Related papers: Regularisation for the approximation of functions …
In this paper we show that simple noise regularisation can be an effective way to address GNN oversmoothing. First we argue that regularisers addressing oversmoothing should both penalise node latent similarity and encourage meaningful node…
We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\left(Y_i-f(X_i)\right)^2+\lambda \Psi(f)\right) \end{equation*} when $\Psi$…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
Due to diverse architectures in deep neural networks (DNNs) with severe overparameterization, regularization techniques are critical for finding optimal solutions in the huge hypothesis space. In this paper, we propose an effective…
The analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear-wave velocity. The range of applicability is extremely wide going, for example, from seismological studies to geotechnical characterizations…
We consider the problem of minimizing the sum of three convex functions: i) a smooth function $f$ in the form of an expectation or a finite average, ii) a non-smooth function $g$ in the form of a finite average of proximable functions…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions --…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
It is proved in Chon{\'e} and Le Meur (2001) that the problem of minimizing a Dirichlet-like functional of the function $u\_h$ discretized with $P\_1$ Finite Elements, under the constraint that $u\_h$ be convex, cannot converge. Here, we…
From the optimization point of view, a difficulty with parallel MRI with simultaneous coil sensitivity estimation is the multiplicative nature of the non-linear forward operator: the image being reconstructed and the coil sensitivities…
We have devised a simple numerical technique to treat rugged data points that arise due to the insufficient gain setting error (or quantization error) of a digital instrument. This is a very wide spread problem that all experimentalists…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Problems in machine learning (ML) can involve noisy input data, and ML classification methods have reached limiting accuracies when based on standard ML data sets consisting of feature vectors and their classes. Greater accuracy will…