kfoldLoss
Loss for cross-validated partitioned regression model
Description
L = kfoldLoss(CVMdl,Name,Value)
Examples
Find the cross-validation loss for a regression ensemble of the carsmall data.
Load the carsmall data set and select displacement, horsepower, and vehicle weight as predictors.
load carsmall
X = [Displacement Horsepower Weight];Train an ensemble of regression trees.
rens = fitrensemble(X,MPG);
Create a cross-validated ensemble from rens and find the k-fold cross-validation loss.
rng(10,'twister') % For reproducibility cvrens = crossval(rens); L = kfoldLoss(cvrens)
L = 28.7114
The mean squared error (MSE) is a measure of model quality. Examine the MSE for each fold of a cross-validated regression model.
Load the carsmall data set. Specify the predictor X and the response data Y.
load carsmall
X = [Cylinders Displacement Horsepower Weight];
Y = MPG;Train a cross-validated regression tree model. By default, the software implements 10-fold cross-validation.
rng('default') % For reproducibility CVMdl = fitrtree(X,Y,'CrossVal','on');
Compute the MSE for each fold. Visualize the distribution of the loss values by using a box plot. Notice that none of the values is an outlier.
losses = kfoldLoss(CVMdl,'Mode','individual')
losses = 10×1
42.5072
20.3995
22.3737
34.4255
40.8005
60.2755
19.5562
9.2060
29.0788
16.3386
boxchart(losses)
Train a cross-validated generalized additive model (GAM) with 10 folds. Then, use kfoldLoss to compute the cumulative cross-validation regression loss (mean squared errors). Use the errors to determine the optimal number of trees per predictor (linear term for predictor) and the optimal number of trees per interaction term.
Alternatively, you can find optimal values of fitrgam name-value arguments by using the OptimizeHyperparameters name-value argument. For an example, see Optimize GAM Using OptimizeHyperparameters.
Load the patients data set.
load patientsCreate a table that contains the predictor variables (Age, Diastolic, Smoker, Weight, Gender, and SelfAssessedHealthStatus) and the response variable (Systolic).
tbl = table(Age,Diastolic,Smoker,Weight,Gender,SelfAssessedHealthStatus,Systolic);
Create a cross-validated GAM by using the default cross-validation option. Specify the 'CrossVal' name-value argument as 'on'. Also, specify to include 5 interaction terms.
rng('default') % For reproducibility CVMdl = fitrgam(tbl,'Systolic','CrossVal','on','Interactions',5);
If you specify 'Mode' as 'cumulative' for kfoldLoss, then the function returns cumulative errors, which are the average errors across all folds obtained using the same number of trees for each fold. Display the number of trees for each fold.
CVMdl.NumTrainedPerFold
ans = struct with fields:
PredictorTrees: [300 300 300 300 300 300 300 300 300 300]
InteractionTrees: [76 100 100 100 100 42 100 100 59 100]
kfoldLoss can compute cumulative errors using up to 300 predictor trees and 42 interaction trees.
Plot the cumulative, 10-fold cross-validated, mean squared errors. Specify 'IncludeInteractions' as false to exclude interaction terms from the computation.
L_noInteractions = kfoldLoss(CVMdl,'Mode','cumulative','IncludeInteractions',false); figure plot(0:min(CVMdl.NumTrainedPerFold.PredictorTrees),L_noInteractions)
The first element of L_noInteractions is the average error over all folds obtained using only the intercept (constant) term. The (J+1)th element of L_noInteractions is the average error obtained using the intercept term and the first J predictor trees per linear term. Plotting the cumulative loss allows you to monitor how the error changes as the number of predictor trees in the GAM increases.
Find the minimum error and the number of predictor trees used to achieve the minimum error.
[M,I] = min(L_noInteractions)
M = 28.0506
I = 6
The GAM achieves the minimum error when it includes 5 predictor trees.
Compute the cumulative mean squared error using both linear terms and interaction terms.
L = kfoldLoss(CVMdl,'Mode','cumulative'); figure plot(0:min(CVMdl.NumTrainedPerFold.InteractionTrees),L)
The first element of L is the average error over all folds obtained using the intercept (constant) term and all predictor trees per linear term. The (J+1)th element of L is the average error obtained using the intercept term, all predictor trees per linear term, and the first J interaction trees per interaction term. The plot shows that the error increases when interaction terms are added.
If you are satisfied with the error when the number of predictor trees is 5, you can create a predictive model by training the univariate GAM again and specifying 'NumTreesPerPredictor',5 without cross-validation.
Input Arguments
Name-Value Arguments
Output Arguments
Alternative Functionality
If you want to compute the cross-validated loss of a tree model, you can avoid
constructing a RegressionPartitionedModel object by calling cvloss. Creating a cross-validated tree object can save you time if you plan to
examine it more than once.
