Data privacy is a central concern in many applications involving ranking from incomplete and noisy pairwise comparisons, such as recommendation systems, educational assessments, and opinion surveys on sensitive topics. In this work, we propose differentially private algorithms for ranking based on pairwise comparisons. Specifically, we develop and analyze ranking methods under two privacy notions: edge differential privacy, which protects the confidentiality of individual comparison outcomes, and individual differential privacy, which safeguards potentially many comparisons contributed by a single individual. Our algorithms--including a perturbed maximum likelihood estimator and a noisy count-based method--are shown to achieve minimax optimal rates of convergence under the respective privacy constraints. We further demonstrate the practical effectiveness of our methods through experiments on both simulated and real-world data.

Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz smoothness condition, which is often not met in common machine learning models. We highlight this issue with specific counterexamples. To address this gap, we revisit the convergence rates of shuffling-type gradient methods without assuming Lipschitz smoothness. Using our stepsize strategy, the shuffling-type gradient algorithm not only converges under weaker assumptions but also match the current best-known convergence rates, thereby broadening its applicability. We prove the convergence rates for nonconvex, strongly convex, and non-strongly convex cases, each under both random reshuffling and arbitrary shuffling schemes, under a general bounded variance condition. Numerical experiments further validate the performance of our shuffling-type gradient algorithm, underscoring its practical efficacy.

Tabular data synthesis for supervised learning ('SL') model training is gaining popularity in industries such as healthcare, finance, and retail. Despite the progress made in tabular data generators, models trained with synthetic data often underperform compared to those trained with original data. This low SL utility of synthetic data stems from class imbalance exaggeration and SL data relationship overlooked by tabular generator. To address these challenges, we draw inspirations from techniques in emerging data-centric artificial intelligence and elucidate Pruning and ReOrdering ('PRRO'), a novel pipeline that integrates data-centric techniques into tabular data synthesis. PRRO incorporates data pruning to guide the table generator towards observations with high signal-to-noise ratio, ensuring that the class distribution of synthetic data closely matches that of the original data. Besides, PRRO employs a column reordering algorithm to align the data modeling structure of generators with that of SL models. These two modules enable PRRO to optimize SL utility of synthetic data. Empirical experiments on 22 public datasets show that synthetic data generated using PRRO enhances predictive performance compared to data generated without PRRO. Specifically, synthetic replacement of original data yields an average improvement of 26.74% and up to 871.46% improvement using PRRO, while synthetic appendant to original data results with PRRO-generated data results in an average improvement of 6.13% and up to 200.32%. Furthermore, experiments on six highly imbalanced datasets show that PRRO enables the generator to produce synthetic data with a class distribution that resembles the original data more closely, achieving a similarity improvement of 43%. Through PRRO, we foster a seamless integration of data synthesis to subsequent SL prediction, promoting quality and accessible data analysis.

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal prediction, is also computationally efficient as it boils down to collecting statistics of the model predictions on some calibration data not yet seen by the model. Nonetheless, these guarantees only hold if the calibration and test data are exchangeable, a condition that is difficult to verify and often violated in practice due to so-called distribution shifts. The literature is rife with methods to mitigate the loss in coverage in this non-exchangeable setting, but these methods require some prior information on the type of distribution shift to be expected at test time. In this work, we study this problem via a new perspective, through the lens of optimal transport, and show that it is possible to estimate the loss in coverage and mitigate it in case of distribution shift.

In this paper, we formulate a mutual information optimal control problem (MIOCP) for discrete-time linear systems. This problem can be regarded as an extension of a maximum entropy optimal control problem (MEOCP). Differently from the MEOCP where the prior is fixed to the uniform distribution, the MIOCP optimizes the policy and prior simultaneously. As analytical results, under the policy and prior classes consisting of Gaussian distributions, we derive the optimal policy and prior of the MIOCP with the prior and policy fixed, respectively. Using the results, we propose an alternating minimization algorithm for the MIOCP. Through numerical experiments, we discuss how our proposed algorithm works.

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC) based on the discretization of reflected Langevin dynamics (RLD) and more generally skew-reflected non-reversible Langevin Monte Carlo (SRNLMC) based on the discretization of skew-reflected non-reversible Langevin dynamics (SRNLD) have been proposed and studied in the literature. This work focuses on the long-time behavior of SRNLD, where a skew-symmetric matrix is added to RLD. Although acceleration for SRNLD has been studied, it is not clear how one should design the skew-symmetric matrix in the dynamics to achieve good performance in practice. We establish a large deviation principle (LDP) for the empirical measure of SRNLD when the skew-symmetric matrix is chosen such that its product with the inward unit normal vector field on the boundary is zero. By explicitly characterizing the rate functions, we show that this choice of the skew-symmetric matrix accelerates the convergence to the target distribution compared to RLD and reduces the asymptotic variance. Numerical experiments for SRNLMC based on the proposed skew-symmetric matrix show superior performance, which validate the theoretical findings from the large deviations theory.

This paper introduces a comprehensive open-source framework for developing correlation kernels, with a particular focus on user-defined and composition of kernels for surrogate modeling. By advancing kernel-based modeling techniques, we incorporate frequency-aware elements that effectively capture complex mechanical behaviors and timefrequency dynamics intrinsic to aircraft systems. Traditional kernel functions, often limited to exponential-based methods, are extended to include a wider range of kernels such as exponential squared sine and rational quadratic kernels, along with their respective firstand second-order derivatives. The proposed methodologies are first validated on a sinus cardinal test case and then applied to forecasting Mauna-Loa Carbon Dioxide (CO 2 ) concentrations and airline passenger traffic. All these advancements are integrated into the open-source Surrogate Modeling Toolbox (SMT 2.0), providing a versatile platform for both standard and customizable kernel configurations. Furthermore, the framework enables the combination of various kernels to leverage their unique strengths into composite models tailored to specific problems. The resulting framework offers a flexible toolset for engineers and researchers, paving the way for numerous future applications in metamodeling for complex, frequency-sensitive domains.

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.

Catastrophic forgetting is the primary challenge that hinders continual learning, which refers to a neural network ability to sequentially learn multiple tasks while retaining previously acquired knowledge. Elastic Weight Consolidation, a regularization-based approach inspired by synaptic consolidation in biological neural systems, has been used to overcome this problem. In this study prior research is replicated and extended by evaluating EWC in supervised learning settings using the PermutedMNIST and RotatedMNIST benchmarks. Through systematic comparisons with L2 regularization and stochastic gradient descent (SGD) without regularization, we analyze how different approaches balance knowledge retention and adaptability. Our results confirm what was shown in previous research, showing that EWC significantly reduces forgetting compared to naive training while slightly compromising learning efficiency on new tasks. Moreover, we investigate the impact of dropout regularization and varying hyperparameters, offering insights into the generalization of EWC across diverse learning scenarios. These results underscore EWC's potential as a viable solution for lifelong learning in neural networks.

The aging population is growing rapidly, and so is the danger of falls in older adults. A major cause of injury is falling, and detection in time can greatly save medical expenses and recovery time. However, to provide timely intervention and avoid unnecessary alarms, detection systems must be effective and reliable while addressing privacy concerns regarding the user. In this work, we propose a framework for detecting falls using several complementary systems: a semi-supervised federated learning-based fall detection system (SF2D), an indoor localization and navigation system, and a vision-based human fall recognition system. A wearable device and an edge device identify a fall scenario in the first system. On top of that, the second system uses an indoor localization technique first to localize the fall location and then navigate a robot to inspect the scenario. A vision-based detection system running on an edge device with a mounted camera on a robot is used to recognize fallen people. Each of the systems of this proposed framework achieves different accuracy rates. Specifically, the SF2D has a 0.81% failure rate equivalent to 99.19% accuracy, while the vision-based fallen people detection achieves 96.3% accuracy. However, when we combine the accuracy of these two systems with the accuracy of the navigation system (95% success rate), our proposed framework creates a highly reliable performance for fall detection, with an overall accuracy of 99.99%. Not only is the proposed framework safe for older adults, but it is also a privacy-preserving solution for detecting falls.