To learn reliable rules that can generalize to novel situations, the brain must be capable of imposing some form of regularization. Here we suggest, through theoretical and computational arguments, that the combination of noise with synchronization provides a plausible mechanism for regularization in the nervous system. The functional role of regularization is considered in a general context in...

Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regulariz...

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, Lq regularization with q ∈ (0, 1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L1 regularization), however, the convergence issue of the corresponding algorithms are more difficult t...

In this paper, we investigate sparsity regularization for electrical impedance tomography (EIT). Here, we combine sparsity regularization with the energy functional approach. The main results of our paper is the well-posedness and convergence rates of the sparsity regularization method.

A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the low-energy analytic structure, implements a low-energy power counting for the one-loop diagrams, and preserves symmetries respected by dimensional regularization.

In this paper we show that regularization methods form a scale-space where the regularization parameter serves as scale. In analogy to nonlinear diiusion ltering we establish continuity with respect to scale, causality in terms of a maximum{minimum principle, simpliica-tion properties by means of Lyapunov functionals and convergence to a constant steady-state. We identify nonlinear regularizati...

A Lavrentiev prox-regularization method for optimal control problems with pointwise state constraints is introduced where both the objective function and the constraints are regularized. The convergence of the controls generated by the iterative Lavrentiev prox-regularization algorithm is studied. For a sequence of regularization parameters that converges to zero, strong convergence of the gene...

Image restoration is an ill-posed inverse problem, which has been introduced the regularization method to suppress over-amplification. In this paper, we propose to apply the iterative regularization method to the image restoration problem and present a nested iterative method, called iterative conjugate gradient regularization method. Convergence properties are established in detail. Based on [...

In this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green's Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, the paper provides an analysis of currently used support vector kernels in the view of regulariz...

This paper studies the effect of covariance regularization for classification of high-dimensional data. This is done by fitting a mixture of Gaussians with a regularized covariance matrix to each class. Three data sets are chosen to suggest the results are applicable to any domain with high-dimensional data. The regularization needs of the data when pre-processed using the dimensionality reduct...