Transfer learning enhances model performance by utilizing knowledge from related domains, particularly when labeled data is scarce. While existing research addresses transfer learning under various distribution shifts in independent settings, handling dependencies in networked data remains challenging. To address this challenge, we propose a high-dimensional transfer learning framework based on network convolutional regression (NCR), inspired by the success of graph convolutional networks (GCNs). The NCR model incorporates random network structure by allowing each node's response to depend on its features and the aggregated features of its neighbors, capturing local dependencies effectively. Our methodology includes a two-step transfer learning algorithm that addresses domain shift between source and target networks, along with a source detection mechanism to identify informative domains. Theoretically, we analyze the lasso estimator in the context of a random graph based on the Erdos-Renyi model assumption, demonstrating that transfer learning improves convergence rates when informative sources are present. Empirical evaluations, including simulations and a real-world application using Sina Weibo data, demonstrate substantial improvements in prediction accuracy, particularly when labeled data in the target domain is limited.

The electrification of powertrains is rising as the objective for a more viable future is intensified. To ensure continuous and reliable operation without undesirable malfunctions, it is essential to monitor the internal temperatures of machines and keep them within safe operating limits. Conventional modeling methods can be complex and usually require expert knowledge. With the amount of data collected these days, it is possible to use information models to assess thermal behaviors. This paper investigates artificial intelligence techniques for monitoring the cooling efficiency of induction machines. Experimental data was collected under specific operating conditions, and three machine-learning models have been developed. The optimal configuration for each approach was determined through rigorous hyperparameter searches, and the models were evaluated using a variety of metrics. The three solutions performed well in monitoring the condition of the machine even under transient operation, highlighting the potential of data-driven methods in improving the thermal management.

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to uncertainty quantification, such as confidence and prediction intervals, provide probability coverage guarantees for the expected outcomes $f(\boldsymbol{x})$ or the realized outcomes $f(\boldsymbol{x})+\epsilon$. Instead, this paper introduces a novel, model-agnostic framework for quantifying uncertainty in continuous and binary outcomes using confidence sets for outcome excursions, where the goal is to identify a subset of the feature space where the expected or realized outcome exceeds a specific value. The proposed method constructs data-dependent inner and outer confidence sets that aim to contain the true feature subset for which the expected or realized outcomes of these features exceed a specified threshold. We establish theoretical guarantees for the probability that these confidence sets contain the true feature subset, both asymptotically and for finite sample sizes. The framework is validated through simulations and applied to real-world datasets, demonstrating its utility in contexts such as housing price prediction and time to sepsis diagnosis in healthcare. This approach provides a unified method for uncertainty quantification that is broadly applicable across various continuous and binary prediction models.

Geomagnetic storms are large-scale disturbances of the Earth's magnetosphere driven by solar wind interactions, posing significant risks to space-based and ground-based infrastructure. The Disturbance Storm Time (Dst) index quantifies geomagnetic storm intensity by measuring global magnetic field variations. This study applies symbolic regression to derive data-driven equations describing the temporal evolution of the Dst index. We use historical data from the NASA OMNIweb database, including solar wind density, bulk velocity, convective electric field, dynamic pressure, and magnetic pressure. The PySR framework, an evolutionary algorithm-based symbolic regression library, is used to identify mathematical expressions linking dDst/dt to key solar wind. The resulting models include a hierarchy of complexity levels and enable a comparison with well-established empirical models such as the Burton-McPherron-Russell and O'Brien-McPherron models. The best-performing symbolic regression models demonstrate superior accuracy in most cases, particularly during moderate geomagnetic storms, while maintaining physical interpretability. Performance evaluation on historical storm events includes the 2003 Halloween Storm, the 2015 St. Patrick's Day Storm, and a 2017 moderate storm. The results provide interpretable, closed-form expressions that capture nonlinear dependencies and thresholding effects in Dst evolution.

-- The number of electrified powertrains is ever increasing today t owards a more sustainable future; thus, it is essential that unwanted failures are prevented, and a reliable operation is secured . Monitoring the internal temperatures of motors and keeping them under their thresholds is an important first step. Conventional modeling methods require expert knowledge and complicated mathematical appro aches . With all the data a modern electric drive collect s nowadays during the system operation, it is feasible to apply data - driven approach es for estimat ing thermal behaviors . In this paper, multiple machine - learning methods are investigated on their capa bility to approximate the temperatures of the stator winding and bearing in induction motors . The explored algorithms vary from linear to neural network s . For this reason, experimental lab data ha ve been captured from a powertrain under predetermined operating conditions. F or each approach, a hyperparameter search is then performed to find the optimal configuration. All the models are evaluated by various metrics, and i t has been found that neur al networks perform satisfactor ily even under transient c onditions. In [1], the percentage share of specific failures in induction machines has been presented .

We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The missingness model, denoted by $S(y)$, is the function that maps any point $y$ in $R^d$ to the subsets of its coordinates that are seen. In this work, we assume that it is known. We study the following two settings: (i) Self-censoring: An observation $x$ is generated by first sampling the true value $y$ from a $d$-dimensional Gaussian $N(\mu*, \Sigma*)$ with unknown $\mu*$ and $\Sigma*$. For each coordinate $i$, there exists a set $S_i$ subseteq $R^d$ such that $x_i = y_i$ if and only if $y_i$ in $S_i$. Otherwise, $x_i$ is missing and takes a generic value (e.g., "?"). We design an algorithm that learns $N(\mu*, \Sigma*)$ up to total variation (TV) distance epsilon, using $poly(d, 1/\epsilon)$ samples, assuming only that each pair of coordinates is observed with sufficiently high probability. (ii) Linear thresholding: An observation $x$ is generated by first sampling $y$ from a $d$-dimensional Gaussian $N(\mu*, \Sigma)$ with unknown $\mu*$ and known $\Sigma$, and then applying the missingness model $S$ where $S(y) = {i in [d] : v_i^T y <= b_i}$ for some $v_1, ..., v_d$ in $R^d$ and $b_1, ..., b_d$ in $R$. We design an efficient mean estimation algorithm, assuming that none of the possible missingness patterns is very rare conditioned on the values of the observed coordinates and that any small subset of coordinates is observed with sufficiently high probability.

Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we propose a novel and simple screening method based on ordering the absolute sample ridge partial correlations. The proposed method takes into account not only the ridge regularized estimates of the regression coefficients but also the ridge regularized partial variances of the predictor variables providing sure screening property without strong assumptions on the marginal correlations. Simulation study and a real data analysis show that the proposed method has a competitive performance compared with the existing screening procedures. A publicly available software implementing the proposed screening accompanies the article.

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential method in the shapr-package (i.e fit one and one model), our method runs in minutes and not in hours. Compared to the iterative method in the shapr-package, we obtain better estimates in less than or almost the same amount of time. When the number of covariates becomes too large, one can still fit thousands of regression models at once using our method. We focus on a linear regression model, but one can easily extend the method to accommodate several types of splines that can be estimated using multivariate linear regression due to linearity in the parameters.

Probabilities or confidence values produced by artificial intelligence (AI) and machine learning (ML) models often do not reflect their true accuracy, with some models being under or over confident in their predictions. For example, if a model is 80% sure of an outcome, is it correct 80% of the time? Probability calibration metrics measure the discrepancy between confidence and accuracy, providing an independent assessment of model calibration performance that complements traditional accuracy metrics. Understanding calibration is important when the outputs of multiple systems are combined, for assurance in safety or business-critical contexts, and for building user trust in models. This paper provides a comprehensive review of probability calibration metrics for classifier and object detection models, organising them according to a number of different categorisations to highlight their relationships. We identify 82 major metrics, which can be grouped into four classifier families (point-based, bin-based, kernel or curve-based, and cumulative) and an object detection family. For each metric, we provide equations where available, facilitating implementation and comparison by future researchers.

The local least squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Both theoretical and empirical evidence suggests that residuals often exhibit distributional properties different from those of a normal distribution, making it worthwhile to consider estimation based on other norms. It is suggested that $L_p$-norm estimators be used to minimize the residuals when these exhibit non-normal kurtosis. In this paper, we propose a local polynomial $L_p$-norm regression that replaces weighted least squares estimation with weighted $L_p$-norm estimation for fitting the polynomial locally. We also introduce a new method for estimating the parameter $p$ from the residuals, enhancing the adaptability of the approach. Through numerical and theoretical investigation, we demonstrate our method's superiority over local least squares in one-dimensional data and show promising outcomes for higher dimensions, specifically in 2D.