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dnnet

Basic feed-forward, fully-connected neural networks, and bootstrap aggregating (bagging).

A simulation for continuous outcome with Gaussian error

suppressMessages(library(deepTL))
library(MASS)
set.seed(1234)  
n <- 500
p <- 20
n_test <- 10000

x <- mvrnorm(n, rep(0, p), diag(p))
y <- x[, 1] + log(1 + (x[, 3] + 1)**2 + x[, 2]**2*2)*2 + x[, 4]*x[, 5] + rnorm(n)

x_test <- mvrnorm(n_test, rep(0, p), diag(p))
y_test <- x_test[, 1] + log(1 + (x_test[, 3] + 1)**2 + x_test[, 2]**2*2)*2 + x_test[, 4]*x_test[, 5] + rnorm(n)

Hyper-parameters

esCtrl <- list(n.hidden = c(50, 40, 30, 20), activate = "relu",
               l1.reg = 10**-4, early.stop.det = 1000, n.batch = 50,
               n.epoch = 100, learning.rate.adaptive = "adam", plot = FALSE)
dnn_obj <- importDnnet(x = x, y = y)
dat_spl <- splitDnnet(dnn_obj, 0.8)

dnnet

dnn_mod <- do.call("dnnet", c(list("train" = dat_spl$train, "validate" = dat_spl$valid), esCtrl))
dnn_pred <- predict(dnn_mod, x_test)

Bootstrap aggregating (Bagging)

dnn_en_mod <- ensemble_dnnet(dnn_obj, 10, esCtrl, verbose = FALSE)
dnn_en_pred <- predict(dnn_en_mod, x_test)

More DNNs in Bagging

dnn_en_100_mod <- ensemble_dnnet(dnn_obj, 100, esCtrl, best.opti = FALSE, verbose = FALSE)
dnn_en_100_pred <- predict(dnn_en_100_mod, x_test)

Bootstrap aggregating (Bagging) with optimal subset of DNNs (details in Mi et al. (2019))

dnn_en_opt_mod <- ensemble_dnnet(dnn_obj, 100, esCtrl, verbose = FALSE)
dnn_en_opt_pred <- predict(dnn_en_opt_mod, x_test)

Performances

data.frame(dnn = c("A single DNN", "Bagging of 10 DNNs", "Bagging of 100 DNNs", "Bagging of 100 DNNs with optimal subset"), 
           mse = c(mean((dnn_pred - y_test)**2), mean((dnn_en_pred - y_test)**2), 
                   mean((dnn_en_100_pred - y_test)**2), mean((dnn_en_opt_pred - y_test)**2)))
##                                       dnn      mse
## 1                            A single DNN 2.395480
## 2                      Bagging of 10 DNNs 2.037568
## 3                     Bagging of 100 DNNs 1.913064
## 4 Bagging of 100 DNNs with optimal subset 1.834117

References

Mi, X., Zou, F., and Zhu, R. (2019), “Bagging and deep learning in optimal individualized treatment rules,” Biometrics, Wiley Online Library, 75, 674–684.