49,006 research outputs found
CONVEX REGULARIZATION IN STATISTICAL INVERSE LEARNING PROBLEMS
No full textWe consider a statistical inverse learning problem, where the task is to estimate a function f based on noisy point evaluations of Af, where A is a linear operator. The function Af is evaluated at i.i.d. random design points u(n), n = 1, ..., N generated by an unknown general probability distribution. We consider Tikhonov regularization with general convex and p-homogeneous penalty functionals and derive concentration rates of the regularized solution to the ground truth measured in the symmetric Bregman distance induced by the penalty functional. We derive concrete rates for Besov norm penalties and numerically demonstrate the correspondence with the observed rates in the context of X-ray tomography
Si può migliorare la memoria? Un'esperienza con gli anziani dell'Università della Terza Età
No full textEffetti dell'età e dell'istruzione sulle prestazioni mnestiche nell'invecchiamento: analisi di compiti verbali
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Il benessere psicologico nella terza età: fattori predittivi del livello di soddisfazione nella vita
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Trust your source: quantifying source condition elements for variational regularisation methods
No full textSource conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse problem case studies in machine learning and image processing: sparse coefficient estimation of a polynomial via LASSO regression and recovering an image from a subset of the coefficients of its discrete Fourier transform. We further demonstrate that the proposed approach can easily be modified to solve the machine learning task of identifying the optimal sampling pattern in the Fourier domain for a given image and variational regularisation method, which has applications in the context of sparsity promoting reconstruction from magnetic resonance imaging data
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