January 2026

arXiv:2506.05544v2 Announce Type: replace Abstract: This paper introduces the MPS (Model Prediction Set), a novel framework for online model selection for nonstationary time series. Classical model selection methods, such as information criteria and cross-validation, rely heavily on the stationarity assumption and often fail in dynamic environments which undergo gradual or abrupt changes over time. Yet real-world data are rarely stationary, and model selection under nonstationarity remains a largely open problem. To tackle this challenge, we combine conformal inference […]

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arXiv:2501.04903v4 Announce Type: replace Abstract: There is a widespread and longstanding belief that machine learning models are biased towards the majority class when learning from imbalanced binary response data, leading them to neglect or ignore the minority class. Motivated by a recent simulation study that found that decision trees can be biased towards the minority class, our paper aims to reconcile the conflict between that study and other published works. First, we critically evaluate past literature on this […]

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arXiv:2601.20738v1 Announce Type: cross Abstract: Biased gradient compression with error feedback (EF) reduces communication in federated learning (FL), but under non-IID data, the residual error can decay slowly, causing gradient mismatch and stalled progress in the early rounds. We propose step-ahead partial error feedback (SA-PEF), which integrates step-ahead (SA) correction with partial error feedback (PEF). SA-PEF recovers EF when the step-ahead coefficient $alpha=0$ and step-ahead EF (SAEF) when $alpha=1$. For non-convex objectives and $delta$-contractive compressors, we establish a […]

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arXiv:2601.20571v1 Announce Type: cross Abstract: Specifications for decentralized learning on resource-constrained edge devices require algorithms that are communication-efficient, robust to data corruption, and lightweight in memory usage. While state-of-the-art gossip-based methods satisfy the first requirement, achieving robustness remains challenging. Asynchronous decentralized ADMM-based methods have been explored for estimating the median, a statistical centrality measure that is notoriously more robust than the mean. However, existing approaches require memory that scales with node degree, making them impractical when memory is […]

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arXiv:2601.20528v1 Announce Type: cross Abstract: We develop a fully intrinsic Bayesian framework for nonparametric regression on the unit sphere based on isotropic Gaussian field priors and the harmonic structure induced by the Laplace-Beltrami operator. Under uniform random design, the regression model admits an exact diagonalization in the spherical harmonic basis, yielding a Gaussian sequence representation with frequency-dependent multiplicities. Exploiting this structure, we derive closed-form posterior distributions, optimal spectral truncation schemes, and sharp posterior contraction rates under integrated squared […]

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arXiv:2601.20498v1 Announce Type: cross Abstract: Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and stochastic issues that are absent in the Euclidean setting. In this work, we develop a diffusion modeling framework defined directly on finite-dimensional spherical harmonic representations of real-valued functions on the sphere. We show that the spherical discrete Fourier transform maps spatial Brownian motion to a […]

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arXiv:2601.20250v1 Announce Type: cross Abstract: Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution. This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single Euler step. Under standard assumptions on the neural network classes used to parameterize the velocity field and data distribution, we prove that rectified flows achieve […]

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arXiv:2601.20043v1 Announce Type: cross Abstract: Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with […]

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arXiv:2601.20020v1 Announce Type: cross Abstract: We consider the problem of graph matching for a sequence of graphs generated under a time-dependent Markov chain noise model. Our edgelighter error model, a variant of the classical lamplighter random walk, iteratively corrupts the graph $G_0$ with edge-dependent noise, creating a sequence of noisy graph copies $(G_t)$. Much of the graph matching literature is focused on anonymization thresholds in edge-independent noise settings, and we establish novel anonymization thresholds in this edge-dependent noise […]

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arXiv:2601.19992v1 Announce Type: cross Abstract: Industrial image anomaly detection is a challenging problem owing to extreme class imbalance and the scarcity of labeled defective samples, particularly in few-shot settings. We propose BayPrAnoMeta, a Bayesian generalization of Proto-MAML for few-shot industrial image anomaly detection. Unlike existing Proto-MAML approaches that rely on deterministic class prototypes and distance-based adaptation, BayPrAnoMeta replaces prototypes with task-specific probabilistic normality models and performs inner-loop adaptation via a Bayesian posterior predictive likelihood. We model normal support […]

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