Related papers: Graph Tikhonov Regularization and Interpolation vi…
Another facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
Graph neural networks have been successful for machine learning, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing graph…
Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…
It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex…
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
Given a non-oriented edge-weighted graph, we show how to make some estimation of the associated Laplacian eigenvalues through Monte Carlo evaluation of spectral quantities computed along Kirchhoff random rooted spanning forest trajectories.…
The theory of spectral filtering is a remarkable tool to understand the statistical properties of learning with kernels. For least squares, it allows to derive various regularization schemes that yield faster convergence rates of the excess…
The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to…
This paper presents a new approach to the solution of Probabilistic Risk Assessment (PRA) models using the combination of Reinforcement Learning (RL) and Graph Neural Networks (GNNs). The paper introduces and demonstrates the concept using…
A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…
Exact eigendecomposition of large matrices is very expensive, and it is practically impossible to compute exact eigenvalues. Instead, one may set a more modest goal of approaching the empirical distribution of the eigenvalues, recovering…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters,…
Finding a good regularization parameter for Tikhonov regularization problems is a though yet often asked question. One approach is to use leave-one-out cross-validation scores to indicate the goodness of fit. This utilizes only the noisy…
Tikhonov regularization is a common technique used when solving poorly behaved optimization problems. Often, and with good reason, this technique is applied by practitioners in an ad hoc fashion. In this note, we systematically illustrate…