Capturing nonlinear relationships without sacrificing interpretability remains a persistent challenge in regression modeling. We introduce SplitWise, a novel framework that enhances stepwise regression. It adaptively transforms numeric predictors into threshold-based binary features using shallow decision trees, but only when such transformations improve model fit, as assessed by the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). This approach preserves the transparency of linear models while flexibly capturing nonlinear effects. Implemented as a user-friendly R package, SplitWise is evaluated on both synthetic and real-world datasets. The results show that it consistently produces more parsimonious and generalizable models than traditional stepwise and penalized regression techniques.

Causal inference determines cause-and-effect relationships between variables and has broad applications across disciplines. Traditional time-series methods often reveal causal links only in a time-averaged sense, while ensemble-based information transfer approaches detect the time evolution of short-term causal relationships but are typically limited to low-dimensional systems. In this paper, a new causal inference framework, called assimilative causal inference (ACI), is developed. Fundamentally different from the state-of-the-art methods, ACI uses a dynamical system and a single realization of a subset of the state variables to identify instantaneous causal relationships and the dynamic evolution of the associated causal influence range (CIR). Instead of quantifying how causes influence effects as done traditionally, ACI solves an inverse problem via Bayesian data assimilation, thus tracing causes backward from observed effects with an implicit Bayesian hypothesis. Causality is determined by assessing whether incorporating the information of the effect variables reduces the uncertainty in recovering the potential cause variables. ACI has several desirable features. First, it captures the dynamic interplay of variables, where their roles as causes and effects can shift repeatedly over time. Second, a mathematically justified objective criterion determines the CIR without empirical thresholds. Third, ACI is scalable to high-dimensional problems by leveraging computationally efficient Bayesian data assimilation techniques. Finally, ACI applies to short time series and incomplete datasets. Notably, ACI does not require observations of candidate causes, which is a key advantage since potential drivers are often unknown or unmeasured. The effectiveness of ACI is demonstrated by complex dynamical systems showcasing intermittency and extreme events.

As machine learning systems are increasingly used in high-stakes domains, there is a growing emphasis placed on making them interpretable to improve trust in these systems. In response, a range of interpretable machine learning (IML) methods have been developed to generate human-understandable insights into otherwise black box models. With these methods, a fundamental question arises: Are these interpretations reliable? Unlike with prediction accuracy or other evaluation metrics for supervised models, the proximity to the true interpretation is difficult to define. Instead, we ask a closely related question that we argue is a prerequisite for reliability: Are these interpretations stable? We define stability as findings that are consistent or reliable under small random perturbations to the data or algorithms. In this study, we conduct the first systematic, large-scale empirical stability study on popular machine learning global interpretations for both supervised and unsupervised tasks on tabular data. Our findings reveal that popular interpretation methods are frequently unstable, notably less stable than the predictions themselves, and that there is no association between the accuracy of machine learning predictions and the stability of their associated interpretations. Moreover, we show that no single method consistently provides the most stable interpretations across a range of benchmark datasets. Overall, these results suggest that interpretability alone does not warrant trust, and underscores the need for rigorous evaluation of interpretation stability in future work. To support these principles, we have developed and released an open source IML dashboard and Python package to enable researchers to assess the stability and reliability of their own data-driven interpretations and discoveries.

This paper explores Uncertainty Quantification (UQ) in SVM predictions, particularly for regression and forecasting tasks. Unlike the Neural Network, the SVM solutions are typically more stable, sparse, optimal and interpretable. However, there are only few literature which addresses the UQ in SVM prediction. At first, we provide a comprehensive summary of existing Prediction Interval (PI) estimation and probabilistic forecasting methods developed in the SVM framework and evaluate them against the key properties expected from an ideal PI model. We find that none of the existing SVM PI models achieves a sparse solution. To introduce sparsity in SVM model, we propose the Sparse Support Vector Quantile Regression (SSVQR) model, which constructs PIs and probabilistic forecasts by solving a pair of linear programs. Further, we develop a feature selection algorithm for PI estimation using SSVQR that effectively eliminates a significant number of features while improving PI quality in case of high-dimensional dataset. Finally we extend the SVM models in Conformal Regression setting for obtaining more stable prediction set with finite test set guarantees. Extensive experiments on artificial, real-world benchmark datasets compare the different characteristics of both existing and proposed SVM-based PI estimation methods and also highlight the advantages of the feature selection in PI estimation. Furthermore, we compare both, the existing and proposed SVM-based PI estimation models, with modern deep learning models for probabilistic forecasting tasks on benchmark datasets. Furthermore, SVM models show comparable or superior performance to modern complex deep learning models for probabilistic forecasting task in our experiments.

We investigate the convergence properties of popular data-augmentation samplers for Bayesian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the associated mixing times (in Kullback-Leibler divergence). The bounds depend explicitly on the design matrix and the prior precision, while they hold uniformly over the vector of responses. We specialize the results for different regimes of statistical interest, when both the number of data points $n$ and parameters $p$ are large: in particular we identify scenarios where the mixing times remain bounded as $n,p\to\infty$, and ones where they do not. The results are shown to be tight (in the worst case with respect to the responses) and provide guidance on choices of prior distributions that provably lead to fast mixing. An empirical analysis based on coupling techniques suggests that the bounds are effective in predicting practically observed behaviours.

This study investigates the multifaceted factors influencing wildfire risk in Iran, focusing on the interplay between climatic conditions and human activities. Utilizing advanced remote sensing, geospatial information system (GIS) processing techniques such as cloud computing, and machine learning algorithms, this research analyzed the impact of climatic parameters, topographic features, and human-related factors on wildfire susceptibility assessment and prediction in Iran. Multiple scenarios were developed for this purpose based on the data sampling strategy. The findings revealed that climatic elements such as soil moisture, temperature, and humidity significantly contribute to wildfire susceptibility, while human activities-particularly population density and proximity to powerlines-also played a crucial role. Furthermore, the seasonal impact of each parameter was separately assessed during warm and cold seasons. The results indicated that human-related factors, rather than climatic variables, had a more prominent influence during the seasonal analyses. This research provided new insights into wildfire dynamics in Iran by generating high-resolution wildfire susceptibility maps using advanced machine learning classifiers. The generated maps identified high risk areas, particularly in the central Zagros region, the northeastern Hyrcanian Forest, and the northern Arasbaran forest, highlighting the urgent need for effective fire management strategies.

Keratoconus (KC) is a corneal disorder that results in blurry and distorted vision. Traditional diagnostic tools, while effective, are often bulky, costly, and require professional operation. In this paper, we present a portable and innovative methodology for diagnosing. Our proposed approach first captures the image reflected on the eye's cornea when a smartphone screen-generated Placido disc sheds its light on an eye, then utilizes a two-stage diagnosis for identifying the KC cornea and pinpointing the location of the KC on the cornea. The first stage estimates the height and width of the Placido disc extracted from the captured image to identify whether it has KC. In this KC identification, k-means clustering is implemented to discern statistical characteristics, such as height and width values of extracted Placido discs, from non-KC (control) and KC-affected groups. The second stage involves the creation of a distance matrix, providing a precise localization of KC on the cornea, which is critical for efficient treatment planning. The analysis of these distance matrices, paired with a logistic regression model and robust statistical analysis, reveals a clear distinction between control and KC groups. The logistic regression model, which classifies small areas on the cornea as either control or KC-affected based on the corresponding inter-disc distances in the distance matrix, reported a classification accuracy of 96.94%, which indicates that we can effectively pinpoint the protrusion caused by KC. This comprehensive, smartphone-based method is expected to detect KC and streamline timely treatment.

Existing research on judicial sentencing prediction predominantly relies on end-to-end models, which often neglect the inherent sentencing logic and lack interpretability-a critical requirement for both scholarly research and judicial practice. To address this challenge, we make three key contributions:First, we propose a novel Saturated Mechanistic Sentencing (SMS) model, which provides inherent legal interpretability by virtue of its foundation in China's Criminal Law. We also introduce the corresponding Momentum Least Mean Squares (MLMS) adaptive algorithm for this model. Second, for the MLMS algorithm based adaptive sentencing predictor, we establish a mathematical theory on the accuracy of adaptive prediction without resorting to any stationarity and independence assumptions on the data. We also provide a best possible upper bound for the prediction accuracy achievable by the best predictor designed in the known parameters case. Third, we construct a Chinese Intentional Bodily Harm (CIBH) dataset. Utilizing this real-world data, extensive experiments demonstrate that our approach achieves a prediction accuracy that is not far from the best possible theoretical upper bound, validating both the model's suitability and the algorithm's accuracy.

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking predictive uncertainty. This work addresses that gap by proposing a novel, model-agnostic uncertainty attribution (UA) method grounded in conformal prediction (CP). By defining cooperative games where CP interval properties-such as width and bounds-serve as value functions, we systematically attribute predictive uncertainty to input features. Extending beyond the traditional Shapley values, we use the richer class of Harsanyi allocations, and in particular the proportional Shapley values, which distribute attribution proportionally to feature importance. We propose a Monte Carlo approximation method with robust statistical guarantees to address computational feasibility, significantly improving runtime efficiency. Our comprehensive experiments on synthetic benchmarks and real-world datasets demonstrate the practical utility and interpretative depth of our approach. By combining cooperative game theory and conformal prediction, we offer a rigorous, flexible toolkit for understanding and communicating predictive uncertainty in high-stakes ML applications.

Transformers have shown a remarkable ability for in-context learning (ICL), making predictions based on contextual examples. However, while theoretical analyses have explored this prediction capability, the nature of the inferred context and its utility for downstream predictions remain open questions. This paper aims to address these questions by examining ICL for inverse linear regression (ILR), where context inference can be characterized by unsupervised learning of underlying weight vectors. Focusing on the challenging scenario of rank-deficient inverse problems, where context length is smaller than the number of unknowns in the weight vectors and regularization is necessary, we introduce a linear transformer to learn the inverse mapping from contextual examples to the underlying weight vector. Our findings reveal that the transformer implicitly learns both a prior distribution and an effective regularization strategy, outperforming traditional ridge regression and regularization methods. A key insight is the necessity of low task dimensionality relative to the context length for successful learning. Furthermore, we numerically verify that the error of the transformer estimator scales linearly with the noise level, the ratio of task dimension to context length, and the condition number of the input data. These results not only demonstrate the potential of transformers for solving ill-posed inverse problems, but also provide a new perspective towards understanding the knowledge extraction mechanism within transformers.