scholarly journals Reducing subspace models for large‐scale covariance regression

Biometrics ◽  
2021 ◽  
Author(s):  
Alexander M. Franks
Keyword(s):  
Large Scale ◽  
Reducing Subspace ◽  
Scale Covariance

scholarly journals No Need for Dark-Matter, Dark-Energy or Inflation, Once Ordinary Matter is Properly Represented?

2018 ◽  
Author(s):  
Yehonatan Knoll
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Large Scale ◽  
Ad Hoc ◽  
Classical Electrodynamics ◽  
Spontaneous Breaking ◽  
Metric Tensor ◽  
Ordinary Matter ◽  
Scale Covariance ◽  
Self Force

In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self force problem of classical electrodynamics is properly solved, it becomes a plausible ontology underlying the statistical description of quantum mechanics. In the current paper we extend this result, showing that ordinary matter, thus represented, possibly suffices in explaining the outstanding observations currently requiring for this task the contrived notions of dark-matter, dark-energy and inflation. The single mandatory `fix' to classical electrodynamics, demystifying both very small and very large scale physics, should be contrasted with other ad hoc solutions to either problems. Instrumental to our cosmological model is scale covariance (and `spontaneous breaking' thereof), a formal symmetry of classical electrodynamics treated on equal footing with its Poincare covariance, which is incompatible with the (absolute) metrical attributes of the GR metric tensor.

scholarly journals No Need for Dark-Matter, Dark-Energy or Inflation, Once Ordinary Matter Is Properly Represented?

2019 ◽  
Author(s):  
Yehonatan Knoll
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Large Scale ◽  
Classical Electrodynamics ◽  
Spontaneous Breaking ◽  
Metric Tensor ◽  
Ordinary Matter ◽  
Scale Covariance ◽  
Self Force ◽  
Force Problem

In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self-force problem of classical electrodynamics is properly solved, it becomes a plausible ontology underlying the statistical description of quantum mechanics. In the current paper we extend this result, showing that ordinary matter, thus represented, possibly suffices in explaining the outstanding observations currently requiring for this task the contrived notions of dark-matter, dark-energy and inflation. The single mandatory 'fix' to classical electrodynamics, demystifying both very small and very large scale physics, should be contrasted with other adhoc solutions to either problems. Instrumental to our cosmological model is scale covariance (and 'spontaneous breaking' thereof), a formal symmetry of classical electrodynamics treated on equal footing with its Poincare covariance, which is incompatible with the (absolute) metrical attributes of the GR metric tensor.

scholarly journals No Need for Dark-Matter, Dark-Energy or Inflation, Once Ordinary Matter is Properly Represented?

2018 ◽  
Author(s):  
Yehonatan Knoll
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Large Scale ◽  
Ad Hoc ◽  
Classical Electrodynamics ◽  
Spontaneous Breaking ◽  
Ordinary Matter ◽  
Scale Covariance ◽  
Self Force ◽  
Force Problem

In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self-force problem of classical electrodynamics is properly solved, the representation of matter which results becomes a plausible ontology underlying QM's statistical description. In the current paper we extend this result, showing that ordinary matter, thus represented, possibly suffices in explaining the outstanding observations currently requiring for this task the contrived notions of dark-matter, dark-energy and inflation. The single `fix' to classical electrodynamics, demystifying both very small and very large scale physics, should be contrasted with other ad hoc solutions to either problems. Instrumental to our cosmological model is scale covariance (and `spontaneous breaking' thereof), a formal symmetry of CE which we consider to be just as important as its Poincare covariance.

A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Juliane Schäfer ◽  
Korbinian Strimmer
Keyword(s):  
Large Scale ◽  
Mean Squared Error ◽  
Small Sample ◽  
Expression Data ◽  
Matrix Estimation ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Covariance Estimator ◽  
Scale Covariance ◽  
Small Sample Sizes

Inferring large-scale covariance matrices from sparse genomic data is an ubiquitous problem in bioinformatics. Clearly, the widely used standard covariance and correlation estimators are ill-suited for this purpose. As statistically efficient and computationally fast alternative we propose a novel shrinkage covariance estimator that exploits the Ledoit-Wolf (2003) lemma for analytic calculation of the optimal shrinkage intensity.Subsequently, we apply this improved covariance estimator (which has guaranteed minimum mean squared error, is well-conditioned, and is always positive definite even for small sample sizes) to the problem of inferring large-scale gene association networks. We show that it performs very favorably compared to competing approaches both in simulations as well as in application to real expression data.

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