Related papers: A divergence formula for regularization methods wi…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection…

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators…

A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…

Finding the hedge ratios for a portfolio and risk compression is the same mathematical problem. Traditionally, regression is used for this purpose. However, regression has its own limitations. For example, in a regression model, we can't…

The L-curve method is a well-known heuristic method for choosing the regularization parameter for ill-posed problems by selecting it according to the maximal curvature of the L-curve. In this article, we propose a simplified version that…

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…

Establishing the convergence of splines can be cast as a variational problem which is amenable to a $\Gamma$-convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, $n$, as…

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality…

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…

We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…

Recent results show that estimates defined by over-parametrized deep neural networks learned by applying gradient descent to a regularized empirical $L_2$ risk are universally consistent and achieve good rates of convergence. In this paper,…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model…

We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve…

We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…

In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…

For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…