void	g05pvc (Integer k, Integer fold, Integer n, Integer m, Nag_DataByObsOrVar sordx, double x[], Integer pdx, double y[], double w[], Integer nt, Integer state[], NagError fail)

The function may be called by the names: g05pvc or nag_rand_kfold_xyw.

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.

g05pvc 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 functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05pvc.

4 References

None.

5 Arguments

1: $k$ – Integer Input

On entry:

K

, the number of folds.

Constraint:

2 \leq k \leq n

2: $fold$ – Integer Input

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

On the first call to g05pvc

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: $n$ – Integer Input

On entry:

n

, the number of observations.

Constraint:

n \geq 1

4: $m$ – Integer Input

On entry:

m

, the number of variables.

Constraint:

m \geq 1

5: $sordx$ – Nag_DataByObsOrVar Input

On entry: determines how variables are stored in x.

Constraint:

sordx = Nag_DataByVar

Nag_DataByObs

6: $x [\dim]$ – double Input/Output

Note: the dimension, dim, of the array x must be at least

$pdx \times m$ when $sordx = Nag_DataByVar$ ;
$pdx \times n$ when $sordx = Nag_DataByObs$ .

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

sordx = Nag_DataByVar

x [(j - 1) \times pdx + i - 1]

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

sordx = Nag_DataByObs

x [(i - 1) \times pdx + j - 1]

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 g05pvc.

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: $pdx$ – Integer Input

On entry: the stride separating row elements in the two-dimensional data stored in the array x.

Constraints:

if $sordx = Nag_DataByObs$ , $pdx \geq m$ ;
otherwise $pdx \geq n$ .

8: $y [\dim]$ – double Input/Output

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

$n$ , when $y is not NULL$ ;
otherwise $y$ is not referenced and may be NULL.

If the original dataset does not include

y_{o}

then y must be set to NULL.

On entry: if

fold \neq 1

, y must not be changed since the last call to g05pvc.

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

9: $w [\dim]$ – double Input/Output

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

$n$ , when $w is not NULL$ ;
otherwise $w$ is not referenced and may be NULL.

If the original dataset does not include

w_{o}

then w must be set to NULL.

On entry: if

fold \neq 1

, w must not be changed since the last call to g05pvc.

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

10: $nt$ – Integer * Output

On exit:

n_{t}

, the number of observations in the training dataset.

11: $state [\dim]$ – Integer Communication Array

Note: the dimension,

\dim

, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).

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

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

12: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_ARRAY_SIZE: On entry, $pdx = 〈value〉$ and $m = 〈value〉$ .
Constraint: if $sordx = Nag_DataByObs$ , $pdx \geq m$ .

On entry, $pdx = 〈value〉$ and $n = 〈value〉$ .
Constraint: if $sordx = Nag_DataByVar$ , $pdx \geq n$ .
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .

On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .
NE_INT_2: On entry, $fold = 〈value〉$ and $k = 〈value〉$ .
Constraint: $1 \leq fold \leq k$ .

On entry, $k = 〈value〉$ and $n = 〈value〉$ .
Constraint: $2 \leq k \leq n$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NW_POTENTIAL_PROBLEM: More than $50 %$ of the data did not move when the data was shuffled. $〈value〉$ of the $〈value〉$ observations stayed put.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05pvc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

g05pvc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

g05pvc will be computationality more efficient if each observation in x is contiguous, that is

sordx = Nag_DataByObs

Because of the way g05pvc 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:

g05pvc 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 g05pvc 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 g05pvc to facilitate

K

-fold cross-validation.

A set of simulated data is split into

5

training and validation datasets. g02gbc is used to fit a logistic regression model to each training dataset and then g02gpc 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.

g05pv: FL CL CPP AD

NAG CL Interfaceg05pvc (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

NAG CL Interface
g05pvc (kfold_xyw)