Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...

Usually when determining parameters with an inverse method, it is assumed that parameters or properties, other than those being sought, are known exactly. When such known parameters are uncertain, the inverse solution can be very sensitive to the degree of uncertainty. The stochastic regularization method can be modi ed to reduce this sensitivity. This paper presents such a modi cation. In addi...

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

We present a practical method for calculating the local gravitational self-force (often called "radiation-reaction force") for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of mode-sum regularization, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies...

The work in this paper shows intensive empirical experiments using 13 datasets to understand the regularization effectiveness of ridge regression, the lasso estimate, and elastic net regularization methods. the study offers a deep understanding of how the datasets affect the goodness of the prediction accuracy of each regularization method for a given problem given the diversity in the datasets...

We introduce a novel regularization approach for a class of inputdriven recurrent neural networks. The regularization of network parameters is constrained to reimplement a previously recorded state trajectory. We derive a closed-form solution for network regularization and show that the method is capable of reimplementing harvested dynamics. We investigate important properties of the method and...

Regularization of matrix-valued data is of importance in medical imaging, motion analysis and scene understanding. In this report we describe a novel method for efficient regularization of matrix group-valued images. Using the augmented Lagrangian framework we separate the total-variation regularization of matrix-valued images into a regularization and projection steps, both of which are fast a...

The work in this paper shows intensive empirical experiments using 13 datasets to understand the regularization effectiveness of ridge regression, the lasso estimate, and elastic net regularization methods. The study offers a deep understanding of how the datasets affect the goodness of the prediction accuracy of each regularization method for a given problem given the diversity in the datasets...

It is well-known that model combination can improve prediction performance of regression model. We investigate the model combination of Support Vector Regression (SVR) with regularization path in this paper. We first define Lε-risk of SVR, and prove that SVR regularization path leads to at least one Lε-risk consistent fitted model. Then we establish the Lε-risk consistency for convex combinatio...

The area of mathematical inverse problems is quite broad and involves the qualitative and quantitative analysis of a wide variety of physical models. Applications include, for example, the problem of inverse heat conduction, image reconstruction, tomography, the inverse scattering problem, and the determination of unknown coefficients or boundary parameters appearing in partial differential equ...