Related papers: On Group Averaging for SO(n,1)
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the…
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described.…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…
Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across…
Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and…
Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy,…
Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models…
Researchers have developed ways to generalize the mean and variance to situations in which a data metric is available. We apply the tools developed in Pennec (2006) to categorical data, and show the generality of this approach by…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
The renormalization group method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and…
The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…