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This article deals with the efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix. For this aim, we rely on projection-based model order…

Continuous pseudo-labeling (PL) algorithms such as slimIPL have recently emerged as a powerful strategy for semi-supervised learning in speech recognition. In contrast with earlier strategies that alternated between training a model and…

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with…

For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…

In this paper, we propose an ordered time series classification framework that is robust against missing classes in the training data, i.e., during testing we can prescribe classes that are missing during training. This framework relies on…

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…

In this paper, we delve into two key techniques in Semi-Supervised Object Detection (SSOD), namely pseudo labeling and consistency training. We observe that these two techniques currently neglect some important properties of object…

Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…

We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is…

This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…

Large language models have shown their ability to become effective few-shot learners with prompting, revolutionizing the paradigm of learning with data scarcity. However, this approach largely depends on the quality of prompt…

Partial-label learning (PLL) is a typical weakly supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. Most existing methods elaborately designed…

The state of neural network pruning has been noticed to be unclear and even confusing for a while, largely due to "a lack of standardized benchmarks and metrics" [3]. To standardize benchmarks, first, we need to answer: what kind of…

In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as introduced in [2]. By using this fact, we are able to embed…

We focus on the robustness of neural networks for classification. To permit a fair comparison between methods to achieve robustness, we first introduce a standard based on the mensuration of a classifier's degradation. Then, we propose…

Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced…

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

Much more attention has been paid to unsupervised feature selection nowadays due to the emergence of massive unlabeled data. The distribution of samples and the latent effect of training a learning method using samples in more effective…