Related papers: On the equivalence between Implicit Regularization…

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fully-extended, orthogonal iCRSs are confluent modulo identification of…

Contrastive losses yield state-of-the-art performance for person re-identification, face verification and few shot learning. They have recently outperformed the cross-entropy loss on classification at the ImageNet scale and outperformed all…

In this paper we illustrate the simplifications produced by FDR in NNLO computations. We show with an explicit example that - due to its four-dimensionality - FDR does not require an order-by-order renormalization and that, unlike the…

Implicit neural representations (INR) have been recently proposed as deep learning (DL) based solutions for image compression. An image can be compressed by training an INR model with fewer weights than the number of image pixels to map the…

Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality…

Low Dose Computed Tomography suffers from a high amount of noise and/or undersampling artefacts in the reconstructed image. In the current article, a Deep Learning technique is exploited as a regularization term for the iterative…

Parallel imaging is a widely-used technique to accelerate magnetic resonance imaging (MRI). However, current methods still perform poorly in reconstructing artifact-free MRI images from highly undersampled k-space data. Recently, implicit…

Power system voltage regulation is crucial to maintain power quality while integrating intermittent renewable resources in distribution grids. However, the system model on the grid edge is often unknown, making it difficult to model…

Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…

Relax, Compensate and then Recover (RCR) is a paradigm for approximate inference in probabilistic graphical models that has previously provided theoretical and practical insights on iterative belief propagation and some of its…

High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far,…

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…

Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…

Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…

Recent progress in the understanding of vacuum expectation values and of infrared divergences in different regularization schemes is reviewed. Vacuum expectation values are gauge and renormalization-scheme dependent quantities. Using a…