Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey
From MaRDI portal
Publication:4554185
DOI10.1007/978-3-319-70824-9_15zbMath1405.62052OpenAlexW2791620295MaRDI QIDQ4554185
No author found.
Publication date: 13 November 2018
Published in: Trends in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-70824-9_15
Applications of statistics to physics (62P35) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Nonparametric inference (62G99)
Related Items (6)
A probabilistic oracle inequality and quantification of uncertainty of a modified discrepancy principle for statistical inverse problems ⋮ Empirical risk minimization as parameter choice rule for general linear regularization methods ⋮ Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal Lepskiĭ-Inspired Tuning ⋮ On the Asymptotical Regularization for Linear Inverse Problems in Presence of White Noise ⋮ Towards adaptivity via a new discrepancy principle for Poisson inverse problems ⋮ Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution
Cites Work
- Risk hull method and regularization by projections of ill-posed inverse problems
- Comparison of parameter choices in regularization algorithms in case of different information about noise level
- Comparing parameter choice methods for regularization of ill-posed problems
- On universal oracle inequalities related to high-dimensional linear models
- Minimax signal detection in ill-posed inverse problems
- The principle of penalized empirical risk in severely ill-posed problems
- On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
- Asymptotic optimality of \(C_ L\) and generalized cross-validation in ridge regression with application to spline smoothing
- Asymptotic optimality for \(C_ p\), \(C_ L\), cross-validation and generalized cross-validation: Discrete index set
- Estimation of the mean of a multivariate normal distribution
- Asymptotic optimality of generalized cross-validation for choosing the regularization parameter
- Ordered linear smoothers
- Improved estimates of statistical regularization parameters in Fourier differentiation and smoothing
- Selection criteria for scatterplot smoothers
- Oracle inequalities for inverse problems
- Sharp adaptation for inverse problems with random noise
- Exponential weighting and oracle inequalities for projection estimates
- On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition
- Spectral cut-off regularizations for ill-posed linear models
- Signal detection for inverse problems in a multidimensional framework
- Adaptive estimation over anisotropic functional classes via oracle approach
- A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level
- Discrepancy based model selection in statistical inverse problems
- Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
- Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
- Regularization of statistical inverse problems and the Bakushinskiĭ veto
- Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
- Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
- A Lepskij-type stopping rule for regularized Newton methods
- Regularization without preliminary knowledge of smoothness and error behaviour
- Regularization of some linear ill-posed problems with discretized random noisy data
- Modern statistical estimation via oracle inequalities
- Nonparametric statistical inverse problems
- The quasi-optimality criterion for classical inverse problems
- The convergence of a new heuristic parameter selection criterion for general regularization methods
- Regularization independent of the noise level: an analysis of quasi-optimality
- Recent results on the quasi-optimality principle
- Optimal Choice of a Truncation Level for the Truncated SVD Solution of Linear First Kind Integral Equations When Data are Noisy
- Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
- A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
- Ideal spatial adaptation by wavelet shrinkage
- Comparisons of parameter choice methods for regularization with discrete noisy data
- Regularization wavelets and multiresolution
- Geometry of linear ill-posed problems in variable Hilbert scales
- Regularization of exponentially ill-posed problems
- Runge–Kutta integrators yield optimal regularization schemes
- Optimal Adaptation for Early Stopping in Statistical Inverse Problems
- On a Problem of Adaptive Estimation in Gaussian White Noise
- Computational Methods for Inverse Problems
- Block Thresholding and Sharp Adaptive Estimation in Severely Ill-Posed Inverse Problems
- On the discrepancy principle and generalised maximum likelihood for regularisation
- Convergence Rates for Inverse Problems with Impulsive Noise
- Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
- How general are general source conditions?
- The Lepskii principle revisited
- Use of the regularization method in non-linear problems
- Some Comments on C P
- A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey
