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sci / sci.stat.math / Q how to maintain the same characteristic of validation unit

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* Q how to maintain the same characteristic of validation unitCosine
`- Re: Q how to maintain the same characteristic of validation unitDavid Jones

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Subject: Q how to maintain the same characteristic of validation unit
From: Cosine
Newsgroups: sci.stat.math
Date: Mon, 17 Apr 2023 10:50 UTC
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Subject: Q how to maintain the same characteristic of validation unit
From: asecant@gmail.com (Cosine)
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Hi:

When collecting a new set of samples for validation is expensive, one alternative is to use the k-fold validation to mimic the situation in that we have k sets of samples for validation.

However, we have to make sure these k units have identical characteristics.. For example, if we have the numbers of normal patients and diseased ones to be 2:3 in the original set of samples, we ought to maintain this ratio for each of the k units. Suppose the original set has two types of patients 2*n1 and 3*n2. We have to choose the k to be a common factor of n1 and n2 so that the two types of patients in each of the k units are 2*m1 and 3*m2, where n1 = k*m1 and n2 = k*m2.

What if both n1 and n2 are prime numbers? More generally, what if n1 and n2 do not have a common factor?

Subject: Re: Q how to maintain the same characteristic of validation unit
From: David Jones
Newsgroups: sci.stat.math
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Date: Mon, 17 Apr 2023 18:19 UTC
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Subject: Re: Q how to maintain the same characteristic of validation unit
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Cosine wrote:

> Hi:
>
> When collecting a new set of samples for validation is expensive,
> one alternative is to use the k-fold validation to mimic the
> situation in that we have k sets of samples for validation.
>
> However, we have to make sure these k units have identical
> characteristics. For example, if we have the numbers of normal
> patients and diseased ones to be 2:3 in the original set of samples,
> we ought to maintain this ratio for each of the k units. Suppose the
> original set has two types of patients 2*n1 and 3*n2. We have to
> choose the k to be a common factor of n1 and n2 so that the two types
> of patients in each of the k units are 2*m1 and 3*m2, where n1 = k*m1
> and n2 = k*m2.
>
> What if both n1 and n2 are prime numbers? More generally, what if
> n1 and n2 do not have a common factor?

THe obvious solution here is to do the analyses in terms of quantities
whose interpretation is not sample-size dependent.

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