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Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$…

Statistics Theory · Mathematics 2022-09-12 Trevor Hastie , Andrea Montanari , Saharon Rosset , Ryan J. Tibshirani

We revisit the classical problem of nonparametric density estimation but impose local differential privacy constraints. Under such constraints, the original multivariate data $X_1,\ldots,X_n \in \mathbb{R}^d$ cannot be directly observed,…

Statistics Theory · Mathematics 2022-11-15 László Györfi , Martin Kroll

Low-rank model compression is a widely used technique for reducing the computational load when training machine learning models. However, existing methods often rely on relaxing the low-rank constraint of the model weights using a…

Signal Processing · Electrical Eng. & Systems 2023-07-05 Ye Xue , Vincent Lau

We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank…

Machine Learning · Computer Science 2016-02-17 Da Kuang , Zuoqiang Shi , Stanley Osher , Andrea Bertozzi

We investigate generalized versions of the Iteratively Regularized Landweber Method, initially introduced in [Appl. Math. Optim., 38(1):45-68, 1998], to address linear and nonlinear ill-posed problems. Our approach is inspired by the…

Numerical Analysis · Mathematics 2023-12-07 Andrea Aspri , Otmar Scherzer

Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

Machine Learning · Statistics 2020-04-07 Rudrasis Chakraborty

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

Methodology · Statistics 2020-11-24 Beste Hamiye Beyaztas , Soutir Bandyopadhyay

This document reports on a method for detecting and preventing overfitting on data regressions, herein applied to mesh-like data structures. The mesh structure allows for the straightforward computation of the Laplace-operator second-order…

Machine Learning · Computer Science 2025-07-10 Enda D. V. Bigarella

From tabulated nuclear and degenerate equations of state to photon and neutrino opacities, to nuclear reaction rates: tabulated data is ubiquitous in computational astrophysics. The dynamic range that must be covered by these tables…

Computational Physics · Physics 2025-01-10 Peter C. Hammond , Jacob M. Fields , Jonah M. Miller , Brandon L. Barker

In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we…

Machine Learning · Computer Science 2025-05-20 James Jackaman , Oliver Sutton

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

Classical Analysis and ODEs · Mathematics 2017-04-14 Hamid Behjat , Zafer Doğan , Dimitri Van De Ville , Leif Sörnmo

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…

Machine Learning · Computer Science 2025-05-22 Johannes Kaiser , Kristian Schwethelm , Daniel Rueckert , Georgios Kaissis

Models related to the Euler's elastica energy have proven to be useful for many applications including image processing. Extending elastica models to color images and multi-channel data is a challenging task, as stable and consistent…

Computer Vision and Pattern Recognition · Computer Science 2021-03-05 Hao Liu , Xue-Cheng Tai , Ron Kimmel , Roland Glowinski

A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…

Computer Vision and Pattern Recognition · Computer Science 2012-05-15 Mohammad Tofighi , Ali Ayremlou , Farokh Marvasti

We introduce and discuss shape based models for finding the best interpolation data in compression of images with noise. The aim is to reconstruct missing regions by means of minimizing data fitting term in the $L^2$-norm between the images…

Numerical Analysis · Mathematics 2020-11-05 Zakaria Belhachmi , Thomas Jacumin

We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…

Image and Video Processing · Electrical Eng. & Systems 2022-05-18 Emilien Valat , Katayoun Farrahi , Thomas Blumensath

Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in…

Statistics Theory · Mathematics 2007-06-27 Matthias Hein , Jean-Yves Audibert , Ulrike von Luxburg

The combination of the Reduced Basis and the Empirical Interpolation Method (EIM) approaches have produced outstanding results in many disciplines. In particular, in gravitational wave (GW) science these results range from building…

Numerical Analysis · Mathematics 2021-07-07 Manuel Tiglio , Aarón Villanueva

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

Multimedia · Computer Science 2016-02-22 Junhui Hou , Lap-Pui Chau , Nadia Magnenat-Thalmann , Ying He

We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…

Numerical Analysis · Mathematics 2023-05-16 Nir Sharon , Rafael Sherbu Cohen , Holger Wendland