1 Neural Networks Models

Neural Networks method (in-sample and out-of-sample performance measure) is illustrated here. The package neuralnet and nnet are used for this purpose.

  1. neuralnet package

The arguments:

  1. nnet package

The arguments:

1.1 Regression

For regression problems, we use neuralnet and add linear.output = TRUE when training model. In practices, the normalization and standardization for predictors and response variable are recommended before training a neural network model. Otherwise, your neural network model may not be able to converge as the following case:

nn <- neuralnet(f, data=train_Boston, hidden=c(5), linear.output=T)
# Algorithm did not converge in 1 of 1 repetition(s) within the stepmax.

I chose to use the min-max method and scale the data in the interval \([0,1]\). Other reference online: [1]


maxs <- apply(Boston, 2, max) 
mins <- apply(Boston, 2, min)

scaled <- as.data.frame(scale(Boston, center = mins, scale = maxs - mins))
index <- sample(1:nrow(Boston),round(0.9*nrow(Boston)))

train_Boston <- scaled[index,]
test_Boston <- scaled[-index,]
  • Plot the fitted neural network model:
f <- as.formula("medv ~ .")

# Or you can do the following way that is general and will ease your pain to manually update formula:
# resp_name <- names(train_Boston)
# f <- as.formula(paste("medv ~", paste(resp_name[!resp_name %in% "medv"], collapse = " + ")))

nn <- neuralnet(f,data=train_Boston, hidden=c(5,3), linear.output=T)

  • Calculate the MSPE of the above neural network model:
pr_nn <- compute(nn, test_Boston[,1:13])

# recover the predicted value back to the original response scale 
pr_nn_org <- pr_nn$net.result*(max(Boston$medv)-min(Boston$medv))+min(Boston$medv)
test_r <- (test_Boston$medv)*(max(Boston$medv)-min(Boston$medv))+min(Boston$medv)

# MSPE of testing set
MSPE_nn <- sum((test_r - pr_nn_org)^2)/nrow(test_Boston)
## [1] 7.435858

Remark: If the testing set is not available in practice, you may try to scale the data based on the training set only. Then the recovering process should be changed accordingly.

1.2 Classification on Bankruptcy dataset

For classification problems, we use neuralnet and add linear.output = FALSE when training model. A common practice is again to scale/standardize predictor variables.

Bank_data_scaled <- Bank_data <- 
  read.csv(file = "https://xiaoruizhu.github.io/Data-Mining-R/lecture/data/bankruptcy.csv", header=T)
# summary(Bank_data)
maxs <- apply(Bank_data[,-c(1:3)], 2, max)
mins <- apply(Bank_data[,-c(1:3)], 2, min)
Bank_data_scaled[,-c(1:3)] <- as.data.frame(scale(Bank_data[,-c(1:3)], center = mins, scale = maxs - mins))

sample_index <- sample(nrow(Bank_data_scaled),nrow(Bank_data_scaled)*0.70)
Bank_train <- Bank_data_scaled[sample_index,]
Bank_test <- Bank_data_scaled[-sample_index,]

f <- as.formula("DLRSN ~ R1 + R2 + R3 + R4 + R5 + R6 + R7 + R8 + R9 + R10")
# You may need to specific the formula rather than 
Bank_nn <- neuralnet(f, data=Bank_train, hidden=c(3), algorithm = 'rprop+', linear.output=F, likelihood = T)