March 2026

arXiv:2603.18032v1 Announce Type: cross Abstract: Anomaly and failure detection methods are crucial in identifying deviations from normal system operational conditions, which allows for actions to be taken in advance, usually preventing more serious damages. Long-lasting deviations indicate failures, while sudden, isolated changes in the data indicate anomalies. However, in many practical applications, changes in the data do not always represent abnormal system states. Such changes may be recognized incorrectly as failures, while being a normal evolution of the […]

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arXiv:2603.19198v1 Announce Type: new Abstract: The signature is a canonical representation of a multidimensional path over an interval. However, it treats all historical information uniformly, offering no intrinsic mechanism for contextualising the relevance of the past. To address this, we introduce the Exponentially Weighted Signature (EWS), generalising the Exponentially Fading Memory (EFM) signature from diagonal to general bounded linear operators. These operators enable cross-channel coupling at the level of temporal weighting together with richer memory dynamics including oscillatory, […]

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arXiv:2603.19041v1 Announce Type: new Abstract: Autoregressive (AR) models remain widely used in time series analysis due to their interpretability, but convencional parameter estimation methods can be computationally expensive and prone to convergence issues. This paper proposes a Neural Network (NN) formulation of AR estimation by embedding the autoregressive structure directly into a feedforward NN, enabling coefficient estimation through backpropagation while preserving interpretability. Simulation experiments on 125,000 synthetic AR(p) time series with short-term dependence (1 <= p <= 5) […]

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arXiv:2603.18985v1 Announce Type: new Abstract: Deep learning models have become the dominant approach for multivariate time series anomaly detection (MTSAD), often reporting substantial performance improvements over classical statistical methods. However, these gains are frequently evaluated under heterogeneous thresholding strategies and evaluation protocols, making fair comparisons difficult. This work revisits OmniAnomaly, a widely used stochastic recurrent model for MTSAD, and systematically compares it with a simple linear baseline based on Principal Component Analysis (PCA) on the Server Machine Dataset […]

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arXiv:2603.18941v1 Announce Type: new Abstract: The topic of Multivariate Time Series Anomaly Detection (MTSAD) has grown rapidly over the past years, with a steady rise in publications and Deep Learning (DL) models becoming the dominant paradigm. To address the lack of systematization in the field, this study introduces a novel and unified taxonomy with eleven dimensions over three parts (Input, Output and Model) for the categorization of DL-based MTSAD methods. The dimensions were established in a two-fold approach. […]

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arXiv:2603.18938v1 Announce Type: new Abstract: We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms correspond to stable decision options and covariates evolve adaptively under the bandit policy. This setting creates significant statistical challenges: the sampling distribution depends on the allocation rule, observations are dependent over time, and inverse-propensity weighting induces […]

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arXiv:2603.18781v1 Announce Type: new Abstract: Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study Recursive Rank Matching (RRM) as a representative instance of this class under a population-anchored reference. In this setting, we establish consistency and an explicit convergence rate for the anchored empirical RRM under the quadratic cost. We then identify a dominant mismatch mechanism responsible for the loss […]

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arXiv:2603.18514v1 Announce Type: new Abstract: Motivated by the principle of satisficing in decision-making, we study satisficing regret guarantees for nonstationary $K$-armed bandits. We show that in the general realizable, piecewise-stationary setting with $L$ stationary segments, the optimal regret is $Theta(Llog T)$ as long as $Lgeq 2$. This stands in sharp contrast to the case of $L=1$ (i.e., the stationary setting), where a $T$-independent $Theta(1)$ satisficing regret is achievable under realizability. In other words, the optimal regret has to […]

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arXiv:2603.18483v1 Announce Type: new Abstract: In the present paper we study the performance of linear denoisers for noisy data of the form $mathbf{x} + mathbf{z}$, where $mathbf{x} in mathbb{R}^d$ is the desired data with zero mean and unknown covariance $mathbf{Sigma}$, and $mathbf{z} sim mathcal{N}(0, mathbf{Sigma}_{mathbf{z}})$ is additive noise. Since the covariance $mathbf{Sigma}$ is not known, the standard Wiener filter cannot be employed for denoising. Instead we assume we are given samples $mathbf{x}_1,dots,mathbf{x}_n in mathbb{R}^d$ from the true distribution. […]

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arXiv:2603.18225v1 Announce Type: new Abstract: Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, […]

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