void	nag_rand_kfold_xyw (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)

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.

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

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 nag_rand_kfold_xyw (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 8 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: $sordx$ – Nag_DataByObsOrVarInput

On entry: determines how variables are stored in x.

Constraint:

sordx = Nag_DataByVar

Nag_DataByObs

6: $x [\dim]$ – doubleInput/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 nag_rand_kfold_xyw (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: $pdx$ – IntegerInput

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: $y [n]$ – doubleInput/Output

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 nag_rand_kfold_xyw (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: $w [n]$ – doubleInput/Output

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 nag_rand_kfold_xyw (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: $state [\dim]$ – IntegerCommunication 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 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation 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

Further Comments

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

sordx = Nag_DataByObs

Because of the way nag_rand_kfold_xyw (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:

nag_rand_kfold_xyw (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 nag_rand_kfold_xyw (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

9

Example

This example uses nag_rand_kfold_xyw (g05pvc) to facilitate

K

-fold cross-validation.

A set of simulated data is split into

5

training and validation datasets. nag_glm_binomial (g02gbc) is used to fit a logistic regression model to each training dataset and then nag_glm_predict (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.

NAG Library Function Document

nag_rand_kfold_xyw (g05pvc)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Further Comments

9

Example

9.1

Program Text

9.2

Program Data

9.3

Program Results