Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial attacks. While numerous adversarial learning methods have been proposed, fundamental questions about their statistical optimality in robust loss remain largely unanswered. In particular, the minimax rate of convergence and the construction of rate-optimal estimators under future $X$-attacks are yet to be worked out. In this paper, we address this issue in the context of nonparametric regression, under suitable assumptions on the smoothness of the regression function and the geometric structure of the input perturbation set. We first establish the minimax rate of convergence under adversarial $L_q$-risks with $1 \leq q \leq \infty$ and propose a piecewise local polynomial estimator that achieves the minimax optimality. The established minimax rate elucidates how the smoothness level and perturbation magnitude affect the fundamental limit of adversarial learning under future $X$-attacks. Furthermore, we construct a data-driven adaptive estimator that is shown to achieve, within a logarithmic factor, the optimal rate across a broad scale of nonparametric and adversarial classes.

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has studied diagonal linear neural networks in the regression setting. These studies have shown that, when initialized with small weights, gradient descent tends to favor solutions with minimal $\ell^1$-norm - an effect known as implicit regularization. In this paper, we investigate implicit regularization in diagonal linear neural networks of depth $D\ge 2$ for overparameterized linear regression problems. We focus on analyzing the approximation error between the limit point of gradient flow trajectories and the solution to the $\ell^1$-minimization problem. By deriving tight upper and lower bounds on the approximation error, we precisely characterize how the approximation error depends on the scale of initialization $α$. Our results reveal a qualitative difference between depths: for $D \ge 3$, the error decreases linearly with $α$, whereas for $D=2$, it decreases at rate $α^{1-\varrho}$, where the parameter $\varrho \in [0,1)$ can be explicitly characterized. Interestingly, this parameter is closely linked to so-called null space property constants studied in the sparse recovery literature. We demonstrate the asymptotic tightness of our bounds through explicit examples. Numerical experiments corroborate our theoretical findings and suggest that deeper networks, i.e., $D \ge 3$, may lead to better generalization, particularly for realistic initialization scales.

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We introduce Bayesian data sketching for varying coefficient models to obviate computational challenges presented by large sample sizes. To address the challenges of analyzing large data, we compress the functional response vector and predictor matrix by a random linear transformation to achieve dimension reduction and conduct inference on the compressed data. Our approach distinguishes itself from several existing methods for analyzing large functional data in that it requires neither the development of new models or algorithms, nor any specialized computational hardware while delivering fully model-based Bayesian inference. Well-established methods and algorithms for varying coefficient regression models can be applied to the compressed data. We establish posterior contraction rates for estimating the varying coefficients and predicting the outcome at new locations with the randomly compressed data model. We use simulation experiments and analyze remote sensed vegetation data to empirically illustrate the inferential and computational efficiency of our approach.

Research on holistic Automated Essay Scoring (AES) is long-dated; yet, there is a notable lack of attention for assessing essays according to individual traits. In this work, we propose TRATES, a novel trait-specific and rubric-based cross-prompt AES framework that is generic yet specific to the underlying trait. The framework leverages a Large Language Model (LLM) that utilizes the trait grading rubrics to generate trait-specific features (represented by assessment questions), then assesses those features given an essay. The trait-specific features are eventually combined with generic writing-quality and prompt-specific features to train a simple classical regression model that predicts trait scores of essays from an unseen prompt. Experiments show that TRATES achieves a new state-of-the-art performance across all traits on a widely-used dataset, with the generated LLM-based features being the most significant.

Rational speakers are supposed to know what they know and what they do not know, and to generate expressions matching the strength of evidence. In contrast, it is still a challenge for current large language models to generate corresponding utterances based on the assessment of facts and confidence in an uncertain real-world environment. While it has recently become popular to estimate and calibrate confidence of LLMs with verbalized uncertainty, what is lacking is a careful examination of the linguistic knowledge of uncertainty encoded in the latent space of LLMs. In this paper, we draw on typological frameworks of epistemic expressions to evaluate LLMs' knowledge of epistemic modality, using controlled stories. Our experiments show that the performance of LLMs in generating epistemic expressions is limited and not robust, and hence the expressions of uncertainty generated by LLMs are not always reliable. To build uncertainty-aware LLMs, it is necessary to enrich semantic knowledge of epistemic modality in LLMs.

Structured data-quality issues, such as missing values correlated with demographics, culturally biased labels, or systemic selection biases, routinely degrade the reliability of machine-learning pipelines. Regulators now increasingly demand evidence that high-stakes systems can withstand these realistic, interdependent errors, yet current robustness evaluations typically use random or overly simplistic corruptions, leaving worst-case scenarios unexplored. We introduce SAVAGE, a causally inspired framework that (i) formally models realistic data-quality issues through dependency graphs and flexible corruption templates, and (ii) systematically discovers corruption patterns that maximally degrade a target performance metric. SAVAGE employs a bi-level optimization approach to efficiently identify vulnerable data subpopulations and fine-tune corruption severity, treating the full ML pipeline, including preprocessing and potentially non-differentiable models, as a black box. Extensive experiments across multiple datasets and ML tasks (data cleaning, fairness-aware learning, uncertainty quantification) demonstrate that even a small fraction (around 5 %) of structured corruptions identified by SAVAGE severely impacts model performance, far exceeding random or manually crafted errors, and invalidating core assumptions of existing techniques. Thus, SAVAGE provides a practical tool for rigorous pipeline stress-testing, a benchmark for evaluating robustness methods, and actionable guidance for designing more resilient data workflows.

This paper is methodological (and experimental) in nature, providing a suite of approaches to differentially-private Bayesian linear regression. The key significance is to revisit DP linear regression in the Bayesian setting, where it is natural to consider 1) how privacy-preserving noise affects posterior estimates; 2) leverage Bayesian inference through directly modelling the noise process, to improve utility (broadly construed including in terms of calibration). The paper does a quality job of exploring how such modelling and inference could be performed based on sufficient statistic perturbation. The paper has high clarity, further adding to the potential practical impact. The main technical ideas are largely inspired by prior work such as Bernstein and Sheldon (2018)'s work on exponential families.

All reviewers consider the paper to make a solid contribution and recommend acceptance.

This paper explores the development of a control and sensor strategy for an industrial wearable wrist exoskeleton by classifying and predicting workers' actions. The study evaluates the correlation between exerted force and effort intensity, along with sensor strategy optimization, for designing purposes. Using data from six healthy subjects in a manufacturing plant, this paper presents EMG-based models for wrist motion classification and force prediction. Wrist motion recognition is achieved through a pattern recognition algorithm developed with surface EMG data from an 8-channel EMG sensor (Myo Armband); while a force regression model uses wrist and hand force measurements from a commercial handheld dynamometer (Vernier GoDirect Hand Dynamometer). This control strategy forms the foundation for a streamlined exoskeleton architecture designed for industrial applications, focusing on simplicity, reduced costs, and minimal sensor use while ensuring reliable and effective assistance.

Multi-task learning (MTL) has emerged as an imperative machine learning tool to solve multiple learning tasks simultaneously and has been successfully applied to healthcare, marketing, and biomedical fields. However, in order to borrow information across different tasks effectively, it is essential to utilize both homogeneous and heterogeneous information. Among the extensive literature on MTL, various forms of heterogeneity are presented in MTL problems, such as block-wise, distribution, and posterior heterogeneity. Existing methods, however, struggle to tackle these forms of heterogeneity simultaneously in a unified framework. In this paper, we propose a two-step learning strategy for MTL which addresses the aforementioned heterogeneity. First, we impute the missing blocks using shared representations extracted from homogeneous source across different tasks. Next, we disentangle the mappings between input features and responses into a shared component and a task-specific component, respectively, thereby enabling information borrowing through the shared component. Our numerical experiments and real-data analysis from the ADNI database demonstrate the superior MTL performance of the proposed method compared to other competing methods.