Conjecture on outlier traps under Λ\Lambda-poisedness

Let Y\mathcal{Y} be the set of experimental points, and let y1,y2,y3Yy^1,y^2,y^3\in\mathcal{Y}. A point is called bad under Λ\Lambda-poisedness when it satisfies the paper's bad-point criterion for Λ\Lambda-poisedness. Outlier-trap conjecture. For every y4Y\{y1,y2,y3}y^4\in\mathcal{Y}\backslash\{y^1,y^2,y^3\}, if

yiy4>2for every i{1,2,3},\lVert y^i-y^4\rVert>2\quad\text{for every }i\in\{1,2,3\},

then there is at least one y5{yYyy42}y^5\in\{y\in\mathcal{Y}\mid\lVert y-y^4\rVert\leq2\} that is bad under Λ\Lambda-poisedness. The conjecture formalizes the experimentally observed association between distant outliers and nearby bad points under Λ\Lambda-poisedness; the paper reports that more than 99%99\% of the relevant experimental points were outlier traps, but does not establish the assertion theoretically.

Sources & referencesView supporting material

Primary source

Qi Zhang and Pengcheng Xie, “On the Relationship between Λ-poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor”, arXiv:2407.17529 (2024).

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