Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning `1 regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parame...

This contribution focuses, within the `1-Potts model, on the automated estimation of the regularization parameter balancing the `1 data fidelity term and the TV`0 penalization. Variational approaches based on total variation gained considerable interest to solve piecewise constant denoising problems thanks to their deterministic setting and low computational cost. However, the quality of the ac...

Abstract Local regularization methods allow for the application of sequential solution techniques for the solution of Volterra problems, retaining the causal structure of the original Volterra problem and leading to fast solution techniques. Stability and convergence of these methods was shown to hold on a large class of linear Volterra problems, i.e., the class of ν-smoothing problems for ν = ...

Sparse logistic regression is an important linear classifier in statistical learning, providing an attractive route for feature selection. A popular approach is based on minimizing an l1-regularization term with a regularization parameter λ that affects the solution sparsity. To determine an appropriate value for the regularization parameter, one can apply the grid search method or the Bayesian...

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice...

Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element disc...

The adaptive cubic regularization method (Cartis et al. in Math. Program. Ser. A 127(2):245–295, 2011; Math. Program. Ser. A. 130(2):295–319, 2011) has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to t...

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are...