Imitation learning holds the promise of equipping robots with versatile skills by learning from expert demonstrations. However, policies trained on finite datasets often struggle to generalize beyond the training distribution. In this work, we present a unified perspective on the generalization capability of imitation learning, grounded in both information theorey and data distribution property. We first show that the generalization gap can be upper bounded by (i) the conditional information bottleneck on intermediate representations and (ii) the mutual information between the model parameters and the training dataset. This characterization provides theoretical guidance for designing effective training strategies in imitation learning, particularly in determining whether to freeze, fine-tune, or train large pretrained encoders (e.g., vision-language models or vision foundation models) from scratch to achieve better generalization. Furthermore, we demonstrate that high conditional entropy from input to output induces a flatter likelihood landscape, thereby reducing the upper bound on the generalization gap. In addition, it shortens the stochastic gradient descent (SGD) escape time from sharp local minima, which may increase the likelihood of reaching global optima under fixed optimization budgets. These insights explain why imitation learning often exhibits limited generalization and underscore the importance of not only scaling the diversity of input data but also enriching the variability of output labels conditioned on the same input.

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.

In the trajectory planning of automated driving, data-driven statistical artificial intelligence (AI) methods are increasingly established for predicting the emergent behavior of other road users. While these methods achieve exceptional performance in defined datasets, they usually rely on the independent and identically distributed (i.i.d.) assumption and thus tend to be vulnerable to distribution shifts that occur in the real world. In addition, these methods lack explainability due to their black box nature, which poses further challenges in terms of the approval process and social trustworthiness. Therefore, in order to use the capabilities of data-driven statistical AI methods in a reliable and trustworthy manner, the concept of TrustMHE is introduced and investigated in this paper. TrustMHE represents a complementary approach, independent of the underlying AI systems, that combines AI-driven out-of-distribution detection with control-driven moving horizon estimation (MHE) to enable not only detection and monitoring, but also intervention. The effectiveness of the proposed TrustMHE is evaluated and proven in three simulation scenarios.

Length of hospital stay is a critical metric for assessing healthcare quality and optimizing hospital resource management. This study aims to identify factors influencing LoS within the Italian healthcare context, using a dataset of hospitalization records from over 60 healthcare facilities in the Piedmont region, spanning from 2020 to 2023. We explored a variety of features, including patient characteristics, comorbidities, admission details, and hospital-specific factors. Significant correlations were found between LoS and features such as age group, comorbidity score, admission type, and the month of admission. Machine learning models, specifically CatBoost and Random Forest, were used to predict LoS. The highest R2 score, 0.49, was achieved with CatBoost, demonstrating good predictive performance.

Balancing performance and interpretability in multivariate time series classification is a significant challenge due to data complexity and high dimensionality. This paper introduces PHeatPruner, a method integrating persistent homology and sheaf theory to address these challenges. Persistent homology facilitates the pruning of up to 45% of the applied variables while maintaining or enhancing the accuracy of models such as Random Forest, CatBoost, XGBoost, and LightGBM, all without depending on posterior probabilities or supervised optimization algorithms. Concurrently, sheaf theory contributes explanatory vectors that provide deeper insights into the data's structural nuances. The approach was validated using the UEA Archive and a mastitis detection dataset for dairy cows. The results demonstrate that PHeatPruner effectively preserves model accuracy. Furthermore, our results highlight PHeatPruner's key features, i.e. simplifying complex data and offering actionable insights without increasing processing time or complexity. This method bridges the gap between complexity reduction and interpretability, suggesting promising applications in various fields.

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods.

Given the high computational complexity of decision tree estimation, classical methods construct a tree by adding one node at a time in a recursive way. To facilitate promoting fairness, we propose a fairness criterion local to the tree nodes. We prove how it is related to the Statistical Parity criterion, popular in the Algorithmic Fairness literature, and show how to incorporate it into standard recursive tree estimation algorithms. We present a tree estimation algorithm called Constrained Logistic Regression Tree (C-LRT), which is a modification of the standard CART algorithm using locally linear classifiers and imposing restrictions as done in Constrained Logistic Regression. Finally, we evaluate the performance of trees estimated with C-LRT on datasets commonly used in the Algorithmic Fairness literature, using various classification and fairness metrics. The results confirm that C-LRT successfully allows to control and balance accuracy and fairness.

Accurate prediction of lithium-ion battery lifespan is vital for ensuring operational reliability and reducing maintenance costs in applications like electric vehicles and smart grids. This study presents a hybrid learning framework for precise battery lifespan prediction, integrating dynamic multi-source data fusion with a stacked ensemble (SE) modeling approach. By leveraging heterogeneous datasets from the National Aeronautics and Space Administration (NASA), Center for Advanced Life Cycle Engineering (CALCE), MIT-Stanford-Toyota Research Institute (TRC), and nickel cobalt aluminum (NCA) chemistries, an entropy-based dynamic weighting mechanism mitigates variability across heterogeneous datasets. The SE model combines Ridge regression, long short-term memory (LSTM) networks, and eXtreme Gradient Boosting (XGBoost), effectively capturing temporal dependencies and nonlinear degradation patterns. It achieves a mean absolute error (MAE) of 0.0058, root mean square error (RMSE) of 0.0092, and coefficient of determination (R2) of 0.9839, outperforming established baseline models with a 46.2% improvement in R2 and an 83.2% reduction in RMSE. Shapley additive explanations (SHAP) analysis identifies differential discharge capacity (Qdlin) and temperature of measurement (Temp_m) as critical aging indicators. This scalable, interpretable framework enhances battery health management, supporting optimized maintenance and safety across diverse energy storage systems, thereby contributing to improved battery health management in energy storage systems.

W e generalize the connection between activation function and spline regression/smoothing and characterize how this choice may influence spectral bias within a 1D shallow network. W e then demonstrate how gradient descent (GD) can be reinterpreted as a shrinkage operator that masks the singular values of a neural network's Jacobian. Viewed this way, GD implicitly selects the number of frequency components to retain, thereby controlling the spectral bias. An explicit relationship is proposed between the choice of GD hyperparameters (learning rate & number of iterations) and bandwidth (the number of active components). GD regularization is shown to be effective only with monotonic activation functions. Finally, we highlight the utility of non-monotonic activation functions (sinc, Gaussian) as iteration-efficient surrogates for spectral bias.

Deep subspace clustering (DSC) algorithms face several challenges that hinder their widespread adoption across variois application domains. First, clustering quality is typically assessed using only the encoder's output layer, disregarding valuable information present in the intermediate layers. Second, most DSC approaches treat representation learning and subspace clustering as independent tasks, limiting their effectiveness. Third, they assume the availability of a held-out dataset for hyperparameter tuning, which is often impractical in real-world scenarios. Fourth, learning termination is commonly based on clustering error monitoring, requiring external labels. Finally, their performance often depends on post-processing techniques that rely on labeled data. To address this limitations, we introduce a novel single-view DSC approach that: (i) minimizes a layer-wise self expression loss using a joint representation matrix; (ii) optimizes a subspace-structured norm to enhance clustering quality; (iii) employs a multi-stage sequential learning framework, consisting of pre-training and fine-tuning, enabling the use of multiple regularization terms without hyperparameter tuning; (iv) incorporates a relative error-based self-stopping mechanism to terminate training without labels; and (v) retains a fixed number of leading coefficients in the learned representation matrix based on prior knowledge. We evaluate the proposed method on six datasets representing faces, digits, and objects. The results show that our method outperforms most linear SC algorithms with careffulyl tuned hyperparameters while maintaining competitive performance with the best performing linear appoaches.