Asymptotic Risk and Bayes Risk of Thresholding and Superefficient Estimates and Optimal Thresholding

2013 ◽  
pp. 41-67
Author(s):  
Anirban DasGupta ◽  
Iain M. Johnstone
Keyword(s):  
Bayes Risk ◽  
Asymptotic Risk

STRETCHING THE NET: MULTIDIMENSIONAL REGULARIZATION

2021 ◽  
pp. 1-30
Author(s):  
Jaume Vives-i-Bastida
Keyword(s):  
Empirical Bayes ◽  
Cross Validation ◽  
Elastic Net ◽  
Shrinkage Estimators ◽  
Expected Loss ◽  
Bayes Risk ◽  
Asymptotic Risk ◽  
Regularization Parameters ◽  
Unbiased Risk ◽  
Sparsity Level

This paper derives asymptotic risk (expected loss) results for shrinkage estimators with multidimensional regularization in high-dimensional settings. We introduce a class of multidimensional shrinkage estimators (MuSEs), which includes the elastic net, and show that—as the number of parameters to estimate grows—the empirical loss converges to the oracle-optimal risk. This result holds when the regularization parameters are estimated empirically via cross-validation or Stein’s unbiased risk estimate. To help guide applied researchers in their choice of estimator, we compare the empirical Bayes risk of the lasso, ridge, and elastic net in a spike and normal setting. Of the three estimators, we find that the elastic net performs best when the data are moderately sparse and the lasso performs best when the data are highly sparse. Our analysis suggests that applied researchers who are unsure about the level of sparsity in their data might benefit from using MuSEs such as the elastic net. We exploit these insights to propose a new estimator, the cubic net, and demonstrate through simulations that it outperforms the three other estimators for any sparsity level.

scholarly journals Nonparametric Bayes-risk estimation

1971 ◽  
Vol 17 (4) ◽  
pp. 440-444 ◽  
Author(s):  
S. Fralick ◽  
R. Scott
Keyword(s):  
Risk Estimation ◽  
Bayes Risk ◽  
Nonparametric Bayes

Data-driven fault diagnosis of satellite power system using fuzzy Bayes risk and SVM

2019 ◽  
Vol 84 ◽  
pp. 1092-1105 ◽  
Author(s):  
Mingliang Suo ◽  
Baolong Zhu ◽  
Ruoming An ◽  
Huimin Sun ◽  
Shengzhong Xu ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Power System ◽  
Data Driven ◽  
Bayes Risk

scholarly journals Minimum Bayes risk combination of translation hypotheses from alternative morphological decompositions

2009 ◽  
Author(s):  
Adrià de Gispert ◽  
Sami Virpioja ◽  
Mikko Kurimo ◽  
William Byrne
Keyword(s):  
Bayes Risk ◽  
Minimum Bayes Risk

scholarly journals On the relation of Bayes risk, word error, and word posteriors in ASR

2010 ◽  
Author(s):  
Ralf Schlüter ◽  
Markus Nußbaum-Thom ◽  
Hermann Ney
Keyword(s):  
Bayes Risk
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