Regularization Of Inverse Problems

By L. Fleischer. 2016

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Citations in the corpus

Density Estimation in Infinite Dimensional Exponential Families (2013, methodology): “Note that this condition is common in the inverse problem theory (see [12]), and it naturally arises here through the connection of f λ,n being a Tikhonov regularized solution to the ill-posed linear system ˆ Cf = − ˆ ξ .”
Modern regularization methods for inverse problems (2018, methodology): “The end of the eighties marks the beginning of the systematic analysis of regularization methods for nonlinear inverse problems (replacing K by a nonlinear operator), in particular with the papers by Seidman and Vogel [339] giving a well-posedness and convergence analysis of Tikhonov regularization ”
Sparse Recovery via Differential Inclusions (2014, background): “ non-convexity or second-stage subset least squares. It is a diﬀerent kind of regularization via early stopping. Early stopping regularization has been studied widely in linear inverse problems, e.g. [EHN96], and recently in Boosting, e.g. [Fri01, BY02, YRC07]. In fact, Linearized Bregman iterations”
Non-parametric Stochastic Approximation with Large Step sizes (2014, background): “Indeed the bias term (see comments below) cannot decrease faster than O(n−2): this phenomenon in known as saturation [44].”
A backward problem for the time‐fractional diffusion equation (2017, background): “, [28, 29]), we expect instability in the fractional inverse problem (see also the results in [19] indicating the ill-posedness of several prototypical fractional inverse problems).”
Classification vs regression in overparameterized regimes: Does the loss function matter? (2020, methodology): “[14] Heinz Werner Engl, Martin Hanke, and Andreas Neubauer.”
Random Expert Distillation: Imitation Learning via Expert Policy Support Estimation (2019, unknown): “Consider the regression problem that admits a minimizer on H inf f∈H ∫ (fθ(x)− f(x))2 dπ(x), The minimal ‖·‖H solution corresponds to fπ,θ = C † πCπfθ = Pπfθ, the orthogonal projection of fθ onto the range of Cπ (see e.g Engl et al., 1996).”
Generalization Properties of Learning with Random Features (2016, unknown): “Then we can use the fact that A(A + λI)−1 = I−λ(A+λI)−1 for any bounded linear operator A and that L̃−1λ = L −1/2 λ (I− B̃) −1L −1/2 λ (see the proof of Prop.”
The Bayesian Approach to Inverse Problems (2013, background): “The classical approach to linear inverse problems is described in numerous books; see, for example, [32,51].”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, background): “The inherent ill-posedness is typically addressed through regularization [13].”
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications (2017, background): “, [18, 16, 20] and [8] for a more recent review which includes over 130 references.”
Kernel ridge vs. principal component regression: Minimax bounds and the qualification of regularization operators (2017, background): “…of the self-adjoint finite-rank operator TX via the functional calculus (see, e.g., Reed and Simon, 1980, Ch. 7); this 2This definition follows Engl et al. (1996) and Bauer et al. (2007), but is slightly more restrictive. is a generalization of standard matrix functions (Tropp, 2015, Ch. 2).”
Stable architectures for deep neural networks (2017, background): “Commonly Tikhonov regularization [19, 26, 48], also referred to as weight decay, has been used [23], although, other possibilities enforcing sparsity or other structure have been proposed [41].”
A tutorial on inverse problems for anomalous diffusion processes (2015, unknown): “For example it is known that the sequence of Dirichlet eigenvalues can uniquely determine a potential q symmetric with respect to the point x = 1 / 2, and together with additional spectral information, one can uniquely determine a general potential q ; see [12, 86] for an overview of results on the…”