11 citations · 33 across the 9 of their papers we have counts for
9 papers
Statistical inverse learning and -regularization
Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin +1
We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\…
Statistical inverse learning problems with random observations
Abhishake Rastogi, Tapio Helin, Nicole Mücke
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regulariza…
Statistical Inverse Problems in Hilbert Scales
Abhishake Rastogi
In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise. The regularizing norm in this schem…
Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses
Niklas Hartung, Martin Wahl, Abhishake Rastogi +1
The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. While covariate selection criteria have been studie…
Inverse learning in Hilbert scales
Abhishake Rastogi, Peter Mathé
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regula…
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
Abhishake Rastogi
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is cons…
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Abhishake Rastogi, Gilles Blanchard, Peter Mathé
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 t…
Manifold regularization based on Nystr{ö}m type subsampling
Abhishake Rastogi, Sivananthan Sampath
In this paper, we study the Nystr{ö}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularizat…
Optimal rates for the regularized learning algorithms under general source condition
Abhishake Rastogi, Sivananthan Sampath
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discu…