stacking_train: Training base and meta models

Description

Training base and meta learners of stacking (an ensemble learning approach). The base and meta learners can be chosen from supervised methods implemented in caret. This function internally calls train_basemodel and train_metamodel. Packages caret, parallel, snow, and packages for base and meta learners should be installed.

Usage

stacking_train(X, Y, Method, Metamodel, core = 1, cross_validation = TRUE,
               use_X = FALSE, TrainEachFold = FALSE, Nfold = 10,
               num_sample = 10, proportion = 0.8)

Value

A list containing the following elements is output.

base: A list output by train_basemodel. See value of train_basemodel for the details
meta: A list output by train_metamodel. See value of train_metamodel for the details

Arguments

X: An N x P matrix of explanatory variables where N is the number of samples and P is the number of variables. Column names are required by caret.
Y: A length N Vector of objective variables. Use a factor for classification.
Method: A list specifying base learners. Each element of the list is a data.frame that contains hyperparameter values of base learners. The names of the list elements specifies the base learners and are passed to caret functions. See details and examples
Metamodel: A strings specifying the meta learner. This strings is passed to caret.
core: Number of cores for parallel processing
cross_validation: A parameter to specify whether to perform cross-validation. Set to TRUE to enable cross-validation or to FALSE to perform random sampling.
use_X: A logical indicating whether the meta-learner uses the original features X along with the base model predictions. If TRUE, it uses both X and the predictions; if FALSE, it uses only the predictions.
TrainEachFold: A logical indicating whether the meta learner learns using the predicted values of the base models at each cross-validation fold/random sample or not. If TRUE, the meta learners learns Nfold/num_sample times using the values predicted by the base models at each fold/sample. If FALSE, the meta learner learns once by pooling the predicted values of the base models of all folds/samples.
Nfold: Number of folds for cross-validation. Required when cross_validation is TRUE.
num_sample: The number of samples of random sampling, applicable when cross_validation is set to FALSE.
proportion: A parameter specifying the proportion of samples to be sampled when cross_validation is set to FALSE.

Author

Taichi Nukui, Tomohiro Ishibashi, Akio Onogi

Details

Stacking by this package consists of the following 2 steps.

(1) Each base learner is trained. The training method can be chosen using the cross_validation argument: If cross_validation is TRUE: The function performs Nfold cross-validation for each base learner. If cross_validation is FALSE: The function trains each base learner using random sampling. The number of samples (num_sample) or the proportion of the data (proportion) can be specified to control the sampling process. (2) Using the predicted values of each learner as the explanatory variables, the meta learner is trained. Steps (1) and (2) are conducted by train_basemodel and train_metamodel, respectively. Another function stacking_train conducts both steps at once by calling these functions (train_basemodel and train_metamodel).

Training of the meta learner can be modified by two arguments, TrainEachFold and use_X. TrainEachFold specifies whether the meta learner is trained for each fold or random sample individually, or once by pooling or combining all predicted values. use_X specifies whether the meta learner is trained with both the original features X and the base model predictions, or with only the base model predictions.

Base learners are specified by Method. For example,
Method = list(glmnet = data.frame(alpha = 0, lambda = 5), pls = data.frame(ncomp = 10))
indicating that the first base learner is glmnet and the second is pls with the corresponding hyperparameters.

When the data.frames have multiple rows as
Method = list(glmnet = data.frame(alpha = c(0, 1), lambda = c(5, 10)))
All combinations of hyperparameter values are automatically created as
[alpha, lambda] = [0, 5], [0, 10], [1, 5], [1, 10]
Thus, in total 5 base learners (4 glmnet and 1 pls) are created.

When the number of candidate values differ among hyperparameters, use NA as
Method = list(glmnet = data.frame(alpha = c(0, 0.5, 1), lambda = c(5, 10, NA)))
resulting in 6 combinations of
[alpha, lambda] = [0, 5], [0, 10], [0.5, 5], [0.5, 10], [1, 5], [1, 10]

When a hyperparameter includes only NA as
Method = list(glmnet = data.frame(alpha = c(0, 0.5, 1), lambda = c(NA, NA, NA)), pls = data.frame(ncomp = NA))
lambda of glmnet and ncomp of pls are automatically tuned by caret. However, it is notable that tuning is conducted assuming that all hyperparameters are unknown, and thus, the tuned lambea in the above example is not the value tuned under the given alpha values (0, 0.5, or 1).

Hyperparameters of meta learners are automatically tuned by caret.

The base and meta learners can be chosen from the methods implemented in caret. The choosable methods can be seen at https://topepo.github.io/caret/available-models.html or using names(getModelInfo()) after loading caret.

Examples

Run this code

#Create a toy example
##Number of training samples
N1 <- 100

##Number of explanatory variables
P <- 200

##Create X of training data
X1 <- matrix(rnorm(N1 * P), nrow = N1, ncol = P)
colnames(X1) <- 1:P#column names are required by caret

##Assume that the first 10 variables have effects on Y
##Then add noise with rnorm
Y1 <- rowSums(X1[, 1:10]) + rnorm(N1)

##Test data
N2 <- 100
X2 <- matrix(rnorm(N2 * P), nrow = N2, ncol = P)
colnames(X2) <- 1:P#Ignored (not required)
Y2 <- rowSums(X2[, 1:10])

#Specify base learners
Method <- list(glmnet = data.frame(alpha = c(0.5, 0.8), lambda = c(0.1, 1)),
               pls = data.frame(ncomp = 5))
#=>This specifies five base learners.
##1. glmnet with alpha = 0.5 and lambda = 0.1
##2. glmnet with alpha = 0.5 and lambda = 1
##3. glmnet with alpha = 0.8 and lambda = 0.1
##4. glmnet with alpha = 0.8 and lambda = 1
##5. pls with ncomp = 5

#The followings are the training and prediction processes
#If glmnet and pls are not installed, please install them in advance.
#Please remove #s before execution

#stacking_train_result <- stacking_train(X = X1,
#                                        Y = Y1,
#                                        Method = Method,
#                                        Metamodel = "lm",
#                                        core = 2,
#                                        cross_validation = TRUE,
#                                        use_X = FALSE,
#                                        TrainEachFold = TRUE,
#                                        Nfold = 5)

#For random sampling, set cross_validation = FALSE and
#specify the number of samples and the sampling proportion
#using num_sample and proportion, respectively.
#To include the original features X when training the meta-model, set use_X = TRUE.
#When use_X is TRUE, simple linear regressions cannot be used
#as the meta learner because of rank deficient.
#The following code reflects the changes made to the relevant arguments.
#stacking_train_result <- stacking_train(X = X1,
#                                        Y = Y1,
#                                        Method = Method,
#                                        Metamodel = "glmnet",
#                                        core = 2,
#                                        cross_validation = FALSE,
#                                        use_X = TRUE,
#                                        TrainEachFold = TRUE,
#                                        num_sample = 5,
#                                        proportion = 0.8)

#Prediction
#result <- stacking_predict(newX = X2, stacking_train_result)
#plot(Y2, result)

#Training using train_basemodel and train_metamodel
#base <- train_basemodel(X = X1,
#                        Y = Y1,
#                        Method = Method,
#                        core = 2,
#                        cross_validation = TRUE,
#                        Nfold = 5)
#meta <- train_metamodel(X,
#                        base,
#                        which_to_use = 1:5,
#                        Metamodel = "lm",
#                        use_X = FALSE,
#                        TrainEachFold = TRUE)
#stacking_train_result <- list(base = base, meta = meta)
#=>The list should have elements named as base and meta to be used in stacking_predict

#Prediction
#result <- stacking_predict(newX = X2, stacking_train_result)
#plot(Y2, result)

#In the simulations of the reference paper (Nukui and Onogi 2023),
#we use 48 base learners as
Method <- list(ranger = data.frame(mtry = c(10, 100, 200),
                                   splitrule = c("extratrees", NA, NA),
                                   min.node.size = c(1, 5, 10)),
               xgbTree = data.frame(colsample_bytree = c(0.6, 0.8),
                                    subsample = c(0.5, 1),
                                    nrounds = c(50, 150),
                                    max_depth = c(6, NA),
                                    eta = c(0.3, NA),
                                    gamma = c(0, NA),
                                    min_child_weight = c(1, NA)),
               gbm = data.frame(interaction.depth = c(1, 3, 5),
                                n.trees = c(50, 100, 150),
                                shrinkage = c(0.1, NA, NA),
                                n.minobsinnode = c(10, NA, NA)),
               svmPoly = data.frame(C = c(0.25, 0.5, 1),
                                    scale = c(0.001, 0.01, 0.1),
                                    degree = c(1, NA, NA)),
               glmnet = data.frame(alpha = c(1, 0.8, 0.6, 0.4, 0.2, 0),
                                   lambda = rep(NA, 6)),
               pls = data.frame(ncomp = seq(2, 70, 10))
)
#mtry of ranger and ncomp of pls should be arranged according to data size.

#In the classification example of the reference paper, for RNA features, we used
Method <- list(ranger = data.frame(mtry = c(10, 100, 500),
                                   splitrule = c("extratrees", NA, NA),
                                   min.node.size = c(1, 5, 10)),
               xgbTree = data.frame(colsample_bytree = c(0.6, 0.8),
                                    subsample = c(0.5, 1),
                                    nrounds = c(50, 150),
                                    max_depth = c(6, NA),
                                    eta = c(0.3, NA),
                                    gamma = c(0, NA),
                                    min_child_weight = c(1, NA)),
               gbm = data.frame(interaction.depth = c(1, 3, 5),
                                n.trees = c(50, 100, 150),
                                shrinkage = c(0.1, NA, NA),
                                n.minobsinnode = c(10, NA, NA)),
               svmPoly = data.frame(C = c(0.25, 0.5, 1),
                                    scale = c(0.001, 0.01, 0.1),
                                    degree = c(1, NA, NA)),
               glmnet = data.frame(alpha = c(1, 0.8, 0.6, 0.4, 0.2, 0),
                                   lambda = rep(NA, 6)),
               pls = data.frame(ncomp = seq(2, 70, 10))
)
#svmRadial was replaced by svmPoly
#These base learners may be a good starting point.

Run the code above in your browser using DataLab