Given $n$ i.i.d. random matrices $A_i \in \mathbb{R}^{d \times d}$ that share a common expectation $Σ$, the objective of Differentially Private Stochastic PCA is to identify a subspace of dimension $k$ that captures the largest variance directions of $Σ$, while preserving differential privacy (DP) of each individual $A_i$. Existing methods either (i) require the sample size $n$ to scale super-linearly with dimension $d$, even under Gaussian assumptions on the $A_i$, or (ii) introduce excessive noise for DP even when the intrinsic randomness within $A_i$ is small. Liu et al. (2022a) addressed these issues for sub-Gaussian data but only for estimating the top eigenvector ($k=1$) using their algorithm DP-PCA. We propose the first algorithm capable of estimating the top $k$ eigenvectors for arbitrary $k \leq d$, whilst overcoming both limitations above. For $k=1$ our algorithm matches the utility guarantees of DP-PCA, achieving near-optimal statistical error even when $n = \tilde{\!O}(d)$. We further provide a lower bound for general $k > 1$, matching our upper bound up to a factor of $k$, and experimentally demonstrate the advantages of our algorithm over comparable baselines.

Parkinson's Disease (PD) medication management presents unique challenges due to heterogeneous disease progression and treatment response. Neurologists must balance symptom control with optimal dopaminergic dosing based on functional disability while minimizing side effects. This balance is crucial as inadequate or abrupt changes can cause levodopa-induced dyskinesia, wearing off, and neuropsychiatric effects, significantly reducing quality of life. Current approaches rely on trial-and-error decisions without systematic predictive methods. Despite machine learning advances, clinical adoption remains limited due to reliance on point predictions that do not account for prediction uncertainty, undermining clinical trust and utility. Clinicians require not only predictions of future medication needs but also reliable confidence measures. Without quantified uncertainty, adjustments risk premature escalation to maximum doses or prolonged inadequate symptom control. We developed a conformal prediction framework anticipating medication needs up to two years in advance with reliable prediction intervals and statistical guarantees. Our approach addresses zero-inflation in PD inpatient data, where patients maintain stable medication regimens between visits. Using electronic health records from 631 inpatient admissions at University of Florida Health (2011-2021), our two-stage approach identifies patients likely to need medication changes, then predicts required levodopa equivalent daily dose adjustments. Our framework achieved marginal coverage while reducing prediction interval lengths compared to traditional approaches, providing precise predictions for short-term planning and wider ranges for long-term forecasting. By quantifying uncertainty, our approach enables evidence-based decisions about levodopa dosing, optimizing symptom control while minimizing side effects and improving life quality.

Sharpness-Aware Minimization (SAM) has been proven to be an effective optimization technique for improving generalization in overparameterized models. While prior works have explored the implicit regularization of SAM in simple two-core scale-invariant settings, its behavior in more general tensorized or scale-invariant models remains underexplored. In this work, we leverage scale-invariance to analyze the norm dynamics of SAM in general tensorized models. We introduce the notion of \emph{Norm Deviation} as a global measure of core norm imbalance, and derive its evolution under SAM using gradient flow analysis. We show that SAM's implicit control of Norm Deviation is governed by the covariance between core norms and their gradient magnitudes. Motivated by these findings, we propose a simple yet effective method, \emph{Deviation-Aware Scaling (DAS)}, which explicitly mimics this regularization behavior by scaling core norms in a data-adaptive manner. Our experiments across tensor completion, noisy training, model compression, and parameter-efficient fine-tuning confirm that DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.

We present BKP, a user-friendly and extensible R package that implements the Beta Kernel Process (BKP) -- a fully nonparametric and computationally efficient framework for modeling spatially varying binomial probabilities. The BKP model combines localized kernel-weighted likelihoods with conjugate beta priors, resulting in closed-form posterior inference without requiring latent variable augmentation or intensive MCMC sampling. The package supports binary and aggregated binomial responses, allows flexible choices of kernel functions and prior specification, and provides loss-based kernel hyperparameter tuning procedures. In addition, BKP extends naturally to the Dirichlet Kernel Process (DKP) for modeling spatially varying multinomial or compositional data. To our knowledge, this is the first publicly available R package for implementing BKP-based methods. We illustrate the use of BKP through several synthetic and real-world datasets, highlighting its interpretability, accuracy, and scalability. The package aims to facilitate practical application and future methodological development of kernel-based beta modeling in statistics and machine learning.

In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of \cite{gibbs2021adaptive}. For any given point-prediction algorithm, their method (ACI) produces a conformal prediction set with an average missed coverage getting close to a pre-specified level $α$ for a long time horizon. We introduce an extended version of this algorithm, called OnlineSCI, allowing the user to additionally select times where such an inference should be made. OnlineSCI encompasses several prominent online selective tasks, such as building prediction intervals for extreme outcomes, classification with abstention, and online testing. While OnlineSCI controls the average missed coverage on the selected in an adversarial setting, our theoretical results also show that it controls the instantaneous error rate (IER) at the selected times, up to a non-asymptotical remainder term. Importantly, our theory covers the case where OnlineSCI updates the point-prediction algorithm at each time step, a property which we refer to as {\it adaptive} capability. We show that the adaptive versions of OnlineSCI can convergence to an optimal solution and provide an explicit convergence rate in each of the aforementioned application cases, under specific mild conditions. Finally, the favorable behavior of OnlineSCI in practice is illustrated by numerical experiments.

The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of point clouds or networks. To overcome certain limitations, such as the restriction to comparisons of measures of equal mass and sensitivity to outliers, several unbalanced or partial transport relaxations of the GW distance have been introduced in the recent literature. This paper is concerned with the Conic Gromov-Wasserstein (CGW) distance introduced by S ejourn e, Vialard, and Peyr e [35]. We provide a novel formulation in terms of semi-couplings, and extend the framework beyond the metric measure space setting, to compare more general network and hypernetwork structures. With this new formulation, we establish several fundamental properties of the CGW metric, including its scaling behavior under dilation, variational convergence in the limit of volume growth constraints, and comparison bounds with established optimal transport metrics. We further derive quantitative bounds that characterize the robustness of the CGW metric to perturbations in the underlying measures. The hypernetwork formulation of CGW admits a simple and provably convergent block coordinate ascent algorithm for its estimation, and we demonstrate the computational tractability and scalability of our approach through experiments on synthetic and real-world high-dimensional and structured datasets.

Recent advancements in machine learning have spurred growing interests in automated interpreting quality assessment. Nevertheless, existing research suffers from insufficient examination of language use quality, unsatisfactory modeling effectiveness due to data scarcity and imbalance, and a lack of efforts to explain model predictions. To address these gaps, we propose a multi-dimensional modeling framework that integrates feature engineering, data augmentation, and explainable machine learning. This approach prioritizes explainability over ``black box'' predictions by utilizing only construct-relevant, transparent features and conducting Shapley Value (SHAP) analysis. Our results demonstrate strong predictive performance on a novel English-Chinese consecutive interpreting dataset, identifying BLEURT and CometKiwi scores to be the strongest predictive features for fidelity, pause-related features for fluency, and Chinese-specific phraseological diversity metrics for language use. Overall, by placing particular emphasis on explainability, we present a scalable, reliable, and transparent alternative to traditional human evaluation, facilitating the provision of detailed diagnostic feedback for learners and supporting self-regulated learning advantages not afforded by automated scores in isolation.

-- Subjective self-disclosure is an important feature of human social interaction. While much has been done in the social and behavioural literature to characterise the features and consequences of subjective self-disclosure, little work has been done thus far to develop computational systems that are able to accurately model it. Even less work has been done that attempts to model specifically how human interactants self-disclose with robotic partners. It is becoming more pressing as we require social robots to work in conjunction with and establish relationships with humans in various social settings. In this paper, our aim is to develop a custom multimodal attention network based on models from the emotion recognition literature, training this model on a large self-collected self-disclosure video corpus, and constructing a new loss function, the scale preserving cross entropy loss, that improves upon both classification and regression versions of this problem. Our results show that the best performing model, trained with our novel loss function, achieves an F1 score of 0.83, an improvement of 0.48 from the best baseline model. This result makes significant headway in the aim of allowing social robots to pick up on an interaction partner's self-disclosures, an ability that will be essential in social robots with social cognition. Self-disclosure is the sharing of one's thoughts, feelings, or personal information during a social interaction [1]. It is an import facet of human social behaviour and can contribute to many aspects of our lives.

ONiO AS, Oslo, NorwayAbstract: This study proposes an antenna simulation framework powered by graphics processing units (GPUs) based on an open-source electromagnetic (EM) simulation software (gprMax) for machine learning applications of antenna design and optimization. Furthermore, it compares the simulation results with those obtained through commercial EM software. The proposed software framework for machine learning and surrogate model applications will produce antenna data sets consisting of a large number of antenna simulation results using GPUs. Although machine learning methods can attain the optimum solutions for many problems, they are known to be data-hungry and require a great deal of samples for the training stage of the algorithms. However, producing a sufficient number of training samples in EM applications within a limited time is challenging due to the high computational complexity of EM simulations. Therefore, GPUs are utilized in this study to simulate a large number of antennas with predefined or random antenna shape parameters to produce data sets. Moreover, this study also compares various machine learning and deep learning models in terms of antenna parameter estimation performance. This study demonstrates that an entry-level GPU substantially outperforms a high-end CPU in terms of computational performance, while a high-end gaming GPU can achieve around 18 times more computational performance compared to a high-end CPU. Moreover, it is shown that the open-source EM simulation software can deliver similar results to those obtained via commercial software in the simulation of microstrip antennas when the spatial resolution of the simulations is sufficiently fine. Key words: antenna simulations, electromagnetic, machine learning, open-source, gprMax 1. Introduction EM simulation software and libraries are paramount for antenna and EM research and engineering since the fabrication and measurements of antenna prototypes are relatively expensive and time-consuming. Accordingly, extensive simulations are generally performed to optimize EM structures and antennas before fabricating them. Due to their high reliability and accuracy, commercial EM software packages are widely used in academia and industry to model, design, and optimize antennas.

Scientific progress is tightly coupled to the emergence of new research tools. Today, machine learning (ML)-especially deep learning (DL)-has become a transformative instrument for quantum science and technology. Owing to the intrinsic complexity of quantum systems, DL enables efficient exploration of large parameter spaces, extraction of patterns from experimental data, and data-driven guidance for research directions. These capabilities already support tasks such as refining quantum control protocols and accelerating the discovery of materials with targeted quantum properties, making ML/DL literacy an essential skill for the next generation of quantum scientists. At the same time, DL's power brings risks: models can overfit noisy data, obscure causal structure, and yield results with limited physical interpretability. Recognizing these limitations and deploying mitigation strategies is crucial for scientific rigor. These lecture notes provide a comprehensive, graduate-level introduction to DL for quantum applications, combining conceptual exposition with hands-on examples. Organized as a progressive sequence, they aim to equip readers to decide when and how to apply DL effectively, to understand its practical constraints, and to adapt AI methods responsibly to problems across quantum physics, chemistry, and engineering.