Integer, Intent (In)	::	k, fold, n, m, sordx, ldx, usey, usew
Integer, Intent (Inout)	::	state(*), ifail
Integer, Intent (Out)	::	nt
Real (Kind=nag_wp), Intent (Inout)	::	x(ldx,), y(), w(*)

C Header Interface

#include nagmk26.h

void	g05pvf_ ( const Integer k, const Integer fold, const Integer n, const Integer m, const Integer sordx, double x[], const Integer ldx, const Integer usey, double y[], const Integer usew, double w[], Integer nt, Integer state[], Integer ifail)

3

Description

Let

X_{o}

denote a matrix of

n

observations on

m

variables and

y_{o}

and

w_{o}

each denote a vector of length

n

. For example,

X_{o}

might represent a matrix of independent variables,

y_{o}

the dependent variable and

w_{o}

the associated weights in a weighted regression.

g05pvf generates a series of training datasets, denoted by the matrix, vector, vector triplet

(X_{t}, y_{t}, w_{t})

n_{t}

observations, and validation datasets, denoted

(X_{v}, y_{v}, w_{v})

with

n_{v}

observations. These training and validation datasets are generated as follows.

Each of the original

n

observations is randomly assigned to one of

K

equally sized groups or folds. For the

k

th sample the validation dataset consists of those observations in group

k

and the training dataset consists of all those observations not in group

k

. Therefore at most

K

samples can be generated.

n

is not divisible by

K

then the observations are assigned to groups as evenly as possible, therefore any group will be at most one observation larger or smaller than any other group.

When using

K = n

the resulting datasets are suitable for leave-one-out cross-validation, or the training dataset on its own for jack-knifing. When using

K \neq n

the resulting datasets are suitable for

K

-fold cross-validation. Datasets suitable for reversed cross-validation can be obtained by switching the training and validation datasets, i.e., use the

k

th group as the training dataset and the rest of the data as the validation dataset.

One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05pvf.

4

References

None.

5

Arguments

1: $k$ – IntegerInput

On entry:

K

, the number of folds.

Constraint:

2 \leq k \leq n

2: $fold$ – IntegerInput

On entry: the number of the fold to return as the validation dataset.

On the first call to g05pvf

fold

should be set to

1

and then incremented by one at each subsequent call until all

K

sets of training and validation datasets have been produced. See Section 9 for more details on how a different calling sequence can be used.

Constraint:

1 \leq fold \leq k

3: $n$ – IntegerInput

On entry:

n

, the number of observations.

Constraint:

n \geq 1

4: $m$ – IntegerInput

On entry:

m

, the number of variables.

Constraint:

m \geq 1

5: $sordx$ – IntegerInput

On entry: determines how variables are stored in x.

Constraint:

sordx = 1

2

6: $x (ldx *)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array x must be at least

m

sordx = 1

and at least

n

sordx = 2

The way the data is stored in x is defined by sordx.

sordx = 1

x (i, j)

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

sordx = 2

x (j, i)

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

On entry: if

fold = 1

, x must hold

X_{o}

, the values of

X

for the original dataset, otherwise, x must not be changed since the last call to g05pvf.

On exit: values of

X

for the training and validation datasets, with

X_{t}

held in observations

1

nt

and

X_{v}

in observations

nt + 1

n

7: $ldx$ – IntegerInput

On entry: the first dimension of the array x as declared in the (sub)program from which g05pvf is called.

Constraints:

if $sordx = 2$ , $ldx \geq m$ ;
otherwise $ldx \geq n$ .

8: $usey$ – IntegerInput

On entry: if

usey = 1

, the original dataset includes

y_{o}

and

y_{o}

will be processed alongside

X_{o}

Constraint:

usey = 0

1

9: $y (*)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array y must be at least

n

usey = 1

usey = 0

, y is not referenced on entry and will not be modified on exit.

On entry: if

fold = 1

, y must hold

y_{o}

, the values of

y

for the original dataset, otherwise y must not be changed since the last call to g05pvf.

On exit: values of

y

for the training and validation datasets, with

y_{t}

held in elements

1

nt

and

y_{v}

in elements

nt + 1

n

10: $usew$ – IntegerInput

On entry: if

usew = 1

, the original dataset includes

w_{o}

and

w_{o}

will be processed alongside

X_{o}

Constraint:

usew = 0

1

11: $w (*)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array w must be at least

n

usew = 1

usew = 0

, w is not referenced on entry and will not be modified on exit.

On entry: if

fold = 1

, w must hold

w_{o}

, the values of

w

for the original dataset, otherwise w must not be changed since the last call to g05pvf.

On exit: values of

w

for the training and validation datasets, with

w_{t}

held in elements

1

nt

and

w_{v}

in elements

nt + 1

n

12: $nt$ – IntegerOutput

On exit:

n_{t}

, the number of observations in the training dataset.

13: $state (*)$ – Integer arrayCommunication Array

Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

14: $ifail$ – IntegerInput/Output

On entry: ifail must be set to

0

- 1 ​ or ​ 1

. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value

- 1 ​ or ​ 1

is recommended. If the output of error messages is undesirable, then the value

1

is recommended. Otherwise, because for this routine the values of the output arguments may be useful even if

ifail \neq 0

on exit, the recommended value is

- 1

. When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Note: g05pvf may return useful information for one or more of the following detected errors or warnings.

Errors or warnings detected by the routine:

$ifail = 11$: On entry, $k = 〈value〉$ and $n = 〈value〉$ .
Constraint: $2 \leq k \leq n$ .

$ifail = 21$: On entry, $fold = 〈value〉$ and $k = 〈value〉$ .
Constraint: $1 \leq fold \leq k$ .

$ifail = 31$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .

$ifail = 41$: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .

$ifail = 51$: On entry, $sordx = 〈value〉$ .
Constraint: $sordx = 1$ or $2$ .

$ifail = 61$: More than $50 %$ of the data did not move when the data was shuffled. $〈value〉$ of the $〈value〉$ observations stayed put.

$ifail = 71$: On entry, $ldx = 〈value〉$ and $n = 〈value〉$ .
Constraint: if $sordx = 1$ , $ldx \geq n$ .

$ifail = 72$: On entry, $ldx = 〈value〉$ and $m = 〈value〉$ .
Constraint: if $sordx = 2$ , $ldx \geq m$ .

$ifail = 81$: Constraint: $usey = 0$ or $1$ .

$ifail = 101$: Constraint: $usew = 0$ or $1$ .

$ifail = 131$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

Not applicable.

8

Parallelism and Performance

g05pvf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

g05pvf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9

Further Comments

g05pvf will be computationality more efficient if each observation in x is contiguous, that is

sordx = 2

Because of the way g05pvf stores the data you should usually generate the

K

training and validation datasets in order, i.e., set

fold = 1

on the first call and increment it by one at each subsequent call. However, there are times when a different calling sequence would be beneficial, for example, when performing different cross-validation analyses on different threads. This is possible, as long as the following is borne in mind:

g05pvf must be called with $fold = 1$ first.
Other than the first set, you can obtain the training and validation dataset in any order, but for a given x you can only obtain each once.

For example, if you have three threads, you would call g05pvf once with

fold = 1

. You would then copy the x returned onto each thread and generate the remaing

k - 1

sets of data by splitting them between the threads. For example, the first thread runs with

fold = 2, \dots, L_{1}

, the second with

fold = L_{1} + 1, \dots, L_{2}

and the third with

fold = L_{2} + 1, \dots, k

10

Example

This example uses g05pvf to facilitate

K

-fold cross-validation.

A set of simulated data is split into

5

training and validation datasets. g02gbf is used to fit a logistic regression model to each training dataset and then g02gpf is used to predict the response for the observations in the validation dataset.

The counts of true and false positives and negatives along with the sensitivity and specificity is then reported.

NAG Library Routine Document

g05pvf (kfold_xyw)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

10.2

Program Data

10.3

Program Results