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https://dx.doi.org/10.48550/ar...
Article . 2019
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Enhanced Balancing of Bias-Variance Tradeoff in Stochastic Estimation: A Minimax Perspective

Enhanced balancing of bias-variance tradeoff in stochastic estimation: a minimax perspective
Authors: Henry Lam; Xinyu Zhang; Xuhui Zhang;

Enhanced Balancing of Bias-Variance Tradeoff in Stochastic Estimation: A Minimax Perspective

Abstract

In “Enhanced Balancing of Bias-Variance Tradeoff in Stochastic Estimation: A Minimax Perspective”, the authors study a framework to construct new classes of stochastic estimators that can consistently beat existing benchmarks regardless of key model parameter values. Oftentimes biased estimators, such as finite-difference estimators in black box stochastic gradient estimation, require selection of tuning parameters to balance bias and variance and ultimately minimize overall errors. Unfortunately, this relies on model knowledge that is unknown a priori and thus leads to ad hoc choices in practice. The authors introduce a new notion called asymptotic minimax risk ratio, which is designed to compare new estimators against existing benchmarks, whose values less than one imply that the new estimators could asymptotically outperform the benchmarks regardless of the model parameter value. Based on this, the authors study an outperforming weighting scheme by explicitly analyzing the asymptotic minimax risk ratio via a tractable reformulation of a nonconvex optimization problem.

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Keywords

FOS: Computer and information sciences, finite difference, minimax analysis, robust optimization, Minimax problems in mathematical programming, stochastic estimation, Methodology (stat.ME), bias-variance tradeoff, Statistics - Methodology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green