Related papers: On Group Averaging for SO(n,1)

Several problems in physics, in particular the averaging problem in gravity, can be described in a formalism derived from the real-space Renormalization Group (RG) methods. It is shown that the RG flow is provided by the Ricci-Hamilton…

Independent from the still ongoing research in measuring individual intelligence, we anticipate and provide a framework for measuring collective intelligence. Collective intelligence refers to the idea that several individuals can…

Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary…

This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended…

Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…

I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…

Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are…

This book provides an introduction to a renormalisation group method in the spirit of that of Wilson. It starts with a concise overview of the theory of critical phenomena and the introduction of several tools required in the…

We study in a rigorous way the XYZ spin model by Renormalization Group methods.

In this paper, we solve a semi-supervised regression problem. Due to the lack of knowledge about the data structure and the presence of random noise, the considered data model is uncertain. We propose a method which combines graph Laplacian…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

In fair machine learning, one source of performance disparities between groups is over-fitting to groups with relatively few training samples. We derive group-specific bounds on the generalization error of welfare-centric fair machine…

This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor…

While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…

The increasing availability of time --and space-- resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world datasets can often…

While the field of algorithmic fairness has brought forth many ways to measure and improve the fairness of machine learning models, these findings are still not widely used in practice. We suspect that one reason for this is that the field…

Machine learning algorithms are increasingly used to inform critical decisions. There is a growing concern about bias, that algorithms may produce uneven outcomes for individuals in different demographic groups. In this work, we measure…

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…

The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…