January 2026

arXiv:2502.16542v3 Announce Type: replace Abstract: The empirical use of variable transformations within (strictly) consistent loss functions is widespread, yet a theoretical understanding is lacking. To address this gap, we develop a theoretical framework that establishes formal characterizations of (strict) consistency for such transformed loss functions. Our analysis focuses on two interrelated cases: (a) transformations applied solely to the realization variable and (b) bijective transformations applied jointly to both the realization and prediction variables. These cases extend the well-established […]

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arXiv:2501.17512v3 Announce Type: replace Abstract: As Federated Learning (FL) expands, the challenge of non-independent and identically distributed (non-IID) data becomes critical. Clustered Federated Learning (CFL) addresses this by training multiple specialized models, each representing a group of clients with similar data distributions. However, the term ”CFL” has increasingly been applied to operational strategies unrelated to data heterogeneity, creating significant ambiguity. This survey provides a systematic review of the CFL literature and introduces a principled taxonomy that classifies algorithms […]

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arXiv:2407.15301v2 Announce Type: replace Abstract: Epigenetic aging clocks play a pivotal role in estimating an individual’s biological age through the examination of DNA methylation patterns at numerous CpG (Cytosine-phosphate-Guanine) sites within their genome. However, making valid inferences on predicted epigenetic ages, or more broadly, on predictions derived from high-dimensional inputs, presents challenges. We introduce a novel U-learning approach via combinatory multi-subsampling for making ensemble predictions and constructing confidence intervals for predictions of continuous outcomes when traditional asymptotic methods […]

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arXiv:2110.01950v3 Announce Type: replace Abstract: We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p times p$ covariance matrix $Sigma$ exhibits a spiked eigenvalue structure and the vector $zeta$, given by the difference between the {em whitened} mean vectors, is sparse. We analyze an adaptive classifier (adaptive with respect to the sparsity $s$) that first performs dimension reduction on the feature vectors prior to classification in the dimensionally reduced space, i.e., […]

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arXiv:2601.14235v1 Announce Type: cross Abstract: The Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, […]

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arXiv:2601.14173v1 Announce Type: cross Abstract: We study low-rank tensor-product B-spline (TPBS) models for regression tasks and investigate Dirichlet energy as a measure of smoothness. We show that TPBS models admit a closed-form expression for the Dirichlet energy, and reveal scenarios where perfect interpolation is possible with exponentially small Dirichlet energy. This renders global Dirichlet energy-based regularization ineffective. To address this limitation, we propose a novel regularization strategy based on local Dirichlet energies defined on small hypercubes centered at […]

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arXiv:2601.14062v1 Announce Type: cross Abstract: Healthcare sector indices consolidate the economic health of pharmaceutical, biotechnology, and healthcare service firms. The short-term movements in these indices are closely intertwined with capital allocation decisions affecting research and development investment, drug availability, and long-term health outcomes. This research investigates whether historical open-high-low-close (OHLC) index data contain sufficient information for predicting the directional movement of the opening index on the subsequent trading day. The problem is formulated as a supervised classification task […]

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arXiv:2601.13776v1 Announce Type: cross Abstract: Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining […]

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arXiv:2601.13474v1 Announce Type: cross Abstract: The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon — particularly the role of gradient orthogonalization — remain poorly understood, with very few works providing end-to-end analyses that rigorously explain its advantages in concrete applications. We take a step by studying the effectiveness of a simplified variant of Muon through two case studies: matrix […]

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arXiv:2601.13272v1 Announce Type: cross Abstract: We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse–fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing […]

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