Estimate loss using crossvalidation
returns a 10fold crossvalidation error estimate for the function
err
= crossval(criterion
,X
,y
,'Predfun',predfun
)predfun
based on the specified criterion
,
either 'mse'
(mean squared error) or 'msc'
(misclassification rate). The rows of X
and y
correspond to observations, and the columns of X
correspond to
predictor variables.
For more information, see General CrossValidation Steps for predfun.
performs 10fold crossvalidation for the function values
= crossval(fun
,X
)fun
, applied to
the data in X
. The rows of X
correspond to
observations, and the columns of X
correspond to variables.
For more information, see General CrossValidation Steps for fun.
___ = crossval(___,
specifies crossvalidation options using one or more namevalue pair arguments in addition
to any of the input argument combinations and output arguments in previous syntaxes. For
example, Name,Value
)'KFold',5
specifies to perform 5fold crossvalidation.
Compute the mean squared error of a regression model by using 10fold crossvalidation.
Load the carsmall
data set. Put the acceleration, horsepower, weight, and miles per gallon (MPG) values into the matrix data
. Remove any rows that contain NaN
values.
load carsmall
data = [Acceleration Horsepower Weight MPG];
data(any(isnan(data),2),:) = [];
Specify the last column of data
, which corresponds to MPG
, as the response variable y
. Specify the other columns of data
as the predictor data X
. Add a column of ones to X
when your regression function uses regress
, as in this example.
Note: regress
is useful when you simply need the coefficient estimates or residuals of a regression model. If you need to investigate a fitted regression model further, create a linear regression model object by using fitlm
. For an example that uses fitlm
and crossval
, see Compute Mean Absolute Error Using CrossValidation.
y = data(:,4); X = [ones(length(y),1) data(:,1:3)];
Create the custom function regf
(shown at the end of this example). This function fits a regression model to training data and then computes predicted values on a test set.
Note: If you use the live script file for this example, the regf
function is already included at the end of the file. Otherwise, you need to create this function at the end of your .m file or add it as a file on the MATLAB® path.
Compute the default 10fold crossvalidation mean squared error for the regression model with predictor data X
and response variable y
.
rng('default') % For reproducibility cvMSE = crossval('mse',X,y,'Predfun',@regf)
cvMSE = 17.5399
This code creates the function regf
.
function yfit = regf(Xtrain,ytrain,Xtest) b = regress(ytrain,Xtrain); yfit = Xtest*b; end
Compute the misclassification error of a logistic regression model trained on numeric and categorical predictor data by using 10fold crossvalidation.
Load the patients
data set. Specify the numeric variables Diastolic
and Systolic
and the categorical variable Gender
as predictors, and specify Smoker
as the response variable.
load patients
X1 = Diastolic;
X2 = categorical(Gender);
X3 = Systolic;
y = Smoker;
Create the custom function classf
(shown at the end of this example). This function fits a logistic regression model to training data and then classifies test data.
Note: If you use the live script file for this example, the classf
function is already included at the end of the file. Otherwise, you need to create this function at the end of your .m file or add it as a file on the MATLAB® path.
Compute the 10fold crossvalidation misclassification error for the model with predictor data X1
, X2
, and X3
and response variable y
. Specify 'Stratify',y
to ensure that training and test sets have roughly the same proportion of smokers.
rng('default') % For reproducibility err = crossval('mcr',X1,X2,X3,y,'Predfun',@classf,'Stratify',y)
err = 0.1100
This code creates the function classf
.
function pred = classf(X1train,X2train,X3train,ytrain,X1test,X2test,X3test) Xtrain = table(X1train,X2train,X3train,ytrain, ... 'VariableNames',{'Diastolic','Gender','Systolic','Smoker'}); Xtest = table(X1test,X2test,X3test, ... 'VariableNames',{'Diastolic','Gender','Systolic'}); modelspec = 'Smoker ~ Diastolic + Gender + Systolic'; mdl = fitglm(Xtrain,modelspec,'Distribution','binomial'); yfit = predict(mdl,Xtest); pred = (yfit > 0.5); end
For a given number of clusters, compute the crossvalidated sum of squared distances between observations and their nearest cluster center. Compare the results for one through ten clusters.
Load the fisheriris
data set. X
is the matrix meas
, which contains flower measurements for 150 different flowers.
load fisheriris
X = meas;
Create the custom function clustf
(shown at the end of this example). This function performs the following steps:
Standardize the training data.
Separate the training data into k
clusters.
Transform the test data using the training data mean and standard deviation.
Compute the distance from each test data point to the nearest cluster center, or centroid.
Compute the sum of the squares of the distances.
Note: If you use the live script file for this example, the clustf
function is already included at the end of the file. Otherwise, you need to create the function at the end of your .m file or add it as a file on the MATLAB® path.
Create a for
loop that specifies the number of clusters k
for each iteration. For each fixed number of clusters, pass the corresponding clustf
function to crossval
. Because crossval
performs 10fold crossvalidation by default, the software computes 10 sums of squared distances, one for each partition of training and test data. Take the sum of those values; the result is the crossvalidated sum of squared distances for the given number of clusters.
rng('default') % For reproducibility cvdist = zeros(5,1); for k = 1:10 fun = @(Xtrain,Xtest)clustf(Xtrain,Xtest,k); distances = crossval(fun,X); cvdist(k) = sum(distances); end
Plot the crossvalidated sum of squared distances for each number of clusters.
plot(cvdist) xlabel('Number of Clusters') ylabel('CV Sum of Squared Distances')
In general, when determining how many clusters to use, consider the greatest number of clusters that corresponds to a significant decrease in the crossvalidated sum of squared distances. For this example, using two or three clusters seems appropriate, but using more than three clusters does not.
This code creates the function clustf
.
function distances = clustf(Xtrain,Xtest,k) [Ztrain,Zmean,Zstd] = zscore(Xtrain); [~,C] = kmeans(Ztrain,k); % Creates k clusters Ztest = (XtestZmean)./Zstd; d = pdist2(C,Ztest,'euclidean','Smallest',1); distances = sum(d.^2); end
Compute the mean absolute error of a regression model by using 10fold crossvalidation.
Load the carsmall
data set. Specify the Acceleration
and Displacement
variables as predictors and the Weight
variable as the response.
load carsmall
X1 = Acceleration;
X2 = Displacement;
y = Weight;
Create the custom function regf
(shown at the end of this example). This function fits a regression model to training data and then computes predicted car weights on a test set. The function compares the predicted car weight values to the true values, and then computes the mean absolute error (MAE) and the MAE adjusted to the range of the test set car weights.
Note: If you use the live script file for this example, the regf
function is already included at the end of the file. Otherwise, you need to create this function at the end of your .m file or add it as a file on the MATLAB® path.
By default, crossval
performs 10fold crossvalidation. For each of the 10 training and test set partitions of the data in X1
, X2
, and y
, compute the MAE and adjusted MAE values using the regf
function. Find the mean MAE and mean adjusted MAE.
rng('default') % For reproducibility values = crossval(@regf,X1,X2,y)
values = 10×2
319.2261 0.1132
342.3722 0.1240
214.3735 0.0902
174.7247 0.1128
189.4835 0.0832
249.4359 0.1003
194.4210 0.0845
348.7437 0.1700
283.1761 0.1187
210.7444 0.1325
mean(values)
ans = 1×2
252.6701 0.1129
This code creates the function regf
.
function errors = regf(X1train,X2train,ytrain,X1test,X2test,ytest) tbltrain = table(X1train,X2train,ytrain, ... 'VariableNames',{'Acceleration','Displacement','Weight'}); tbltest = table(X1test,X2test,ytest, ... 'VariableNames',{'Acceleration','Displacement','Weight'}); mdl = fitlm(tbltrain,'Weight ~ Acceleration + Displacement'); yfit = predict(mdl,tbltest); MAE = mean(abs(yfittbltest.Weight)); adjMAE = MAE/range(tbltest.Weight); errors = [MAE adjMAE]; end
Compute the misclassification error of a classification tree by using principal component analysis (PCA) and 5fold crossvalidation.
Load the fisheriris
data set. The meas
matrix contains flower measurements for 150 different flowers. The species
variable lists the species for each flower.
load fisheriris
Create the custom function classf
(shown at the end of this example). This function fits a classification tree to training data and then classifies test data. Use PCA inside the function to reduce the number of predictors used to create the tree model.
Note: If you use the live script file for this example, the classf
function is already included at the end of the file. Otherwise, you need to create this function at the end of your .m file or add it as a file on the MATLAB® path.
Create a cvpartition
object for stratified 5fold crossvalidation. By default, cvpartition
ensures that training and test sets have roughly the same proportions of flower species.
rng('default') % For reproducibility cvp = cvpartition(species,'KFold',5);
Compute the 5fold crossvalidation misclassification error for the classification tree with predictor data meas
and response variable species
.
cvError = crossval('mcr',meas,species,'Predfun',@classf,'Partition',cvp)
cvError = 0.1067
This code creates the function classf
.
function yfit = classf(Xtrain,ytrain,Xtest) % Standardize the training predictor data. Then, find the % principal components for the standardized training predictor % data. [Ztrain,Zmean,Zstd] = zscore(Xtrain); [coeff,scoreTrain,~,~,explained,mu] = pca(Ztrain); % Find the lowest number of principal components that account % for at least 95% of the variability. n = find(cumsum(explained)>=95,1); % Find the n principal component scores for the standardized % training predictor data. Train a classification tree model % using only these scores. scoreTrain95 = scoreTrain(:,1:n); mdl = fitctree(scoreTrain95,ytrain); % Find the n principal component scores for the transformed % test data. Classify the test data. Ztest = (XtestZmean)./Zstd; scoreTest95 = (Ztestmu)*coeff(:,1:n); yfit = predict(mdl,scoreTest95); end
Create a confusion matrix from the 10fold crossvalidation results of a discriminant analysis model.
Note: Use classify
when training speed is a concern. Otherwise, use fitcdiscr
to create a discriminant analysis model. For an example that shows the same workflow as this example, but uses fitcdiscr
, see Create Confusion Matrix Using CrossValidation Predictions.
Load the fisheriris
data set. X
contains flower measurements for 150 different flowers, and y
lists the species for each flower. Create a variable order
that specifies the order of the flower species.
load fisheriris
X = meas;
y = species;
order = unique(y)
order = 3x1 cell
{'setosa' }
{'versicolor'}
{'virginica' }
Create a function handle named func
for a function that completes the following steps:
Take in training data (Xtrain
and ytrain
) and test data (Xtest
and ytest
).
Use the training data to create a discriminant analysis model that classifies new data (Xtest
). Create this model and classify new data by using the classify
function.
Compare the true test data classes (ytest
) to the predicted test data values, and create a confusion matrix of the results by using the confusionmat
function. Specify the class order by using 'Order',order
.
func = @(Xtrain,ytrain,Xtest,ytest)confusionmat(ytest, ... classify(Xtest,Xtrain,ytrain),'Order',order);
Create a cvpartition
object for stratified 10fold crossvalidation. By default, cvpartition
ensures that training and test sets have roughly the same proportions of flower species.
rng('default') % For reproducibility cvp = cvpartition(y,'Kfold',10);
Compute the 10 test set confusion matrices for each partition of the predictor data X
and response variable y
. Each row of confMat
corresponds to the confusion matrix results for one test set. Aggregate the results and create the final confusion matrix cvMat
.
confMat = crossval(func,X,y,'Partition',cvp);
cvMat = reshape(sum(confMat),3,3)
cvMat = 3×3
50 0 0
0 48 2
0 1 49
Plot the confusion matrix as a confusion matrix chart by using confusionchart
.
confusionchart(cvMat,order)
criterion
— Type of error estimate'mse'
 'mcr'
Type of error estimate, specified as either 'mse'
or
'mcr'
.
Value  Description 

'mse'  Mean squared error (MSE) — Appropriate for regression algorithms only 
'mcr'  Misclassification rate, or proportion of misclassified observations — Appropriate for classification algorithms only 
X
— Data setData set, specified as a column vector, matrix, or array. The rows of
X
correspond to observations, and the columns of
X
generally correspond to variables. If you pass multiple data
sets X1,...,XN
to crossval
, then all data sets
must have the same number of rows.
Data Types: single
 double
 logical
 char
 string
 cell
 categorical
y
— Response dataResponse data, specified as a column vector or character array. The rows of
y
correspond to observations, and y
must
have the same number of rows as the predictor data X
or
X1,...,XN
.
Data Types: single
 double
 logical
 char
 string
 cell
 categorical
predfun
— Prediction functionPrediction function, specified as a function handle. You must create this function as an anonymous function, a function defined at the end of the .m or .mlx file containing the rest of your code, or a file on the MATLAB^{®} path.
This table describes the required function syntax, given the type of predictor data
passed to crossval
.
Value  Predictor Data  Function Syntax 

@myfunction  X 
function yfit = myfunction(Xtrain,ytrain,Xtest) % Calculate predicted response ... end

@myfunction  X1,...,XN 
function yfit = myfunction(X1train,...,XNtrain,ytrain,X1test,...,XNtest) % Calculate predicted response ... end

Example: @(Xtrain,ytrain,Xtest)(Xtest*regress(ytrain,Xtrain));
Data Types: function_handle
fun
— Function to crossvalidateFunction to crossvalidate, specified as a function handle. You must create this function as an anonymous function, a function defined at the end of the .m or .mlx file containing the rest of your code, or a file on the MATLAB path.
This table describes the required function syntax, given the type of data passed to
crossval
.
Value  Data  Function Syntax 

@myfunction  X 
function value = myfunction(Xtrain,Xtest) % Calculation of value ... end

@myfunction  X1,...,XN 
function value = myfunction(X1train,...,XNtrain,X1test,...,XNtest) % Calculation of value ... end

Data Types: function_handle
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
crossval('mcr',meas,species,'Predfun',@classf,'KFold',5,'Stratify',species)
specifies to compute the stratified 5fold crossvalidation misclassification rate for the
classf
function with predictor data meas
and
response variable species
.'Holdout'
— Fraction or number of observations used for holdout validation[]
(default)  scalar value in the range (0,1)  positive integer scalarFraction or number of observations used for holdout validation, specified as the
commaseparated pair consisting of 'Holdout'
and a scalar value in
the range (0,1) or a positive integer scalar.
If the Holdout
value p
is a scalar
in the range (0,1), then crossval
randomly selects and
reserves approximately p*100
% of the observations as test
data.
If the Holdout
value p
is a positive
integer scalar, then crossval
randomly selects and reserves
p
observations as test data.
In either case, crossval
then trains the model
specified by either fun
or predfun
using the
rest of the data. Finally, the function uses the test data along with the trained
model to compute either values
or
err
.
You can use only one of these four namevalue pair arguments:
Holdout
, KFold
,
Leaveout
, and Partition
.
Example: 'Holdout',0.3
Example: 'Holdout',50
Data Types: single
 double
'KFold'
— Number of folds10
(default)  positive integer scalar greater than 1Number of folds for kfold crossvalidation, specified as the commaseparated pair
consisting of 'KFold'
and a positive integer scalar greater than
1.
If you specify 'KFold',k
, then crossval
randomly partitions the data into k
sets. For each set, the
function reserves the set as test data, and trains the model specified by either
fun
or predfun
using the other
k
– 1 sets. crossval
then uses the test data
along with the trained model to compute either values
or
err
.
You can use only one of these four namevalue pair arguments:
Holdout
, KFold
,
Leaveout
, and Partition
.
Example: 'KFold',5
Data Types: single
 double
'Leaveout'
— Leaveoneout crossvalidation[]
(default)  1
Leaveoneout crossvalidation, specified as the commaseparated pair consisting
of 'Leaveout'
and 1
.
If you specify 'Leaveout',1
, then for each observation,
crossval
reserves the observation as test data, and trains the
model specified by either fun
or predfun
using the other observations. The function then uses the test observation along with
the trained model to compute either values
or
err
.
You can use only one of these four namevalue pair arguments:
Holdout
, KFold
,
Leaveout
, and Partition
.
Example: 'Leaveout',1
Data Types: single
 double
'MCReps'
— Number of Monte Carlo repetitions1
(default)  positive integer scalarNumber of Monte Carlo repetitions for validation, specified as the commaseparated
pair consisting of 'MCReps'
and a positive integer scalar. If the
first input of crossval
is 'mse'
or
'mcr'
(see criterion
), then
crossval
returns the mean MSE or misclassification rate across
all Monte Carlo repetitions. Otherwise, crossval
concatenates the
values from all Monte Carlo repetitions along the first dimension.
If you specify both Partition
and
MCReps
, then the first Monte Carlo repetition uses the partition
information in the cvpartition
object, and the software calls the
repartition
object function to generate
new partitions for each of the remaining repetitions.
Example: 'MCReps',5
Data Types: single
 double
'Partition'
— Crossvalidation partition[]
(default)  cvpartition
partition objectCrossvalidation partition, specified as the commaseparated pair consisting of
'Partition'
and a cvpartition
partition object
created by cvpartition
. The partition object
specifies the type of crossvalidation and the indexing for the training and test
sets.
When you use crossval
, you cannot specify both
Partition
and Stratify
. Instead, directly
specify a stratified partition when you create the cvpartition
partition object.
You can use only one of these four namevalue pair arguments:
Holdout
, KFold
,
Leaveout
, and Partition
.
'Stratify'
— Variable specifying groups used for stratificationVariable specifying the groups used for stratification, specified as the
commaseparated pair consisting of 'Stratify'
and a column vector
with the same number of rows as the data X
or
X1,...,XN
.
When you specify Stratify
, both the training and test sets
have roughly the same class proportions as in the Stratify
vector. The software treats NaN
s, empty character vectors, empty
strings, <missing>
values, and <undefined>
values in Stratify
as missing data values, and ignores the
corresponding rows of the data.
A good practice is to use stratification when you use crossvalidation with classification algorithms. Otherwise, some test sets might not include observations for all classes.
When you use crossval
, you cannot specify both
Partition
and Stratify
. Instead, directly
specify a stratified partition when you create the cvpartition
partition object.
Data Types: single
 double
 logical
 string
 cell
 categorical
'Options'
— Options for running in parallel and setting random streamsOptions for running computations in parallel and setting random streams, specified as a
structure. Create the Options
structure with statset
. This table lists the option fields and their
values.
Field Name  Value  Default 

UseParallel  Set this value to true to run computations in
parallel.  false 
UseSubstreams  Set this value to To compute reproducibly, set
 false 
Streams  Specify this value as a RandStream object or
a cell array consisting of one such object.  If you do not specify Streams , then
crossval uses the default
stream. 
Note
You need Parallel Computing Toolbox™ to run computations in parallel.
Example: 'Options',statset('UseParallel',true)
Data Types: struct
err
— Mean squared error or misclassification rateMean squared error or misclassification rate, returned as a numeric scalar. The type
of error depends on the criterion
value.
values
— Loss valuesLoss values, returned as a column vector or matrix. Each row of
values
corresponds to the output of fun
for
one partition of training and test data.
If the output returned by fun
is multidimensional, then
crossval
reshapes the output and fits it into one row of
values
. For an example, see Create Confusion Matrix Using CrossValidation.
A good practice is to use stratification (see Stratify
) when you
use crossvalidation with classification algorithms. Otherwise, some test sets might not
include observations for all classes.
predfun
When you use predfun
, the crossval
function
typically performs 10fold crossvalidation as follows:
Split the observations in the predictor data X
and the
response variable y
into 10 groups, each of which has
approximately the same number of observations.
Use the last nine groups of observations to train a model as specified in
predfun
. Use the first group of observations as test data, pass
the test predictor data to the trained model, and compute predicted values as
specified in predfun
. Compute the error specified by
criterion
.
Use the first group and the last eight groups of observations to train a model as
specified in predfun
. Use the second group of observations as
test data, pass the test data to the trained model, and compute predicted values as
specified in predfun
. Compute the error specified by
criterion
.
Proceed in a similar manner until each group of observations is used as test data exactly once.
Return the mean error estimate as the scalar err
.
fun
When you use fun
, the crossval
function
typically performs 10fold crossvalidation as follows:
Split the data in X
into 10 groups, each of which has
approximately the same number of observations.
Use the last nine groups of data to train a model as specified in
fun
. Use the first group of data as a test set, pass the test
set to the trained model, and compute some value (for example, loss) as specified in
fun
.
Use the first group and the last eight groups of data to train a model as
specified in fun
. Use the second group of data as a test set,
pass the test set to the trained model, and compute some value as specified in
fun
.
Proceed in a similar manner until each group of data is used as a test set exactly once.
Return the 10 computed values as the vector values
.
Many classification and regression functions allow you to perform crossvalidation directly.
When you use fit functions such as fitcsvm
, fitctree
, and fitrtree
, you can specify crossvalidation options by using namevalue
pair arguments. Alternatively, you can first create models with these fit functions and
then create a partitioned object by using the crossval
object
function. Use the kfoldLoss
and kfoldPredict
object functions to compute the loss and predicted values for the partitioned object.
For more information, see ClassificationPartitionedModel
and RegressionPartitionedModel
.
You can also specify crossvalidation options when you perform lasso or elastic net
regularization using lasso
and lassoglm
.
To run in parallel, specify the 'Options'
namevalue argument in the call
to this function and set the 'UseParallel'
field of the options
structure to true
using statset
.
For example: 'Options',statset('UseParallel',true)
For more information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
classify
 confusionmat
 cvpartition
 kmeans
 pca
 regress
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