Online learning and model reference adaptive control have many interesting intersections. One area where they differ however is in how the algorithms are analyzed and what objective or metric is used to discriminate "good" algorithms from "bad" algorithms. In adaptive control there are usually two objectives: 1) prove that all time varying parameters/states of the system are bounded, and 2) that the instantaneous error between the adaptively controlled system and a reference system converges to zero over time (or at least a compact set). For online learning the performance of algorithms is often characterized by the regret the algorithm incurs. Regret is defined as the cumulative loss (cost) over time from the online algorithm minus the cumulative loss (cost) of the single optimal fixed parameter choice in hindsight. Another significant difference between the two areas of research is with regard to the assumptions made in order to obtain said results. Adaptive control makes assumptions about the input-output properties of the control problem and derives solutions for a fixed error model or optimization task. In the online learning literature results are derived for classes of loss functions (i.e. convex) while a priori assuming that all time varying parameters are bounded, which for many optimization tasks is not unrealistic, but is a non starter in control applications. In this work we discuss these differences in detail through the regret based analysis of gradient descent for convex functions and the control based analysis of a streaming regression problem. We close with a discussion about the newly defined paradigm of online adaptive control and ask the following question "Are regret optimal control strategies deployable?"

Accurate imputation of missing laboratory values in electronic health records (EHRs) is critical to enable robust clinical predictions and reduce biases in AI systems in healthcare. Existing methods, such as variational autoencoders (VAEs) and decision tree-based approaches such as XGBoost, struggle to model the complex temporal and contextual dependencies in EHR data, mainly in underrepresented groups. In this work, we propose Lab-MAE, a novel transformer-based masked autoencoder framework that leverages self-supervised learning for the imputation of continuous sequential lab values. Lab-MAE introduces a structured encoding scheme that jointly models laboratory test values and their corresponding timestamps, enabling explicit capturing temporal dependencies. Empirical evaluation on the MIMIC-IV dataset demonstrates that Lab-MAE significantly outperforms the state-of-the-art baselines such as XGBoost across multiple metrics, including root mean square error (RMSE), R-squared (R2), and Wasserstein distance (WD). Notably, Lab-MAE achieves equitable performance across demographic groups of patients, advancing fairness in clinical predictions. We further investigate the role of follow-up laboratory values as potential shortcut features, revealing Lab-MAE's robustness in scenarios where such data is unavailable. The findings suggest that our transformer-based architecture, adapted to the characteristics of the EHR data, offers a foundation model for more accurate and fair clinical imputation models. In addition, we measure and compare the carbon footprint of Lab-MAE with the baseline XGBoost model, highlighting its environmental requirements.

In the realm of time series analysis, tackling the phenomenon of concept drift poses a significant challenge. Concept drift - characterized by the evolving statistical properties of time series data, affects the reliability and accuracy of conventional analysis models. This is particularly evident in co-evolving scenarios where interactions among variables are crucial. This paper presents Drift2Matrix, a novel framework that leverages kernel-induced self-representation for adaptive responses to concept drift in time series. Drift2Matrix employs a kernel-based learning mechanism to generate a representation matrix, encapsulating the inherent dynamics of co-evolving time series. This matrix serves as a key tool for identification and adaptation to concept drift by observing its temporal variations. Furthermore, Drift2Matrix effectively identifies prevailing patterns and offers insights into emerging trends through pattern evolution analysis. Our empirical evaluation of Drift2Matrix across various datasets demonstrates its effectiveness in handling the complexities of concept drift. This approach introduces a novel perspective in the theoretical domain of co-evolving time series analysis, enhancing adaptability and accuracy in the face of dynamic data environments. Co-evolving time series data analysis plays a crucial role in diverse sectors including finance, healthcare, and meteorology. Within these areas, multiple time series evolve simultaneously and interact with one another, forming complex, dynamic systems. A particularly pervasive issue is concept drift Lu et al. (2018b); Yu et al. (2024), which refers to shifts in the underlying data distribution over time, thereby undermining the effectiveness of static models. Traditional time series approaches commonly rely on the assumptions of stationarity and linear relationships. Methods such as ARIMA and VAR Box (2013), for instance, perform well in circumstances with stable and predictable dynamics. Conversely, machine learning methodologies Li et al. (2022); Wen et al. (2020), such as diverse neural network architectures Ho et al. (2022); Li et al. (2023); Yang et al. (2024), offer more flexibility but often require large amounts of data and face difficulties in terms of interpretability and adaptability, especially in dynamic contexts. The evolving study has steered the field towards more adaptive and dynamic models.

Temporal alignment of sequences is a fundamental challenge in many applications, such as computer vision and bioinformatics, where local time shifting needs to be accounted for. Misalignment can lead to poor model generalization, especially in high-dimensional sequences. Existing methods often struggle with optimization when dealing with high-dimensional sparse data, falling into poor alignments. Feature selection is frequently used to enhance model performance for sparse data. However, a fixed set of selected features would not generally work for dynamically changing sequences and would need to be modified based on the state of the sequence. Therefore, modifying the selected feature based on contextual input would result in better alignment. Our suggested method, Conditional Deep Canonical Temporal Time Warping (CDCTW), is designed for temporal alignment in sparse temporal data to address these challenges. CDCTW enhances alignment accuracy for high dimensional time-dependent views be performing dynamic time warping on data embedded in maximally correlated subspace which handles sparsity with novel feature selection method. We validate the effectiveness of CDCTW through extensive experiments on various datasets, demonstrating superior performance over previous techniques.

As a natural evolution of traditional regression methods [3], ML models such as Support Vector Regression (SVR) [4] and Artificial Neural Networks (ANN) [5] have been developed to handle non-linear relationships and highdimensional datasets [6] with increasing accuracy and robustness. For instance, SVR has proven to be a robust regression tool because it can generalize well with limited data and capture nonlinear relationships using kernel functions [7]. Similarly, ANN, inspired by the neural architecture of the human brain, has become foundational to ML [5]. Typically, these methods use inputs (X) and outputs (Y) to construct surrogate models that aim to minimize the difference between the predicted and actual output values. These models have found applications across diverse fields, including engineering, medicine, and economics, demonstrating their versatility and potential [8], [9], [10]. In many real-world applications, additional prior information regarding the output model can be leveraged to enhance its accuracy and robustness [11] [12]. For instance, in physical systems, knowledge of the governing laws of physics has been successfully incorporated into ML by developing physics-informed neural networks (PINNs) [13], leading to improved efficiency and accuracy in prediction tasks [14]. In addition to physical laws, probabilistic information about the structure of the problem may also exist in practical scenarios [15]. Moreover, in many systems, the output variable is inherently probabilistic, necessitating models to approximate the probabilistic structure of the output [16].

Uncertainty estimations for machine learning interatomic potentials (MLIPs) are crucial for quantifying model error and identifying informative training samples in active learning strategies. In this study, we evaluate uncertainty estimations of Gaussian process regression (GPR)-based MLIPs, including the predictive GPR standard deviation and ensemble-based uncertainties. We do this in terms of calibration and in terms of impact on model performance in an active learning scheme. We consider GPR models with Coulomb and Smooth Overlap of Atomic Positions (SOAP) representations as inputs to predict potential energy surfaces and excitation energies of molecules. Regarding calibration, we find that ensemble-based uncertainty estimations show already poor global calibration (e.g., averaged over the whole test set). In contrast, the GPR standard deviation shows good global calibration, but when grouping predictions by their uncertainty, we observe a systematical bias for predictions with high uncertainty. Although an increasing uncertainty correlates with an increasing bias, the bias is not captured quantitatively by the uncertainty. Therefore, the GPR standard deviation can be useful to identify predictions with a high bias and error but, without further knowledge, should not be interpreted as a quantitative measure for a potential error range. Selecting the samples with the highest GPR standard deviation from a fixed configuration space leads to a model that overemphasizes the borders of the configuration space represented in the fixed dataset. This may result in worse performance in more densely sampled areas but better generalization for extrapolation tasks.

We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarantees, discussing natural regularity condition on the convolution kernel. More precisely, we assume the convolution kernel is a function in a translation invariant Hilbert space and analyze a natural ridge regression (RR) estimator. Building on existing results for RR, we characterize the accuracy of the estimator in terms of finite sample bounds. Interestingly, regularity assumptions which are classical in the analysis of RR, have a novel and natural interpretation in terms of space/frequency localization. Theoretical results are illustrated by numerical simulations.

Multiple supervised learning scenarios are composed by a sequence of classification tasks. For instance, multi-task learning and continual learning aim to learn a sequence of tasks that is either fixed or grows over time. Existing techniques for learning tasks that are in a sequence are tailored to specific scenarios, lacking adaptability to others. In addition, most of existing techniques consider situations in which the order of the tasks in the sequence is not relevant. However, it is common that tasks in a sequence are evolving in the sense that consecutive tasks often have a higher similarity. This paper presents a learning methodology that is applicable to multiple supervised learning scenarios and adapts to evolving tasks. Differently from existing techniques, we provide computable tight performance guarantees and analytically characterize the increase in the effective sample size. Experiments on benchmark datasets show the performance improvement of the proposed methodology in multiple scenarios and the reliability of the presented performance guarantees.

High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse feature spaces, increasing the risk of overfitting and reducing scalability. This paper introduces novel encoding techniques, including means encoding, low\-rank encoding, and multinomial logistic regression encoding, to address these challenges. These methods leverage sufficient representations to generate compact and informative embeddings of categorical data. We conduct rigorous theoretical analyses and empirical validations on diverse datasets, demonstrating significant improvements in model performance and computational efficiency compared to baseline methods. The proposed techniques are particularly effective in domains requiring scalable solutions for large datasets, paving the way for more robust and efficient applications in machine learning.

Graph few-shot learning has garnered significant attention for its ability to rapidly adapt to downstream tasks with limited labeled data, sparking considerable interest among researchers. Recent advancements in graph few-shot learning models have exhibited superior performance across diverse applications. Despite their successes, several limitations still exist. First, existing models in the meta-training phase predominantly focus on instance-level features within tasks, neglecting crucial set-level features essential for distinguishing between different categories. Second, these models often utilize query sets directly on classifiers trained with support sets containing only a few labeled examples, overlooking potential distribution shifts between these sets and leading to suboptimal performance. Finally, previous models typically require necessitate abundant labeled data from base classes to extract transferable knowledge, which is typically infeasible in real-world scenarios. To address these issues, we propose a novel model named STAR, which leverages Set funcTions and optimAl tRansport for enhancing unsupervised graph few-shot learning. Specifically, STAR utilizes expressive set functions to obtain set-level features in an unsupervised manner and employs optimal transport principles to align the distributions of support and query sets, thereby mitigating distribution shift effects. Theoretical analysis demonstrates that STAR can capture more task-relevant information and enhance generalization capabilities. Empirically, extensive experiments across multiple datasets validate the effectiveness of STAR. Our code can be found here.