scholarly journals Some applications of concentration inequalities to statistics

2000 ◽  
Vol 9 (2) ◽  
pp. 245-303 ◽  
Author(s):  
Pascal Massart
Keyword(s):  
Concentration Inequalities

Accelerating FAB-MAP With Concentration Inequalities

2010 ◽  
Vol 26 (6) ◽  
pp. 1042-1050 ◽  
Author(s):  
Mark Cummins ◽  
Paul Newman
Keyword(s):  
Concentration Inequalities

scholarly journals Concentration inequalities for a removal-driven thinning process

2017 ◽  
Vol 75 (4) ◽  
pp. 677-696 ◽  
Author(s):  
Joe Klobusicky ◽  
Govind Menon
Keyword(s):  
Concentration Inequalities ◽  
Thinning Process

scholarly journals Statistical agnostic mapping: a framework in neuroimaging based on concentration inequalities

2019 ◽  
Author(s):  
J.M. Gorriz ◽  
◽  
◽  
Keyword(s):  
Large Error ◽  
Small Sample ◽  
Concentration Inequalities ◽  
P Value ◽  
Sample Sizes ◽  
Limited Sample ◽  
Pattern Recognition Problem ◽  
Actual Risk ◽  
Out Of Sample

ABSTRACTIn the 70s a novel branch of statistics emerged focusing its effort in selecting a function in the pattern recognition problem, which fulfils a definite relationship between the quality of the approximation and its complexity. These data-driven approaches are mainly devoted to problems of estimating dependencies with limited sample sizes and comprise all the empirical out-of sample generalization approaches, e.g. cross validation (CV) approaches. Although the latter are not designed for testing competing hypothesis or comparing different models in neuroimaging, there are a number of theoretical developments within this theory which could be employed to derive a Statistical Agnostic (non-parametric) Mapping (SAM) at voxel or multi-voxel level. Moreover, SAMs could relieve i) the problem of instability in limited sample sizes when estimating the actual risk via the CV approaches, e.g. large error bars, and provide ii) an alternative way of Family-wise-error (FWE) corrected p-value maps in inferential statistics for hypothesis testing. In this sense, we propose a novel framework in neuroimaging based on concentration inequalities, which results in (i) a rigorous development for model validation with a small sample/dimension ratio, and (ii) a less-conservative procedure than FWE p-value correction, to determine the brain significance maps from the inferences made using small upper bounds of the actual risk.

scholarly journals Random walk in cooling random environment: ergodic limits and concentration inequalities

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Luca Avena ◽  
Yuki Chino ◽  
Conrado da Costa ◽  
Frank den Hollander
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Concentration Inequalities
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