Examples of complicated metrics for which minimal metrics are zero ones

1986 ◽  
Vol 34 (2) ◽  
pp. 1481-1482 ◽  
Author(s):  
A. M. Zubkov
Keyword(s):  
Minimal Metrics

A Transformation Property of Minimal Metrics

1991 ◽  
Vol 35 (1) ◽  
pp. 110-117 ◽  
Author(s):  
S. T. Rachev ◽  
L. Ruschendorf
Keyword(s):  
Transformation Property ◽  
Minimal Metrics

On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle

1993 ◽  
Vol 45 (3) ◽  
pp. 662-672
Author(s):  
Piotr M. Zelewski
Keyword(s):  
Vector Bundle ◽  
Euclidean Space ◽  
Convex Subset ◽  
Vector Bundles ◽  
Einstein Tensor ◽  
Algebraic Criterion ◽  
Holomorphic Vector Bundles ◽  
Suitable Sense ◽  
Minimal Metrics

AbstractWe prove that any holomorphic, homogenous vector bundle admits a homogenous minimal metric—a metric for which the Hermitian-Einstein tensor is diagonal in a suitable sense. The concept of minimality depends on the choice of the Jordan-Holder filtration of the corresponding parabolic module. We show that the set of all admissible Hermitian-Einstein tensors of certain class of minimal metrics is a convex subset of the euclidean space. As an application, we obtain an algebraic criterion for semistability of homogenous holomorphic vector bundles.

scholarly journals Individual Fairness Revisited: Transferring Techniques from Adversarial Robustness

2020 ◽  
Author(s):  
Samuel Yeom ◽  
Matt Fredrikson
Keyword(s):  
Neural Networks ◽  
Linear Models ◽  
A Priori ◽  
Definition Of ◽  
Lp Metric ◽  
Minimal Metrics

We turn the definition of individual fairness on its head - rather than ascertaining the fairness of a model given a predetermined metric, we find a metric for a given model that satisfies individual fairness. This can facilitate the discussion on the fairness of a model, addressing the issue that it may be difficult to specify a priori a suitable metric. Our contributions are twofold: First, we introduce the definition of a minimal metric and characterize the behavior of models in terms of minimal metrics. Second, for more complicated models, we apply the mechanism of randomized smoothing from adversarial robustness to make them individually fair under a given weighted Lp metric. Our experiments show that adapting the minimal metrics of linear models to more complicated neural networks can lead to meaningful and interpretable fairness guarantees at little cost to utility.

K -Minimal Metrics

2012 ◽  
pp. 169-197
Author(s):  
Svetlozar T. Rachev ◽  
Lev B. Klebanov ◽  
Stoyan V. Stoyanov ◽  
Frank J. Fabozzi
Keyword(s):  
Minimal Metrics
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