NAG Library Function Document
nag_rand_kfold_xyw (g05pvc)
1 Purpose
nag_rand_kfold_xyw (g05pvc) generates training and validation datasets suitable for use in crossvalidation or jackknifing.
2 Specification
#include <nag.h> 
#include <nagg05.h> 
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 $\left({X}_{t},{y}_{t},{w}_{t}\right)$ of ${n}_{t}$ observations, and validation datasets, denoted $\left({X}_{v},{y}_{v},{w}_{v}\right)$ 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.
If $n$ 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 leaveoneout crossvalidation, or the training dataset on its own for jackknifing. When using $K\ne n$ the resulting datasets are suitable for $K$fold crossvalidation. Datasets suitable for reversed crossvalidation 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 nonrepeatable sequence) must be called prior to the first call to nag_rand_kfold_xyw (g05pvc).
4 References
None.
5 Arguments
 1:
$\mathbf{k}$ – IntegerInput

On entry: $K$, the number of folds.
Constraint:
$2\le {\mathbf{k}}\le {\mathbf{n}}$.
 2:
$\mathbf{fold}$ – IntegerInput

On entry: the number of the fold to return as the validation dataset.
On the first call to nag_rand_kfold_xyw (g05pvc)
${\mathbf{fold}}$ 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:
$1\le {\mathbf{fold}}\le {\mathbf{k}}$.
 3:
$\mathbf{n}$ – IntegerInput

On entry: $n$, the number of observations.
Constraint:
${\mathbf{n}}\ge 1$.
 4:
$\mathbf{m}$ – IntegerInput

On entry: $m$, the number of variables.
Constraint:
${\mathbf{m}}\ge 1$.
 5:
$\mathbf{sordx}$ – Nag_DataByObsOrVarInput

On entry: determines how variables are stored in
x.
Constraint:
${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$ or $\mathrm{Nag\_DataByObs}$.
 6:
$\mathbf{x}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension,
dim, of the array
x
must be at least
 ${\mathbf{pdx}}\times {\mathbf{m}}$ when
${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$;
 ${\mathbf{pdx}}\times {\mathbf{n}}$ when
${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$.
The way the data is stored in
x is defined by
sordx.
If ${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$, ${\mathbf{x}}\left[\left(\mathit{j}1\right)\times {\mathbf{pdx}}+\mathit{i}1\right]$ contains the $\mathit{i}$th observation for the $\mathit{j}$th variable, for $i=1,2,\dots ,{\mathbf{n}}$ and $j=1,2,\dots ,{\mathbf{m}}$.
If ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{x}}\left[\left(\mathit{i}1\right)\times {\mathbf{pdx}}+\mathit{j}1\right]$ contains the $\mathit{i}$th observation for the $\mathit{j}$th variable, for $i=1,2,\dots ,{\mathbf{n}}$ and $j=1,2,\dots ,{\mathbf{m}}$.
On entry: if
${\mathbf{fold}}=1$,
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 $1$ to ${\mathbf{nt}}$ and ${X}_{v}$ in observations ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 7:
$\mathbf{pdx}$ – IntegerInput

On entry: the stride separating row elements in the twodimensional data stored in the array
x.
Constraints:
 if ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{pdx}}\ge {\mathbf{m}}$;
 otherwise ${\mathbf{pdx}}\ge {\mathbf{n}}$.
 8:
$\mathbf{y}\left[{\mathbf{n}}\right]$ – doubleInput/Output

If the original dataset does not include
${y}_{o}$ then
y must be set to
NULL.
On entry: if
${\mathbf{fold}}\ne 1$,
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 $1$ to ${\mathbf{nt}}$ and ${y}_{v}$ in elements ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 9:
$\mathbf{w}\left[{\mathbf{n}}\right]$ – doubleInput/Output

If the original dataset does not include
${w}_{o}$ then
w must be set to
NULL.
On entry: if
${\mathbf{fold}}\ne 1$,
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 $1$ to ${\mathbf{nt}}$ and ${w}_{v}$ in elements ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 10:
$\mathbf{nt}$ – Integer *Output

On exit: ${n}_{t}$, the number of observations in the training dataset.
 11:
$\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication Array

Note: the dimension,
$\mathit{dim}$, 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:
$\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see
Section 3.6 in the Essential Introduction).
6 Error Indicators and Warnings
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 3.2.1.2 in the Essential Introduction for further information.
 NE_ARRAY_SIZE

On entry, ${\mathbf{pdx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{pdx}}\ge {\mathbf{m}}$.
On entry, ${\mathbf{pdx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$, ${\mathbf{pdx}}\ge {\mathbf{n}}$.
 NE_BAD_PARAM

On entry, argument $\u2329\mathit{\text{value}}\u232a$ had an illegal value.
 NE_INT

On entry, ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{m}}\ge 1$.
On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge 1$.
 NE_INT_2

On entry, ${\mathbf{fold}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{k}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: $1\le {\mathbf{fold}}\le {\mathbf{k}}$.
On entry, ${\mathbf{k}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: $2\le {\mathbf{k}}\le {\mathbf{n}}$.
 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.
An unexpected error has been triggered by this function. Please contact
NAG.
See
Section 3.6.6 in the Essential Introduction 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 3.6.5 in the Essential Introduction for further information.
 NW_POTENTIAL_PROBLEM

More than $50\%$ of the data did not move when the data was shuffled. $\u2329\mathit{\text{value}}\u232a$ of the $\u2329\mathit{\text{value}}\u232a$ observations stayed put.
7 Accuracy
Not applicable.
nag_rand_kfold_xyw (g05pvc) will be computationality more efficient if each observation in
x is contiguous, that is
${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$.
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
${\mathbf{fold}}=1$ 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 crossvalidation 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 ${\mathbf{fold}}=1$ 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
${\mathbf{fold}}=1$. You would then copy the
x returned onto each thread and generate the remaing
${\mathbf{k}}1$ sets of data by splitting them between the threads. For example, the first thread runs with
${\mathbf{fold}}=2,\dots ,{L}_{1}$, the second with
${\mathbf{fold}}={L}_{1}+1,\dots ,{L}_{2}$ and the third with
${\mathbf{fold}}={L}_{2}+1,\dots ,{\mathbf{k}}$.
9 Example
This example uses nag_rand_kfold_xyw (g05pvc) to facilitate $K$fold crossvalidation.
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.
9.1 Program Text
Program Text (g05pvce.c)
9.2 Program Data
Program Data (g05pvce.d)
9.3 Program Results
Program Results (g05pvce.r)