相关论文: On group averaging for non-compact groups

A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method.…

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

In many situations it could be interesting to ascertain whether nonparametric regression curves can be grouped, especially when confronted with a considerable number of curves. The proposed testing procedure allows to determine groups with…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…

In this paper we study sigma models in which a noneffective group action has been gauged. Such gauged sigma models turn out to be different from gauged sigma models in which an effectively-acting group is gauged, because of nonperturbative…

Identifying anomalies in multi-dimensional datasets is an important task in many real-world applications. A special case arises when anomalies are occluded in a small set of attributes, typically referred to as a subspace, and not…

Many machine learning tasks in the natural sciences are precisely equivariant to particular symmetries. Nonetheless, equivariant methods are often not employed, perhaps because training is perceived to be challenging, or the symmetry is…

This paper provides a description of a new method for information processing based on holistic approach wherein analysis is a direct product of synthesis. The core of the method is iterative averaging of all the elements of a system…

Basic elements of the exact renormalization group method and recent results within this approach are reviewed. Topics covered are the derivation of equations for the effective action and relations between them, derivative expansion,…

In contrast to standard critical phenomena, disordered systems need to be treated via the Functional Renormalization Group. The latter leads to a coarse grained disorder landscape, which after a finite renormalization becomes non-analytic,…

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…

Methods for extending -- generalizing or transporting -- inferences from a randomized trial to a target population involve conditioning on a large set of covariates that is sufficient for rendering the randomized and non-randomized groups…

The study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings, provided the system is large enough. Careful examination suggests that…

We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then…

In this paper, a subgroup least squares and a convex clustering are introduced for inferring a partially heterogenous linear regression that has potential application in the areas of precision marketing and precision medicine. The…

Traditionally model averaging has been viewed as an alternative to model selection with the ultimate goal to incorporate the uncertainty associated with the model selection process in standard errors and confidence intervals by using a…