit poor performance in practice, and even be inconsistent in some settings. Our theoretical insights are empirically validated through simulations.

Although conceptually related, variable selection and relative importance (RI) analysis have been treated quite differently in the literature. While RI is typically used for post-hoc model explanation, this paper explores its potential for variable ranking and filter-based selection before model creation. Specifically, we anticipate strong performance from the RI measures because they incorporate both direct and combined effects of predictors, addressing a key limitation of marginal correlation that ignores dependencies among predictors. We implement and evaluate the RI-based variable selection methods using general dominance (GD), comprehensive relative importance (CRI), and a newly proposed, computationally efficient variant termed CRI.Z. We first demonstrate how the RI measures more accurately rank the variables than the marginal correlation, especially when there are suppressed or weak predictors. We then show that predictive models built on these rankings are highly competitive, often outperforming state-of-the-art methods such as the lasso and relaxed lasso. The proposed RI-based methods are particularly effective in challenging cases involving clusters of highly correlated predictors, a setting known to cause failures in many benchmark methods. Although lasso methods have dominated the recent literature on variable selection, our study reveals that the RI-based method is a powerful and competitive alternative. We believe these underutilized tools deserve greater attention in statistics and machine learning communities. The code is available at: https://github.com/tien-endotchang/RI-variable-selection.

Understanding how atmospheric molecular clusters form and grow is key to resolving one of the biggest uncertainties in climate modelling: the formation of new aerosol particles. While quantum chemistry offers accurate insights into these early-stage clusters, its steep computational costs limit large-scale exploration. In this work, we present a fast, interpretable, and surprisingly powerful alternative: $k$-nearest neighbour ($k$-NN) regression model. By leveraging chemically informed distance metrics, including a kernel-induced metric and one learned via metric learning for kernel regression (MLKR), we show that simple $k$-NN models can rival more complex kernel ridge regression (KRR) models in accuracy, while reducing computational time by orders of magnitude. We perform this comparison with the well-established Faber-Christensen-Huang-Lilienfeld (FCHL19) molecular descriptor, but other descriptors (e.g., FCHL18, MBDF, and CM) can be shown to have similar performance. Applied to both simple organic molecules in the QM9 benchmark set and large datasets of atmospheric molecular clusters (sulphuric acid-water and sulphuric-multibase -base systems), our $k$-NN models achieve near-chemical accuracy, scale seamlessly to datasets with over 250,000 entries, and even appears to extrapolate to larger unseen clusters with minimal error (often nearing 1 kcal/mol). With built-in interpretability and straightforward uncertainty estimation, this work positions $k$-NN as a potent tool for accelerating discovery in atmospheric chemistry and beyond.

Predicting default is essential for banks to ensure profitability and financial stability. While modern machine learning methods often outperform traditional regression techniques, their lack of transparency limits their use in regulated environments. Explainable artificial intelligence (XAI) has emerged as a solution in domains like credit scoring. However, most XAI research focuses on post-hoc interpretation of black-box models, which does not produce models lightweight or transparent enough to meet regulatory requirements, such as those for Internal Ratings-Based (IRB) models. This paper proposes a hybrid approach: post-hoc interpretations of black-box models guide feature selection, followed by training glass-box models that maintain both predictive power and transparency. Using the Lending Club dataset, we demonstrate that this approach achieves performance comparable to a benchmark black-box model while using only 10 features - an 88.5% reduction. In our example, SHapley Additive exPlanations (SHAP) is used for feature selection, eXtreme Gradient Boosting (XGBoost) serves as the benchmark and the base black-box model, and Explainable Boosting Machine (EBM) and Penalized Logistic Tree Regression (PLTR) are the investigated glass-box models. We also show that model refinement using feature interaction analysis, correlation checks, and expert input can further enhance model interpretability and robustness.

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and careful observations. A modern alternative is to automate part of this process with symbolic regression (SR). The SR algorithms search for a function that adequately fits the observed data while trying to enforce sparsity, in the hopes of generating an interpretable equation. A particularly interesting extension to these algorithms is the Multi-view Symbolic Regression (MvSR). It searches for a parametric function capable of describing multiple datasets generated by the same phenomena, which helps to mitigate the common problems of overfitting and data scarcity. Recently, multiple implementations added support to MvSR with small differences between them. In this paper, we test and compare MvSR as supported in Operon, PySR, phy-SO, and eggp, in different real-world datasets. We show that they all often achieve good accuracy while proposing solutions with only few free parameters. However, we find that certain features enable a more frequent generation of better models. We conclude by providing guidelines for future MvSR developments.

This study addresses the problem of hallucinated span detection in the outputs of large language models. It has received less attention than output-level hallucination detection despite its practical importance. Prior work has shown that attentions often exhibit irregular patterns when hallucinations occur. Motivated by these findings, we extract features from the attention matrix that provide complementary views capturing (a) whether certain tokens are influential or ignored, (b) whether attention is biased toward specific subsets, and (c) whether a token is generated referring to a narrow or broad context, in the generation. These features are input to a Transformer-based classifier to conduct sequential labelling to identify hallucinated spans. Experimental results indicate that the proposed method outperforms strong baselines on hallucinated span detection with longer input contexts, such as data-to-text and summarisation tasks.

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

We propose and study Sparse Polyak, a variant of Polyak's adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such settings, the standard Polyak step size performs poorly, requiring an increasing number of iterations to achieve optimal statistical precision-even when, the problem remains well conditioned and/or the achievable precision itself does not degrade with problem size. We trace this limitation to a mismatch in how smoothness is measured: in high dimensions, it is no longer effective to estimate the Lipschitz smoothness constant. Instead, it is more appropriate to estimate the smoothness restricted to specific directions relevant to the problem (restricted Lipschitz smoothness constant). Sparse Polyak overcomes this issue by modifying the step size to estimate the restricted Lipschitz smoothness constant. We support our approach with both theoretical analysis and numerical experiments, demonstrating its improved performance.