Leave-One-Out Error

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A Leave-One-Out Error is an error estimate that is obtained by a leave-one-out cross-validation.



References

2018a

  • (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Leave-one-out_error Retrieved:2018-9-16.
    • Leave-one-out cross-validation (CVloo) Stability An algorithm f has CVloo stability β with respect to the loss function V if the following holds: [math]\displaystyle{ \forall i\in\{1,...,m\}, \mathbb{P}_S\{\sup_{z\in Z}|V(f_S,z_i)-V(f_{S^{|i}},z_i)|\leq\beta_{CV}\}\geq1-\delta_{CV} }[/math]

      Expected-to-leave-one-out error ([math]\displaystyle{ Eloo_{err} }[/math] ) Stability An algorithm f has [math]\displaystyle{ Eloo_{err} }[/math] stability if for each n there exists a [math]\displaystyle{ \beta_{EL}^m }[/math] and a [math]\displaystyle{ \delta_{EL}^m }[/math] such that: [math]\displaystyle{ \forall i\in\{1,...,m\}, \mathbb{P}_S\{|I[f_S]-\frac{1}{m}\sum_{i=1}^m V(f_{S^{|i}},z_i)|\leq\beta_{EL}^m\}\geq1-\delta_{EL}^m }[/math] , with [math]\displaystyle{ \beta_{EL}^m }[/math] and [math]\displaystyle{ \delta_{EL}^m }[/math] going to zero for [math]\displaystyle{ n\rightarrow\inf }[/math]

2018b

2017b

2004

2003

1999

1989

1958

  • (Tukey, 1958) ⇒ J.W. Tukey (1958). “Bias and confidence in not-quite large samples". Annals of Math. Stat., 29.

1949