Loss estimate using cross validation
vals = crossval(fun,X)
vals = crossval(fun,X,Y,...)
mse = crossval('mse',X,y,'Predfun',predfun)
mcr = crossval('mcr',X,y,'Predfun',predfun)
val = crossval(criterion
,X1,X2,...,y,'Predfun',predfun)
vals = crossval(...,'name
',value
)
vals = crossval(fun,X)
performs 10fold
cross validation for the function fun
, applied
to the data in X
.
fun
is a function handle to a function with
two inputs, the training subset of X
, XTRAIN
,
and the test subset of X
, XTEST
,
as follows:
testval = fun(XTRAIN,XTEST)
Each time it is called, fun
should use XTRAIN
to
fit a model, then return some criterion testval
computed
on XTEST
using that fitted model.
X
can be a column vector or a matrix. Rows
of X
correspond to observations; columns correspond
to variables or features. Each row of vals
contains
the result of applying fun
to one test set. If testval
is
a nonscalar value, crossval
converts it to a row
vector using linear indexing and stored in one row of vals
.
vals = crossval(fun,X,Y,...)
is used when
data are stored in separate variables X
, Y
,
... . All variables (column vectors, matrices, or arrays) must have
the same number of rows. fun
is called with the
training subsets of X
, Y
, ...
, followed by the test subsets of X
, Y
,
... , as follows:
testvals = fun(XTRAIN,YTRAIN,...,XTEST,YTEST,...)
mse = crossval('mse',X,y,'Predfun',predfun)
returns mse
,
a scalar containing a 10fold cross validation estimate of meansquared
error for the function predfun
. X
can
be a column vector, matrix, or array of predictors. y
is
a column vector of response values. X
and y
must
have the same number of rows.
predfun
is a function handle called with
the training subset of X
, the training subset of y
,
and the test subset of X
as follows:
yfit = predfun(XTRAIN,ytrain,XTEST)
Each time it is called, predfun
should use XTRAIN
and ytrain
to
fit a regression model and then return fitted values in a column vector
yfit
. Each row of yfit
contains
the predicted values for the corresponding row of XTEST
. crossval
computes
the squared errors between yfit
and the corresponding
response test set, and returns the overall mean across all test sets.
mcr = crossval('mcr',X,y,'Predfun',predfun)
returns mcr
,
a scalar containing a 10fold cross validation estimate of misclassification
rate (the proportion of misclassified samples) for the function predfun
.
The matrix X
contains predictor values and the
vector y
contains class labels. predfun
should
use XTRAIN
and YTRAIN
to fit
a classification model and return yfit
as the predicted
class labels for XTEST
. crossval
computes
the number of misclassifications between yfit
and
the corresponding response test set, and returns the overall misclassification
rate across all test sets.
val = crossval(
,
where criterion
,X1,X2,...,y,'Predfun',predfun)criterion
is 'mse'
or 'mcr'
,
returns a cross validation estimate of meansquared error (for a regression
model) or misclassification rate (for a classification model) with
predictor values in X1
, X2
,
... and, respectively, response values or class labels in y
. X1
, X2
,
... and y
must have the same number of rows. predfun
is
a function handle called with the training subsets of X1
, X2
,
..., the training subset of y
, and the test subsets
of X1
, X2
, ..., as follows:
yfit=predfun(X1TRAIN,X2TRAIN,...,ytrain,X1TEST,X2TEST,...)
yfit
should be a column vector containing
the fitted values.
vals = crossval(...,'
specifies
one or more optional parameter name/value pairs from the following
table. Specify name
',value
)name
inside single quotes.
Name  Value 

holdout  A scalar specifying the ratio or the number of observations 
kfold  A positive integer that is greater than 1 specifying
the number of folds 
leaveout  Specifies leaveoneout cross validation. The value must
be 
mcreps  A positive integer specifying the number of MonteCarlo
repetitions for validation. Ifthe first input of 
partition  An object 
stratify  A column vector 
options  A structure that specifies whether to run in parallel,
and specifies the random stream or streams. Create the

Only one of kfold
, holdout
, leaveout
,
or partition
can be specified, and partition
cannot
be specified with stratify
. If both partition
and mcreps
are
specified, the first MonteCarlo repetition uses the partition information
in the cvpartition
object, and the repartition
method
is called to generate new partitions for each of the remaining repetitions.
If no cross validation type is specified, the default is 10fold cross
validation.
Note: When using cross validation with classification algorithms, stratification is preferred. Otherwise, some test sets may not include observations from all classes. 
Compute meansquared error for regression using 10fold cross validation:
load('fisheriris'); y = meas(:,1); X = [ones(size(y,1),1),meas(:,2:4)]; regf=@(XTRAIN,ytrain,XTEST)(XTEST*regress(ytrain,XTRAIN)); cvMse = crossval('mse',X,y,'predfun',regf) cvMse = 0.1015
Compute misclassification rate using stratified 10fold cross validation:
load('fisheriris'); y = species; X = meas; cp = cvpartition(y,'k',10); % Stratified crossvalidation classf = @(XTRAIN, ytrain,XTEST)(classify(XTEST,XTRAIN,... ytrain)); cvMCR = crossval('mcr',X,y,'predfun',classf,'partition',cp) cvMCR = 0.0200
Compute the confusion matrix using stratified 10fold cross validation:
load('fisheriris'); y = species; X = meas; order = unique(y); % Order of the group labels cp = cvpartition(y,'k',10); % Stratified crossvalidation f = @(xtr,ytr,xte,yte)confusionmat(yte,... classify(xte,xtr,ytr),'order',order); cfMat = crossval(f,X,y,'partition',cp); cfMat = reshape(sum(cfMat),3,3) cfMat = 50 0 0 0 48 2 0 1 49
cfMat
is the summation of 10 confusion matrices
from 10 test sets.
[1] Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. New York: Springer, 2001.