HessianMLP function

Sensitivity of MLP models

Function for evaluating the sensitivities of the inputs variables in a mlp model

HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  ...
)

## Default S3 method:
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  trData,
  actfunc = NULL,
  deractfunc = NULL,
  der2actfunc = NULL,
  preProc = NULL,
  terms = NULL,
  output_name = NULL,
  ...
)

## S3 method for class 'train'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  ...
)

## S3 method for class 'H2OMultinomialModel'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  ...
)

## S3 method for class 'H2ORegressionModel'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  ...
)

## S3 method for class 'list'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  trData,
  actfunc,
  ...
)

## S3 method for class 'mlp'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  trData,
  preProc = NULL,
  terms = NULL,
  ...
)

## S3 method for class 'nn'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  preProc = NULL,
  terms = NULL,
  ...
)

## S3 method for class 'nnet'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  trData,
  preProc = NULL,
  terms = NULL,
  ...
)

## S3 method for class 'nnetar'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  ...
)

## S3 method for class 'numeric'
HessianMLP(
  MLP.fit,
  .returnSens = TRUE,
  plot = TRUE,
  .rawSens = FALSE,
  sens_origin_layer = 1,
  sens_end_layer = "last",
  sens_origin_input = TRUE,
  sens_end_input = FALSE,
  trData,
  actfunc = NULL,
  preProc = NULL,
  terms = NULL,
  ...
)

Arguments

• MLP.fit: fitted neural network model
• .returnSens: DEPRECATED
• plot: logical whether or not to plot the analysis. By default is TRUE.
• .rawSens: DEPRECATED
• sens_origin_layer: numeric specifies the layer of neurons with respect to which the derivative must be calculated. The input layer is specified by 1 (default).
• sens_end_layer: numeric specifies the layer of neurons of which the derivative is calculated. It may also be 'last' to specify the output layer (default).
• sens_origin_input: logical specifies if the derivative must be calculated with respect to the inputs (TRUE) or output (FALSE) of the sens_origin_layer layer of the model. By default is TRUE.
• sens_end_input: logical specifies if the derivative calculated is of the output (FALSE) or from the input (TRUE) of the sens_end_layer layer of the model. By default is FALSE.
• ...: additional arguments passed to or from other methods
• trData: data.frame containing the data to evaluate the sensitivity of the model
• actfunc: character vector indicating the activation function of each neurons layer.
• deractfunc: character vector indicating the derivative of the activation function of each neurons layer.
• der2actfunc: character vector indicating the second derivative of the activation function of each neurons layer.
• preProc: preProcess structure applied to the training data. See also preProcess
• terms: function applied to the training data to create factors. See also train
• output_name: character name of the output variable in order to avoid changing the name of the output variable in trData to '.outcome'

Returns

SensMLP object with the sensitivity metrics and sensitivities of the MLP model passed to the function.

Details

In case of using an input of class factor and a package which need to enter the input data as matrix, the dummies must be created before training the neural network.

After that, the training data must be given to the function using the trData argument.

Plots

• Plot 1: colorful plot with the classification of the classes in a 2D map
• Plot 2: b/w plot with probability of the chosen class in a 2D map
• Plot 3: plot with the stats::predictions of the data provided

Examples

## Load data -------------------------------------------------------------------
data("DAILY_DEMAND_TR")
fdata <- DAILY_DEMAND_TR
## Parameters of the NNET ------------------------------------------------------
hidden_neurons <- 5
iters <- 100
decay <- 0.1

################################################################################
#########################  REGRESSION NNET #####################################
################################################################################
## Regression dataframe --------------------------------------------------------
# Scale the data
fdata.Reg.tr <- fdata[,2:ncol(fdata)]
fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10
fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000

# Normalize the data for some models
preProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))
nntrData <- predict(preProc, fdata.Reg.tr)

#' ## TRAIN nnet NNET --------------------------------------------------------
# Create a formula to train NNET
form <- paste(names(fdata.Reg.tr)[2:ncol(fdata.Reg.tr)], collapse = " + ")
form <- formula(paste(names(fdata.Reg.tr)[1], form, sep = " ~ "))

set.seed(150)
nnetmod <- nnet::nnet(form,
                      data = nntrData,
                      linear.output = TRUE,
                      size = hidden_neurons,
                      decay = decay,
                      maxit = iters)
# Try HessianMLP
NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)

# Try HessianMLP to calculate sensitivities with respect to output of hidden neurones
NeuralSens::HessianMLP(nnetmod, trData = nntrData,
                             sens_origin_layer = 2,
                             sens_end_layer = "last",
                             sens_origin_input = FALSE,
                             sens_end_input = FALSE)
## Train caret NNET ------------------------------------------------------------
# Create trainControl
ctrl_tune <- caret::trainControl(method = "boot",
                                 savePredictions = FALSE,
                                 summaryFunction = caret::defaultSummary)
set.seed(150) #For replication
caretmod <- caret::train(form = DEM~.,
                              data = fdata.Reg.tr,
                              method = "nnet",
                              linout = TRUE,
                              tuneGrid = data.frame(size = 3,
                                                    decay = decay),
                              maxit = iters,
                              preProcess = c("center","scale"),
                              trControl = ctrl_tune,
                              metric = "RMSE")

# Try HessianMLP
NeuralSens::HessianMLP(caretmod)

## Train h2o NNET --------------------------------------------------------------
# Create a cluster with 4 available cores
h2o::h2o.init(ip = "localhost",
              nthreads = 4)

# Reset the cluster
h2o::h2o.removeAll()
fdata_h2o <- h2o::as.h2o(x = fdata.Reg.tr, destination_frame = "fdata_h2o")

set.seed(150)
h2omod <-h2o:: h2o.deeplearning(x = names(fdata.Reg.tr)[2:ncol(fdata.Reg.tr)],
                                     y = names(fdata.Reg.tr)[1],
                                     distribution = "AUTO",
                                     training_frame = fdata_h2o,
                                     standardize = TRUE,
                                     activation = "Tanh",
                                     hidden = c(hidden_neurons),
                                     stopping_rounds = 0,
                                     epochs = iters,
                                     seed = 150,
                                     model_id = "nnet_h2o",
                                     adaptive_rate = FALSE,
                                     rate_decay = decay,
                                     export_weights_and_biases = TRUE)

# Try HessianMLP
NeuralSens::HessianMLP(h2omod)

# Turn off the cluster
h2o::h2o.shutdown(prompt = FALSE)
rm(fdata_h2o)

## Train RSNNS NNET ------------------------------------------------------------
# Normalize data using RSNNS algorithms
trData <- as.data.frame(RSNNS::normalizeData(fdata.Reg.tr))
names(trData) <- names(fdata.Reg.tr)
set.seed(150)
RSNNSmod <-RSNNS::mlp(x = trData[,2:ncol(trData)],
                           y = trData[,1],
                           size = hidden_neurons,
                           linOut = TRUE,
                           learnFuncParams=c(decay),
                           maxit=iters)

# Try HessianMLP
NeuralSens::HessianMLP(RSNNSmod, trData = trData, output_name = "DEM")

## USE DEFAULT METHOD ----------------------------------------------------------
NeuralSens::HessianMLP(caretmod$finalModel$wts,
                            trData = fdata.Reg.tr,
                            mlpstr = caretmod$finalModel$n,
                            coefnames = caretmod$coefnames,
                            actfun = c("linear","sigmoid","linear"),
                            output_name = "DEM")

################################################################################
#########################  CLASSIFICATION NNET #################################
################################################################################
## Regression dataframe --------------------------------------------------------
# Scale the data
fdata.Reg.cl <- fdata[,2:ncol(fdata)]
fdata.Reg.cl[,2:3] <- fdata.Reg.cl[,2:3]/10
fdata.Reg.cl[,1] <- fdata.Reg.cl[,1]/1000

# Normalize the data for some models
preProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))
nntrData <- predict(preProc, fdata.Reg.cl)

# Factorize the output
fdata.Reg.cl$DEM <- factor(round(fdata.Reg.cl$DEM, digits = 1))

# Normalize the data for some models
preProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))
nntrData <- predict(preProc, fdata.Reg.cl)

## Train caret NNET ------------------------------------------------------------
# Create trainControl
ctrl_tune <- caret::trainControl(method = "boot",
                                 savePredictions = FALSE,
                                 summaryFunction = caret::defaultSummary)
set.seed(150) #For replication
caretmod <- caret::train(form = DEM~.,
                                data = fdata.Reg.cl,
                                method = "nnet",
                                linout = FALSE,
                                tuneGrid = data.frame(size = hidden_neurons,
                                                      decay = decay),
                                maxit = iters,
                                preProcess = c("center","scale"),
                                trControl = ctrl_tune,
                                metric = "Accuracy")

# Try HessianMLP
NeuralSens::HessianMLP(caretmod)

## Train h2o NNET --------------------------------------------------------------
# Create local cluster with 4 available cores
h2o::h2o.init(ip = "localhost",
              nthreads = 4)

# Reset the cluster
h2o::h2o.removeAll()
fdata_h2o <- h2o::as.h2o(x = fdata.Reg.cl, destination_frame = "fdata_h2o")

set.seed(150)
h2omod <- h2o::h2o.deeplearning(x = names(fdata.Reg.cl)[2:ncol(fdata.Reg.cl)],
                                       y = names(fdata.Reg.cl)[1],
                                       distribution = "AUTO",
                                       training_frame = fdata_h2o,
                                       standardize = TRUE,
                                       activation = "Tanh",
                                       hidden = c(hidden_neurons),
                                       stopping_rounds = 0,
                                       epochs = iters,
                                       seed = 150,
                                       model_id = "nnet_h2o",
                                       adaptive_rate = FALSE,
                                       rate_decay = decay,
                                       export_weights_and_biases = TRUE)

# Try HessianMLP
NeuralSens::HessianMLP(h2omod)

# Apaga el cluster
h2o::h2o.shutdown(prompt = FALSE)
rm(fdata_h2o)

## TRAIN nnet NNET --------------------------------------------------------
# Create a formula to train NNET
form <- paste(names(fdata.Reg.tr)[2:ncol(fdata.Reg.tr)], collapse = " + ")
form <- formula(paste(names(fdata.Reg.tr)[1], form, sep = " ~ "))

set.seed(150)
nnetmod <- nnet::nnet(form,
                      data = nntrData,
                      linear.output = TRUE,
                      size = hidden_neurons,
                      decay = decay,
                      maxit = iters)
# Try HessianMLP
NeuralSens::HessianMLP(nnetmod, trData = nntrData)