This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our model exhibits the following challenges. First, the regularization term can be nonconvex and nonsmooth, necessitating the introduction of infinite dimensional variational analysis and nonsmooth analysis into the asymptotic normality discussion. Second, our network must expand (in width, sparsity level and depth) as more samples are observed, thereby introducing additional difficulties for theoretical analysis. Third, the oracle of the proposed estimator is itself defined through a ultra high-dimensional, nonconvex, and discontinuous optimization problem, which already entails substantial computational and theoretical challenges. Under such the challenges, we establish the consistency, convergence rate, and asymptotic normality of the estimator. Furthermore, we analyze the oracle problem itself and its continuous relaxation. We study the convergence of a proximal subgradient method for both formulations, highlighting their structural differences lead to distinct computational subproblems along the iterations. In particular, the relaxed formulation admits significantly cheaper proximal updates, reflecting an inherent trade-off between statistical accuracy and computational tractability.

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets whose samples lie on low-dimensional manifolds requires robust techniques capable of separating meaningful signal from noise. We propose a principled framework for statistical inference of similarity and alignment between distributions supported on manifolds underlying high-dimensional datasets in the presence of heterogeneous noise. The key idea is to link the low-rank structure of observed data matrices to their underlying manifold geometry. By analyzing the spectrum of the sample covariance under a manifold signal-plus-noise model, we develop a scale-invariant distance measure between datasets based on their principal variance structures. We further introduce a consistent estimator for this distance and a statistical test for manifold alignability, and establish their asymptotic properties using random matrix theory. The proposed framework accommodates heterogeneous noise across datasets and offers an efficient, theoretically grounded approach for comparing high-dimensional datasets with low-dimensional manifold structures. Through extensive simulations and analyses of multi-sample single-cell datasets, we demonstrate that our method achieves superior robustness and statistical power compared with existing approaches.

This paper presents a fully blind phase-aware expectation-maximization (EM) algorithm for OFDM systems with the phase-shift keying (PSK) modulation. We address the well-known local maximum problem of the EM algorithm for blind channel estimation. This is primarily caused by the unknown phase ambiguity in the channel estimates, which conventional blind EM estimators cannot resolve. To overcome this limitation, we propose to exploit the extrinsic information from the decoder as model evidence metrics. A finite set of candidate models is generated based on the inherent symmetries of PSK modulation, and the decoder selects the most likely candidate model. Simulation results demonstrate that, when combined with a simple convolutional code, the phase-aware EM algorithm reliably resolves phase ambiguity during the initialization stage and reduces the local convergence rate from 80% to nearly 0% in frequency-selective channels with a constant phase ambiguity. The algorithm is invoked only once after the EM initialization stage, resulting in negligible additional complexity during subsequent turbo iterations.

Large language models are increasingly capable of producing creative texts, yet most studies on AI-generated poetry focus on English -- a language that dominates training data. In this paper, we examine the perception of AI- and human-written Czech poetry. We ask if Czech native speakers are able to identify it and how they aesthetically judge it. Participants performed at chance level when guessing authorship (45.8\% correct on average), indicating that Czech AI-generated poems were largely indistinguishable from human-written ones. Aesthetic evaluations revealed a strong authorship bias: when participants believed a poem was AI-generated, they rated it as less favorably, even though AI poems were in fact rated equally or more favorably than human ones on average. The logistic regression model uncovered that the more the people liked a poem, the less probable was that they accurately assign the authorship. Familiarity with poetry or literary background had no effect on recognition accuracy. Our findings show that AI can convincingly produce poetry even in a morphologically complex, low-resource (with respect of the training data of AI models) Slavic language such as Czech. The results suggest that readers' beliefs about authorship and the aesthetic evaluation of the poem are interconnected.

Handling missing data is a central challenge in data-driven analysis. Modern imputation methods not only aim for accurate reconstruction but also differ in how they represent and quantify uncertainty. Yet, the reliability and calibration of these uncertainty estimates remain poorly understood. This paper presents a systematic empirical study of uncertainty in imputation, comparing representative methods from three major families: statistical (MICE, SoftImpute), distribution alignment (OT-Impute), and deep generative (GAIN, MIWAE, TabCSDI). Experiments span multiple datasets, missingness mechanisms (MCAR, MAR, MNAR), and missingness rates. Uncertainty is estimated through three complementary routes: multi-run variability, conditional sampling, and predictive-distribution modeling, and evaluated using calibration curves and the Expected Calibration Error (ECE). Results show that accuracy and calibration are often misaligned: models with high reconstruction accuracy do not necessarily yield reliable uncertainty. We analyze method-specific trade-offs among accuracy, calibration, and runtime, identify stable configurations, and offer guidelines for selecting uncertainty-aware imputers in data cleaning and downstream machine learning pipelines.

The rise of generative AI has enabled the production of high-fidelity synthetic tabular data across fields such as healthcare, finance, and public policy, raising growing concerns about data provenance and misuse. Watermarking offers a promising solution to address these concerns by ensuring the traceability of synthetic data, but existing methods face many limitations: they are computationally expensive due to reliance on large diffusion models, struggle with mixed discrete-continuous data, or lack robustness to post-modifications. To address them, we propose TAB-DRW, an efficient and robust post-editing watermarking scheme for generative tabular data. TAB-DRW embeds watermark signals in the frequency domain: it normalizes heterogeneous features via the Yeo-Johnson transformation and standardization, applies the discrete Fourier transform (DFT), and adjusts the imaginary parts of adaptively selected entries according to precomputed pseudorandom bits. To further enhance robustness and efficiency, we introduce a novel rank-based pseudorandom bit generation method that enables row-wise retrieval without incurring storage overhead. Experiments on five benchmark tabular datasets show that TAB-DRW achieves strong detectability and robustness against common post-processing attacks, while preserving high data fidelity and fully supporting mixed-type features.

We consider the problem of strategic classification, where the act of deploying a classifier leads to strategic behaviour that induces a distribution shift on subsequent observations. Current approaches to learning classifiers in strategic settings are focused primarily on the linear setting, but in many cases non-linear classifiers are more suitable. A central limitation to progress for non-linear classifiers arises from the inability to compute best responses in these settings. We present a novel method for computing the best response by optimising the Lagrangian dual of the Agents' objective. We demonstrate that our method reproduces best responses in linear settings, identifying key weaknesses in existing approaches. We present further results demonstrating our method can be straight-forwardly applied to non-linear classifier settings, where it is useful for both evaluation and training.

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

-- Type 1 Diabetes (T1D) affects millions worldwide, requiring continuous monitoring to prevent severe hypo-and hyperglycemic events. While continuous glucose monitoring has improved blood glucose management, deploying predictive models on wearable devices remains challenging due to computational and memory constraints. T o address this, we propose a novel Lightweight Sequential Transformer model designed for blood glucose prediction in T1D. The model is optimized for deployment on resource-constrained edge devices and incorporates a balanced loss function to handle the inherent data imbalance in hypo-and hyperglycemic events. Experiments on two benchmark datasets, OhioT1DM and DiaTrend, demonstrate that the proposed model outperforms state-of-the-art methods in predicting glucose levels and detecting adverse events. This work fills the gap between high-performance modeling and practical deployment, providing a reliable and efficient T1D management solution. Type 1 Diabetes (T1D) [1] is a chronic autoimmune condition requiring lifelong blood glucose concentration (BGC) monitoring to prevent life-threatening complications such as hypoglycemia (BGC below 70 mg/dL [2]) and hyperglycemia (BGC above 180 mg/dL [3]).

The utility of an explanation method critically depends on its fidelity to the underlying machine learning model. Especially in high-stakes medical settings, clinicians and regulators require explanations that faithfully reflect the model's decision process. Existing fidelity metrics such as Infidelity rely on Monte Carlo approximation, which demands numerous model evaluations and introduces uncertainty due to random sampling. This work proposes a novel metric for evaluating the fidelity of local feature attribution methods by modifying the existing Prediction Change (PC) metric within the Guided Perturbation Experiment. By incorporating the direction of both perturbation and attribution, the proposed Directed Prediction Change (DPC) metric achieves an almost tenfold speedup and eliminates randomness, resulting in a deterministic and trustworthy evaluation procedure that measures the same property as local Infidelity. DPC is evaluated on two datasets (skin lesion images and financial tabular data), two black-box models, seven explanation algorithms, and a wide range of hyperparameters. Across $4\,744$ distinct explanations, the results demonstrate that DPC, together with PC, enables a holistic and computationally efficient evaluation of both baseline-oriented and local feature attribution methods, while providing deterministic and reproducible outcomes.