Applications of concentration inequalities for statistical scoring and ranking problems

Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

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Accelerating FAB-MAP With Concentration Inequalities

IEEE Transactions on Robotics ◽

10.1109/tro.2010.2080390 ◽

2010 ◽

Vol 26 (6) ◽

pp. 1042-1050 ◽

Cited By ~ 25

Author(s):

Mark Cummins ◽

Paul Newman

Keyword(s):

Concentration Inequalities

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Concentration inequalities for a removal-driven thinning process

Quarterly of Applied Mathematics ◽

10.1090/qam/1474 ◽

2017 ◽

Vol 75 (4) ◽

pp. 677-696 ◽

Cited By ~ 1

Author(s):

Joe Klobusicky ◽

Govind Menon

Keyword(s):

Concentration Inequalities ◽

Thinning Process

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Nonconventional moderate deviations theorems and exponential concentration inequalities

Annales de l Institut Henri Poincaré Probabilités et Statistiques ◽

10.1214/19-aihp967 ◽

2020 ◽

Vol 56 (1) ◽

pp. 428-448 ◽

Cited By ~ 1

Author(s):

Yeor Hafouta

Keyword(s):

Moderate Deviations ◽

Concentration Inequalities

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Talagrand concentration inequalities for stochastic heat-type equations under uniform distance

Electronic Journal of Probability ◽

10.1214/19-ejp388 ◽

2019 ◽

Vol 24 (0) ◽

Author(s):

Shijie Shang ◽

Tusheng Zhang

Keyword(s):

Concentration Inequalities ◽

Uniform Distance

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

10.1101/2019.12.27.889436 ◽

2019 ◽

Author(s):

J.M. Gorriz ◽

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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.

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