The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods ...

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with an edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inver...

The generalization ability of a neural network can sometimes be improved dramatically by regularization. To analyze the improvement one needs more refined results than the asymptotic distribution of the weight vector. Here we study the simple case of one-dimensional linear regression under quadratic regularization, i.e., ridge regression. We study the random design, misspecified case, where we ...

We derive the correspondence between regularization operators used in Regularization Networks and Hilbert Schmidt Kernels appearing in Support VectorMachines. More specifically, we prove that the Green’s Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. As a by–product we show that a large number of Radial Basis Fun...

In this paper, we proposed a new model with nuclear-norm and L1-norm regularization for image reconstruction in aerospace remote sensing. The curvelet based L1-norm regularization promotes sparse reconstruction, while the low-rank based nuclear-norm regularization leads to a principle component solution. Split Bregman method is used to solve this problem. Numerical experiments show the proposed...

In this paper, we study a Tikhonov-type regularization for restricted Boltzmann machines (RBM). We present two alternative formulations of the Tikhonov-type regularization which encourage an RBM to learn a smoother probability distribution. Both formulations turn out to be combinations of the widely used weight-decay and sparsity regularization. We empirically evaluate the effect of the propose...

In this paper we present a new scheme of a kernel adaptive regularization algorithm, where the kernel and the regularization parameter are adaptively chosen within regularization procedure. The construction of such fully adaptive regularization algorithm is motivated by the problem of reading the blood glucose concentration of diabetic patients. We describe how proposed scheme can be used for t...

This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value of the regularization parameter for these ...

An l(p) (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the l(p) sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization pr...

In this paper we study automatic regularization techniques for the fusion of automatic speaker recognition systems. Parameter regularization could dramatically reduce the fusion training time. In addition, there will not be any need for splitting the development set into different folds for crossvalidation. We utilize majorization-minimization approach to automatic ridge regression learning and...