Cross-validation is one of the most widely used methods for model selection and evaluation; its efficiency for large covariance matrix estimation appears robust in practice, but little is known about the theoretical behavior of its error. In this paper, we derive the expected Frobenius error of the holdout method, a particular cross-validation procedure that involves a single train and test split, for a generic rotationally invariant multiplicative noise model, therefore extending previous results to non-Gaussian data distributions. Our approach involves using the Weingarten calculus and the Ledoit-Péché formula to derive the oracle eigenvalues in the high-dimensional limit. When the population covariance matrix follows an inverse Wishart distribution, we approximate the expected holdout error, first with a linear shrinkage, then with a quadratic shrinkage to approximate the oracle eigenvalues. Under the linear approximation, we find that the optimal train-test split ratio is proportional to the square root of the matrix dimension. Then we compute Monte Carlo simulations of the holdout error for different distributions of the norm of the noise, such as the Gaussian, Student, and Laplace distributions and observe that the quadratic approximation yields a substantial improvement, especially around the optimal train-test split ratio. We also observe that a higher fourth-order moment of the Euclidean norm of the noise vector sharpens the holdout error curve near the optimal split and lowers the ideal train-test ratio, making the choice of the train-test ratio more important when performing the holdout method.

Abstract-- With the rapid development of the new energy vehicle industry, the efficient disassembly and recycling of power batteries have become a critical challenge for the circular economy. In current unstructured disassembly scenarios, the dynamic nature of the environment severely limits the robustness of robotic perception, posing a significant barrier to autonomous disassembly in industrial applications. This paper proposes a continual learning framework based on Neuro-Symbolic task and motion planning (T AMP) to enhance the adaptability of embodied intelligence systems in dynamic environments. Our approach integrates a multimodal perception cross-validation mechanism into a bidirectional reasoning flow: the forward working flow dynamically refines and optimizes action strategies, while the backward learning flow autonomously collects effective data from historical task executions to facilitate continual system learning, enabling self-optimization. Experimental results show that the proposed framework improves the task success rate in dynamic disassembly scenarios from 81.68% to 100%, while reducing the average number of perception misjudgments from 3.389 to 1.128. This research provides a new paradigm for enhancing the robustness and adaptability of embodied intelligence in complex industrial environments. I. INTRODUCTION With the rapid development of Industry 4.0 and the circular economy, industrial disassembly has become a critical link in intelligent manufacturing and resource recycling, facing unprecedented technical challenges [1], [2].

In response to the prevalent concern of TCP SYN flood attacks within the context of Software-Defined Internet of Vehicles (SD-IoV), this study addresses the significant challenge of network security in rapidly evolving vehicular communication systems. This research focuses on optimizing a Random Forest Classifier model to achieve maximum accuracy and minimal detection time, thereby enhancing vehicular network security. The methodology involves preprocessing a dataset containing SYN attack instances, employing feature scaling and label encoding techniques, and applying Stratified K-Fold cross-validation to target key metrics such as accuracy, precision, recall, and F1-score. This research achieved an average value of 0.999998 for all metrics with a SYN DoS attack detection time of 0.24 seconds. Results show that the fine-tuned Random Forest model, configured with 20 estimators and a depth of 10, effectively differentiates between normal and malicious traffic with high accuracy and minimal detection time, which is crucial for SD-IoV networks. This approach marks a significant advancement and introduces a state-of-the-art algorithm in detecting SYN flood attacks, combining high accuracy with minimal detection time. It contributes to vehicular network security by providing a robust solution against TCP SYN flood attacks while maintaining network efficiency and reliability.

Out-of-distribution (OOD) detection plays a key role in enhancing the robustness of artificial intelligence systems by identifying inputs that differ significantly from the training distribution, thereby preventing unreliable predictions and enabling appropriate fallback mechanisms. Developing reliable OOD detection methods is a significant challenge, and rigorous evaluation of these techniques is essential for ensuring their effectiveness, as it allows researchers to assess their performance under diverse conditions and to identify potential limitations or failure modes. Cross-validation (CV) has proven to be a highly effective tool for providing a reasonable estimate of the performance of a learning algorithm. Although OOD scenarios exhibit particular characteristics, an appropriate adaptation of CV can lead to a suitable evaluation framework for this setting. This work proposes a dual CV framework for robust evaluation of OOD detection models, aimed at improving the reliability of their assessment. The proposed evaluation framework aims to effectively integrate in-distribution (ID) and OOD data while accounting for their differing characteristics. To achieve this, ID data are partitioned using a conventional approach, whereas OOD data are divided by grouping samples based on their classes. Furthermore, we analyze the context of data with class hierarchy to propose a data splitting that considers the entire class hierarchy to obtain fair ID-OOD partitions to apply the proposed evaluation framework. This framework is called Dual Cross-Validation for Robust Out-of-Distribution Detection (DCV-ROOD). To test the validity of the evaluation framework, we selected a set of state-of-the-art OOD detection methods, both with and without outlier exposure. The results show that the method achieves very fast convergence to the true performance.

Cross-validation plays a fundamental role in Machine Learning, enabling robust evaluation of model performance and preventing overestimation on training and validation data. However, one of its drawbacks is the potential to create data subsets (folds) that do not adequately represent the diversity of the original dataset, which can lead to biased performance estimates. The objective of this work is to deepen the investigation of cluster-based cross-validation strategies by analyzing the performance of different clustering algorithms through experimental comparison. Additionally, a new cross-validation technique that combines Mini Batch K-Means with class stratification is proposed. Experiments were conducted on 20 datasets (both balanced and imbalanced) using four supervised learning algorithms, comparing cross-validation strategies in terms of bias, variance, and computational cost. The technique that uses Mini Batch K-Means with class stratification outperformed others in terms of bias and variance on balanced datasets, though it did not significantly reduce computational cost. On imbalanced datasets, traditional stratified cross-validation consistently performed better, showing lower bias, variance, and computational cost, making it a safe choice for performance evaluation in scenarios with class imbalance. In the comparison of different clustering algorithms, no single algorithm consistently stood out as superior. Overall, this work contributes to improving predictive model evaluation strategies by providing a deeper understanding of the potential of cluster-based data splitting techniques and reaffirming the effectiveness of well-established strategies like stratified cross-validation. Moreover, it highlights perspectives for increasing the robustness and reliability of model evaluations, especially in datasets with clustering characteristics.

I develop an algorithm to produce the piecewise quadratic that computes leave-one-out cross-validation for the lasso as a function of its hyperparameter. The algorithm can be used to find exact hyperparameters that optimize leave-one-out cross-validation either globally or locally, and its practicality is demonstrated on real-world data sets.

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees.

This work develops central limit theorems for cross-validation and consistent estimators of its asymptotic variance under weak stability conditions on the learning algorithm. Together, these results provide practical, asymptotically-exact confidence intervals for k -fold test error and valid, powerful hypothesis tests of whether one learning algorithm has smaller k -fold test error than another. These results are also the first of their kind for the popular choice of leave-one-out cross-validation. In our real-data experiments with diverse learning algorithms, the resulting intervals and tests outperform the most popular alternative methods from the literature.

Existing work has shown that cross-validation (CV) can be used to provide an asymptotic confidence interval for the test error of a stable machine learning algorithm, and existing stability results for many popular algorithms can be applied to derive positive instances where such confidence intervals will be valid. However, in the common setting where CV is used to compare two algorithms, it becomes necessary to consider a notion of relative stability which cannot easily be derived from existing stability results, even for simple algorithms. To better understand relative stability and when CV provides valid confidence intervals for the test error difference of two algorithms, we study the soft-thresholded least squares algorithm, a close cousin of the Lasso. We prove that while stability holds when assessing the individual test error of this algorithm, relative stability fails to hold when comparing the test error of two such algorithms, even in a sparse low-dimensional linear model setting. Additionally, we empirically confirm the invalidity of CV confidence intervals for the test error difference when either soft-thresholding or the Lasso is used. In short, caution is needed when quantifying the uncertainty of CV estimates of the performance difference of two machine learning algorithms, even when both algorithms are individually stable.

--Calibration data are necessary to formally quantify the uncertainty of the decisions produced by an existing artificial intelligence (AI) model. T o overcome the common issue of scarce calibration data, a promising approach is to employ synthetic labels produced by a (generally different) predictive model. This paper introduces a novel approach that efficiently utilizes limited calibration data to simultaneously fine-tune a predictor and estimate the bias of the synthetic labels. The proposed method yields prediction sets with rigorous coverage guarantees for AI-generated decisions. N many AI applications, it is critical to quantify the uncertainty in model decisions by constructing prediction sets or confidence intervals.