Regularized interpolation for noisy data

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We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly w ...

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

This article investigates the performance and accuracy of continuous Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) position tracking for hydromorphological surveys, based on a comprehensive river restoration monitoring campaign. The a ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood H ...

Remote photoplethysmography (rPPG) using camera-based imaging has shown excellent potential recently in vital signs monitoring due to its contactless nature. However, the optimum filter selection for pre-processing rPPG data in signal conditioning is still ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

This paper introduces Wireless IoT-based Noise Cancellation (WINC) which defines a framework for leveraging a wireless network of IoT microphones to enhance active noise cancellation in noise-canceling headphones. The IoT microphones forward ambient noise ...

A multi-agent system consists of a collection of decision-making or learning agents subjected to streaming observations from some real-world phenomenon. The goal of the system is to solve some global learning or optimization problem in a distributed or dec ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

This paper proposes a novel method to improve georeferencing of airborne laser scanning by improved trajectory estimation using Vehicle Dynamic Model. In Vehicle Dynamic Model (VDM), the relationship between the dynamics of the platform and control inputs ...

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

Air traffic noise emissions are responsible for a significant part of the overall environmental noise, especially in the vicinity of airports. Exposure to environmental noise is known to negatively impact health and to be associated with cardiovascular dis ...

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

Regularized interpolation for noisy data

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Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Interpolation and Quantifiers in Ortholattices

Exploiting the Signal-Leak Bias in Diffusion Models

Efficient local linearity regularization to overcome catastrophic overfitting

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Disentangling 1/f noise from confined ion dynamics

Optimal digital filter selection for remote photoplethysmography (rPPG) signal conditioning

Functional data analysis with rough sample paths?

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

WINC: A Wireless IoT Network for Multi-Noise Source Cancellation

Multi-agent Learning with Privacy Guarantees

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Model-based constraints for trajectory determination of quad-copters: Design, calibration & merits for direct orientation

Universal and adaptive methods for robust stochastic optimization

Robust tunable acoustic impedance control on electroacoustic resonators for aircraft noise reduction

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Benign Overfitting in Deep Neural Networks under Lazy Training

Computer-assisted proof of kernel inequalities