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Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…

Optimization and Control · Mathematics 2024-10-28 Bai Yan , Qi Zhao , Jin Zhang , J. Andrew Zhang , Xin Yao

The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…

Data Structures and Algorithms · Computer Science 2021-09-06 Vladimir Braverman , Viska Wei , Samson Zhou

We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a…

Machine Learning · Statistics 2019-02-04 Michael Unser

Latency and efficiency issues are often overlooked when evaluating IR models based on Pretrained Language Models (PLMs) in reason of multiple hardware and software testing scenarios. Nevertheless, efficiency is an important part of such…

Information Retrieval · Computer Science 2022-07-11 Carlos Lassance , Stéphane Clinchant

Kalman smoothers reconstruct the state of a dynamical system starting from noisy output samples. While the classical estimator relies on quadratic penalization of process deviations and measurement errors, extensions that exploit Piecewise…

Optimization and Control · Mathematics 2011-11-14 Aleksandr Y. Aravkin , James V. Burke , Gianluigi Pillonetto

Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…

Optimization and Control · Mathematics 2025-07-01 Måns Williamson , Tony Stillfjord

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Numerical Analysis · Mathematics 2015-09-15 Adam M. Oberman , Yuanlong Ruan

We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…

Numerical Analysis · Mathematics 2017-04-20 Ludwig J. Cromme , Jens Kunath , Andreas Krebs

Minimization of the $L_\infty$ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving…

Computer Vision and Pattern Recognition · Computer Science 2013-04-05 Fumin Shen , Chunhua Shen , Rhys Hill , Anton van den Hengel , Zhenmin Tang

We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx, to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with…

Computer Vision and Pattern Recognition · Computer Science 2011-10-06 Subhransu Maji

Label smoothing (LS) is a popular regularisation method for training neural networks as it is effective in improving test accuracy and is simple to implement. ``Hard'' one-hot labels are ``smoothed'' by uniformly distributing probability…

Machine Learning · Computer Science 2025-02-21 Guoxuan Xia , Olivier Laurent , Gianni Franchi , Christos-Savvas Bouganis

Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…

Methodology · Statistics 2025-01-09 Rosanna Campagna , Serena Crisci , Gabriele Santin , Gerardo Toraldo , Marco Viola

Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…

Computational Geometry · Computer Science 2022-08-18 Alexander Dobler , Martin Nöllenburg

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques…

Optimization and Control · Mathematics 2011-10-17 Julien Mairal , Rodolphe Jenatton , Guillaume Obozinski , Francis Bach

We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers (Eilers and Marx, 1996) are applied simultaneously along both coordinates. The new smoother has a sandwich form which suggested the name…

Methodology · Statistics 2013-05-30 Luo Xiao , Yingxing Li , David Ruppert

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total…

Functional Analysis · Mathematics 2019-03-19 Michael Unser , Julien Fageot , John Paul Ward

In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…

Instrumentation and Methods for Astrophysics · Physics 2015-05-13 N. Cardiel

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

Machine Learning · Statistics 2025-03-31 Michael Unser , Alexis Goujon , Stanislas Ducotterd

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…

Econometrics · Economics 2024-12-10 Jad Beyhum , Elia Lapenta , Pascal Lavergne

Neural operations that rely on neighborhood information are much more expensive when deployed on point clouds than on grid data due to the irregular distances between points in a point cloud. In a grid, on the other hand, we can compute the…

Computer Vision and Pattern Recognition · Computer Science 2023-07-28 Putri A. van der Linden , David W. Romero , Erik J. Bekkers