The utilization of Machine Learning (ML) in contemporary software systems is extensive and continually expanding. However, its usage is energy-intensive, contributing to increased carbon emissions and demanding significant resources. While numerous studies examine the performance and accuracy of ML, only a limited few focus on its environmental aspects, particularly energy consumption. In addition, despite emerging efforts to compare energy consumption across various programming languages for specific algorithms and tasks, there remains a gap specifically in comparing these languages for ML-based tasks. This paper aims to raise awareness of the energy costs associated with employing different programming languages for ML model training and inference. Through this empirical study, we measure and compare the energy consumption along with run-time performance of five regression and five classification tasks implemented in Python and R, the two most popular programming languages in this context. Our study results reveal a statistically significant difference in costs between the two languages in 95% of the cases examined. Furthermore, our analysis demonstrates that the choice of programming language can influence energy efficiency significantly, up to 99.16% during model training and up to 99.8% during inferences, for a given ML task.

Imagine decision-makers uploading data and, within minutes, receiving clear, actionable insights delivered straight to their fingertips. That is the promise of the AI Data Scientist, an autonomous Agent powered by large language models (LLMs) that closes the gap between evidence and action. Rather than simply writing code or responding to prompts, it reasons through questions, tests ideas, and delivers end-to-end insights at a pace far beyond traditional workflows. Guided by the scientific tenet of the hypothesis, this Agent uncovers explanatory patterns in data, evaluates their statistical significance, and uses them to inform predictive modeling. It then translates these results into recommendations that are both rigorous and accessible. At the core of the AI Data Scientist is a team of specialized LLM Subagents, each responsible for a distinct task such as data cleaning, statistical testing, validation, and plain-language communication. These Subagents write their own code, reason about causality, and identify when additional data is needed to support sound conclusions. Together, they achieve in minutes what might otherwise take days or weeks, enabling a new kind of interaction that makes deep data science both accessible and actionable.

Tabular regression is a well-studied problem with numerous industrial applications, yet most existing approaches focus on point estimation, often leading to overconfident predictions. This issue is particularly critical in industrial automation, where trustworthy decision-making is essential. Probabilistic regression models address this challenge by modeling prediction uncertainty. However, many conventional methods assume a fixed-shape distribution (typically Gaussian), and resort to estimating distribution parameters. This assumption is often restrictive, as real-world target distributions can be highly complex. To overcome this limitation, we introduce TabResFlow, a Normalizing Spline Flow model designed specifically for univariate tabular regression, where commonly used simple flow networks like RealNVP and Masked Autoregressive Flow (MAF) are unsuitable. TabResFlow consists of three key components: (1) An MLP encoder for each numerical feature. (2) A fully connected ResNet backbone for expressive feature extraction. (3) A conditional spline-based normalizing flow for flexible and tractable density estimation. We evaluate TabResFlow on nine public benchmark datasets, demonstrating that it consistently surpasses existing probabilistic regression models on likelihood scores. Our results demonstrate 9.64% improvement compared to the strongest probabilistic regression model (TreeFlow), and on average 5.6 times speed-up in inference time compared to the strongest deep learning alternative (NodeFlow). Additionally, we validate the practical applicability of TabResFlow in a real-world used car price prediction task under selective regression. To measure performance in this setting, we introduce a novel Area Under Risk Coverage (AURC) metric and show that TabResFlow achieves superior results across this metric.

Regression under uncertainty is fundamental across science and engineering. We present an Anchored Mixture of Experts (Anchor-MoE), a model that handles both probabilistic and point regression. For simplicity, we use a tuned gradient-boosting model to furnish the anchor mean; however, any off-the-shelf point regressor can serve as the anchor. The anchor prediction is projected into a latent space, where a learnable metric-window kernel scores locality and a soft router dispatches each sample to a small set of mixture-density-network experts; the experts produce a heteroscedastic correction and predictive variance. We train by minimizing negative log-likelihood, and on a disjoint calibration split fit a post-hoc linear map on predicted means to improve point accuracy. On the theory side, assuming a Hölder smooth regression function of order~$α$ and fixed Lipschitz partition-of-unity weights with bounded overlap, we show that Anchor-MoE attains the minimax-optimal $L^2$ risk rate $O\!\big(N^{-2α/(2α+d)}\big)$. In addition, the CRPS test generalization gap scales as $\widetilde{O}\!\Big(\sqrt{(\log(Mh)+P+K)/N}\Big)$; it is logarithmic in $Mh$ and scales as the square root in $P$ and $K$. Under bounded-overlap routing, $K$ can be replaced by $k$, and any dependence on a latent dimension is absorbed into $P$. Under uniformly bounded means and variances, an analogous $\widetilde{O}\!\big(\sqrt{(\log(Mh)+P+K)/N}\big)$ scaling holds for the test NLL up to constants. Empirically, across standard UCI regressions, Anchor-MoE consistently matches or surpasses the strong NGBoost baseline in RMSE and NLL; on several datasets it achieves new state-of-the-art probabilistic regression results on our benchmark suite. Code is available at https://github.com/BaozhuoSU/Probabilistic_Regression.

Understanding the factors that shape students' mathematics performance is vital for designing effective educational policies. This study applies explainable artificial intelligence (XAI) techniques to PISA 2018 data to predict math achievement and identify key predictors across ten countries (67,329 students). We tested four models: Multiple Linear Regression (MLR), Random Forest (RF), CATBoost, and Artificial Neural Networks (ANN), using student, family, and school variables. Models were trained on 70% of the data (with 5-fold cross-validation) and tested on 30%, stratified by country. Performance was assessed with R^2 and Mean Absolute Error (MAE). To ensure interpretability, we used feature importance, SHAP values, and decision tree visualizations. Non-linear models, especially RF and ANN, outperformed MLR, with RF balancing accuracy and generalizability. Key predictors included socio-economic status, study time, teacher motivation, and students' attitudes toward mathematics, though their impact varied across countries. Visual diagnostics such as scatterplots of predicted vs actual scores showed RF and CATBoost aligned closely with actual performance. Findings highlight the non-linear and context-dependent nature of achievement and the value of XAI in educational research. This study uncovers cross-national patterns, informs equity-focused reforms, and supports the development of personalized learning strategies.

In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution $p(x)\propto e^{-f(x)}$ is strongly log-concave and has varying degrees of smoothness. Precisely, under the assumptions that the gradient and Hessian of $f$ are Lipschitz continuous, our algorithm achieves a 2-Wasserstein error of $\varepsilon$ in $\mathcal{O}(\sqrt{d}/\varepsilon)$ and $\mathcal{O}(\sqrt{d}/\sqrt{\varepsilon})$ steps respectively. Therefore, our algorithm has a similar complexity as other popular Langevin MCMC algorithms under matching assumptions. However, if we additionally assume that the third derivative of $f$ is Lipschitz continuous, then our algorithm achieves a 2-Wasserstein error of $\varepsilon$ in $\mathcal{O}(\sqrt{d}/\varepsilon^{\frac{1}{3}})$ steps. To the best of our knowledge, this is the first gradient-only method for ULD with third order convergence. To support our theory, we perform Bayesian logistic regression across a range of real-world datasets, where our algorithm achieves competitive performance compared to an existing underdamped Langevin MCMC algorithm and the popular No U-Turn Sampler (NUTS).

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of the original matrix of predictor variables or features, each observation is mapped into an enlarged feature space. Second, a ridge penalty term is used to shrink the coefficients on the features in the enlarged feature space. Third, the solution is not obtained in this enlarged feature space, but through solving a dual problem in the observation space. A major drawback in the present use of kernels is that the interpretation in terms of the original features is lost. In this paper, we argue that in the case of a wide matrix of features, where there are more features than observations, the kernel solution can be re-expressed in terms of a linear combination of the original matrix of features and a ridge penalty that involves a special metric. Consequently, the exact same predicted values can be obtained as a weighted linear combination of the features in the usual manner and thus can be interpreted. In the case where the number of features is less than the number of observations, we discuss a least-squares approximation of the kernel matrix that still allows the interpretation in terms of a linear combination. It is shown that these results hold for any function of a linear combination that minimizes the coefficients and has a ridge penalty on these coefficients, such as in kernel logistic regression and kernel Poisson regression. This work makes a contribution to interpretable artificial intelligence.

Rail and wheel interaction functionality is pivotal to the railway system safety, requiring accurate measurement systems for optimal safety monitoring operation. This paper introduces an innovative onboard measurement system for monitoring wheel flange wear depth, utilizing displacement and temperature sensors. Laboratory experiments are conducted to emulate wheel flange wear depth and surrounding temperature fluctuations in different periods of time. Employing collected data, the training of machine learning algorithms that are based on regression models, is dynamically automated. Further experimentation results, using standards procedures, validate the system's efficacy. To enhance accuracy, an infinite impulse response filter (IIR) that mitigates vehicle dynamics and sensor noise is designed. Filter parameters were computed based on specifications derived from a Fast Fourier Transform analysis of locomotive simulations and emulation experiments data. The results show that the dynamic machine learning algorithm effectively counter sensor nonlinear response to temperature effects, achieving an accuracy of 96.5 %, with a minimal runtime. The real-time noise reduction via IIR filter enhances the accuracy up to 98.2 %. Integrated with railway communication embedded systems such as Internet of Things devices, this advanced monitoring system offers unparalleled real-time insights into wheel flange wear and track irregular conditions that cause it, ensuring heightened safety and efficiency in railway systems operations.

The result follows. 1 B Gradient Derivations B.1 Weights gradient First, we compute the gradient with respect to weights vector w R B.2 Location gradients Here we take the gradient with respect to a single pseudopoint u Increasing this number is typically expensive to obtain in practice. Bayesian Logistic Regression experiment presented in Section 4. Posterior approximation metrics, coreset gradients and learning rates Estimation of differential privacy cost at all experiments was based on TensorFlow privacy implementation of moments accountant for the subsampled Gaussian mechanism. Experiments were performed on a CPU cluster node with a 2x Intel Xeon Gold 6142 and 12GB RAM.