Movatterモバイル変換

Version:

1.1.3

Title:

Sensitivity Analysis of Neural Networks

Description:

Analysis functions to quantify inputs importance in neural network models. Functions are available for calculating and plotting the inputs importance and obtaining the activation function of each neuron layer and its derivatives. The importance of a given input is defined as the distribution of the derivatives of the output with respect to that input in each training data point <doi:10.18637/jss.v102.i07>.

Author:

José Portela González [aut], Antonio Muñoz San Roque [aut], Jaime Pizarroso Gonzalo [aut, ctb, cre]

Maintainer:

Jaime Pizarroso Gonzalo <jpizarroso@comillas.edu>

Imports:

ggplot2, gridExtra, NeuralNetTools, reshape2, caret,fastDummies, stringr, Hmisc, ggforce, scales, ggnewscale,magrittr, ggrepel, ggbreak, dplyr

Suggests:

h2o, RSNNS, nnet, neuralnet, plotly, e1071

RoxygenNote:

7.3.1

NeedsCompilation:

URL:

https://github.com/JaiPizGon/NeuralSens

BugReports:

https://github.com/JaiPizGon/NeuralSens/issues

License:

GPL-2 |GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

LazyData:

true

Packaged:

2024-05-11 19:26:10 UTC; jpizarroso

Repository:

CRAN

Date/Publication:

2024-05-11 19:43:03 UTC

NeuralSens: Sensitivity Analysis of Neural Networks

Description

Visualization and analysis tools to aid in the interpretation ofneural network models.

Author(s)

Maintainer: Jaime Pizarroso Gonzalojpizarroso@comillas.edu [contributor]

Authors:

José Portela GonzálezJose.Portela@iit.comillas.edu
Antonio Muñoz San Roqueantonio.munoz@iit.comillas.edu

Activation function of neuron

Description

Evaluate activation function of a neuron

Usage

ActFunc(type = "sigmoid", ...)

Arguments

type

character name of the activation function

...

extra arguments needed to calculate the functions

Value

numeric output of the neuron

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

# Return the sigmoid activation function of a neuronActivationFunction <- ActFunc("sigmoid")# Return the tanh activation function of a neuronActivationFunction <- ActFunc("tanh")# Return the activation function of several layers of neuronsactfuncs <- c("linear","sigmoid","linear")ActivationFunctions <- sapply(actfuncs, ActFunc)

Sensitivity alpha-curve associated to MLP function

Description

Obtain sensitivity alpha-curves associated to MLP function obtained fromthe sensitivities returned bySensAnalysisMLP.

Usage

AlphaSensAnalysis(  sens,  tol = NULL,  max_alpha = 15,  curve_equal_origin = FALSE,  inp_var = NULL,  line_width = 1,  title = "Alpha curve of Lp norm values",  alpha_bar = 1,  kind = "line")

Arguments

sens

sensitivity object returned bySensAnalysisMLP

tol

difference between M_alpha and maximum sensitivity of the sensitivity of each input variable

max_alpha

maximum alpha value to analyze

curve_equal_origin

make all the curves begin at (1,0)

inp_var

character indicating which input variable to show in density plot. Only useful whenchoosing plot_type='raw' to show the density plot of one input variable. IfNULL, all variablesare plotted in density plot. By default isNULL.

line_width

int width of the line in the plot.

title

char title of the alpha-curves plot

alpha_bar

int alpha value to show as column plot.

kind

char select the type of plot: "line" or "bar"

Value

alpha-curves of the MLP function

Examples

mod <- RSNNS::mlp(simdata[, c("X1", "X2", "X3")], simdata[, "Y"],                 maxit = 1000, size = 15, linOut = TRUE)sens <- SensAnalysisMLP(mod, trData = simdata,                        output_name = "Y", plot = FALSE)AlphaSensAnalysis(sens)

Sensitivity alpha-curve associated to MLP function of an input variable

Description

Obtain sensitivity alpha-curve associated to MLP function obtained fromthe sensitivities returned bySensAnalysisMLP of an input variable.

Usage

AlphaSensCurve(sens, tol = NULL, max_alpha = 100)

Arguments

sens

raw sensitivities of the MLP output with respect to input variable.

tol

difference between M_alpha and maximum sensitivity of the sensitivity of each input variable

max_alpha

maximum alpha value to analyze

Value

alpha-curve of the MLP function

Examples

mod <- RSNNS::mlp(simdata[, c("X1", "X2", "X3")], simdata[, "Y"],                 maxit = 1000, size = 15, linOut = TRUE)sens <- SensAnalysisMLP(mod, trData = simdata,                        output_name = "Y", plot = FALSE)AlphaSensCurve(sens$raw_sens[[1]][,1])

Change significance of boot SensMLP Class

Description

For a SensMLP Class object, change the significance level of the statistical tests

Usage

ChangeBootAlpha(x, boot.alpha)

Arguments

x

SensMLP object created bySensAnalysisMLP

boot.alpha

float significance level

Value

SensMLP object with changed significance level. All boot relatedmetrics are changed

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000## TRAIN nnet NNET --------------------------------------------------------set.seed(150)nnetmod <- caret::train(DEM ~ .,                 data = fdata.Reg.tr,                 method = "nnet",                 tuneGrid = expand.grid(size = c(1), decay = c(0.01)),                 trControl = caret::trainControl(method="none"),                 preProcess = c('center', 'scale'),                 linout = FALSE,                 trace = FALSE,                 maxit = 300)# Try SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = fdata.Reg.tr,                                    plot = FALSE, boot.R=2, output_name='DEM')NeuralSens::ChangeBootAlpha(sens, boot.alpha=0.1)

Sensitivity analysis plot over time of the data

Description

Plot of sensitivity of the neural network output respectto the inputs over the time variable from the data provided

Usage

CombineSens(object, comb_type = "mean")

Arguments

object

SensMLP object generated bySensAnalysisMLPwith several outputs (classification MLP)

comb_type

Function to combine the matrixes of theraw_sens component ofobject.It can be "mean", "median" or "sqmean". It can also be a function to combine the rows of the matrixes

Value

SensMLP object with the sensitivities combined

Examples

fdata <- iris## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- paste(names(fdata)[1:ncol(fdata)-1], collapse = " + ")form <- formula(paste(names(fdata)[5], form, sep = " ~ "))set.seed(150)mod <- nnet::nnet(form,                  data = fdata,                  linear.output = TRUE,                  size = hidden_neurons,                  decay = decay,                  maxit = iters)# mod should be a neural network classification modelsens <- SensAnalysisMLP(mod, trData = fdata, output_name = 'Species')combinesens <- CombineSens(sens, "sqmean")

Plot sensitivities of a neural network model

Description

Function to plot the sensitivities created bySensAnalysisMLP.

Usage

ComputeHessMeasures(sens)

Arguments

sens

SensAnalysisMLP object created bySensAnalysisMLP.

Value

SensAnalysisMLP object with the sensitivities calculated

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)

Plot sensitivities of a neural network model

Description

Function to plot the sensitivities created bySensAnalysisMLP.

Usage

ComputeSensMeasures(sens)

Arguments

sens

SensAnalysisMLP object created bySensAnalysisMLP.

Value

SensAnalysisMLP object with the sensitivities calculated

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)

Data frame with 4 variables

Description

Training dataset with values of temperature and working day to predict electrical demand

Format

A data frame with 1980 rows and 4 variables:

DATE: date of the measure
DEM: electrical demand
WD: Working Day: index which express how much work is made that day
TEMP: weather temperature

Author(s)

Jose Portela Gonzalez

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Data frame with 3 variables

Description

Validation dataset with values of temperature and working day to predict electrical demand

Format

A data frame with 7 rows and 3 variables:

DATE: date of the measure
WD: Working Day: index which express how much work is made that day
TEMP: weather temperature

Author(s)

Jose Portela Gonzalez

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Second derivative of activation function of neuron

Description

Evaluate second derivative of activation function of a neuron

Usage

Der2ActFunc(type = "sigmoid", ...)

Arguments

type

character name of the activation function

...

extra arguments needed to calculate the functions

Value

numeric output of the neuron

Examples

# Return derivative of the sigmoid activation function of a neuronActivationFunction <- Der2ActFunc("sigmoid")# Return derivative of the tanh activation function of a neuronActivationFunction <- Der2ActFunc("tanh")# Return derivative of the activation function of several layers of neuronsactfuncs <- c("linear","sigmoid","linear")ActivationFunctions <- sapply(actfuncs, Der2ActFunc)

Third derivative of activation function of neuron

Description

Evaluate third derivative of activation function of a neuron

Usage

Der3ActFunc(type = "sigmoid", ...)

Arguments

type

character name of the activation function

...

extra arguments needed to calculate the functions

Value

numeric output of the neuron

Examples

# Return derivative of the sigmoid activation function of a neuronActivationFunction <- Der3ActFunc("sigmoid")# Return derivative of the tanh activation function of a neuronActivationFunction <- Der3ActFunc("tanh")# Return derivative of the activation function of several layers of neuronsactfuncs <- c("linear","sigmoid","linear")ActivationFunctions <- sapply(actfuncs, Der3ActFunc)

Derivative of activation function of neuron

Description

Evaluate derivative of activation function of a neuron

Usage

DerActFunc(type = "sigmoid", ...)

Arguments

type

character name of the activation function

...

extra arguments needed to calculate the functions

Value

numeric output of the neuron

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

# Return derivative of the sigmoid activation function of a neuronActivationFunction <- DerActFunc("sigmoid")# Return derivative of the tanh activation function of a neuronActivationFunction <- DerActFunc("tanh")# Return derivative of the activation function of several layers of neuronsactfuncs <- c("linear","sigmoid","linear")ActivationFunctions <- sapply(actfuncs, DerActFunc)

Second derivatives 3D scatter or surface plot against input values

Description

3D Plot of second derivatives of the neural network output respectto the inputs. This function useplotly instead ofggplot2 toachieve better visualization

Usage

HessDotPlot(  object,  fdata = NULL,  input_vars = "all",  input_vars2 = "all",  output_vars = "all",  surface = FALSE,  grid = FALSE,  color = NULL,  ...)

Arguments

object

fitted neural network model orarray containing the rawsecond derivatives from the functionHessianMLP

fdata

data.frame containing the data to evaluate the second derivatives of the model.

input_vars

character vector with the variables to create the scatter plot in x-axis. If"all",then scatter plots are created for all the input variables infdata.

input_vars2

character vector with the variables to create the scatter plot in y-axis. If"all",then scatter plots are created for all the input variables infdata.

output_vars

character vector with the variables to create the scatter plot. If"all",then scatter plots are created for all the output variables infdata.

surface

logical ifTRUE, a 3D surface is created instead of 3D scatter plot(only for combinations of different inputs)

grid

logical. IfTRUE, plots created are show together usingarrangeGrob.It does not work on Windows platforms due to bugs inplotly library.

color

character specifying the name of anumeric variable offdata to color the 3D scatter plot.

...

further arguments that should be passed toHessianMLP function

Value

list of 3Dgeom_point plots for the inputs variables representing thesensitivity of each output respect to the inputs

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessDotPlotNeuralSens::HessDotPlot(nnetmod, fdata = nntrData, surface = TRUE, color = "WD")

Feature sensitivity plot

Description

Show the distribution of the sensitivities of the outputingeom_sina() plot which color depends on the input values

Usage

HessFeaturePlot(object, fdata = NULL, ...)

Arguments

object

fitted neural network model orarray containing the rawsensitivities from the functionSensAnalysisMLP

fdata

data.frame containing the data to evaluate the sensitivity of the model.Not needed if the raw sensitivities has been passed asobject

...

further arguments that should be passed toSensAnalysisMLP function

Value

list of Feature sensitivity plot as described inhttps://www.r-bloggers.com/2019/03/a-gentle-introduction-to-shap-values-in-r/

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPhess <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)NeuralSens::HessFeaturePlot(hess)

Constructor of the HessMLP Class

Description

Create an object of HessMLP class

Usage

HessMLP(  sens = list(),  raw_sens = list(),  mlp_struct = numeric(),  trData = data.frame(),  coefnames = character(),  output_name = character())

Arguments

sens

list of sensitivity measures, onelist per output neuron

raw_sens

list of sensitivities, onearray per output neuron

mlp_struct

numeric vector describing the structur of the MLP model

trData

data.frame with the data used to calculate the sensitivities

coefnames

character vector with the name of the predictor(s)

output_name

character vector with the name of the output(s)

Value

HessMLP object

Convert a HessMLP to a SensMLP object

Description

Auxiliary function to turn a HessMLP object to a SensMLP object in order to use the plot-related functionsassociated with SensMLP

Usage

HessToSensMLP(x)

Arguments

x

HessMLP object

Value

SensMLP object

Sensitivity of MLP models

Description

Function for evaluating the sensitivities of the inputsvariables in a mlp model

Usage

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 isTRUE.

.rawSens

DEPRECATED

sens_origin_layer

numeric specifies the layer of neurons withrespect to which the derivative must be calculated. The input layer isspecified by 1 (default).

sens_end_layer

numeric specifies the layer of neurons of whichthe derivative is calculated. It may also be 'last' to specify the outputlayer (default).

sens_origin_input

logical specifies if the derivative must becalculated with respect to the inputs (TRUE) or output(FALSE) of thesens_origin_layer layer of the model. Bydefault isTRUE.

sens_end_input

logical specifies if the derivative calculatedis of the output (FALSE) or from the input (TRUE) of thesens_end_layer layer of the model. By default isFALSE.

...

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 eachneurons layer.

deractfunc

character vector indicating the derivative of the activationfunction of each neurons layer.

der2actfunc

character vector indicating the second derivative of the activationfunction of each neurons layer.

preProc

preProcess structure applied to the training data. See alsopreProcess

terms

function applied to the training data to create factors. Seealsotrain

output_name

character name of the output variable in order toavoid changing the name of the output variable intrData to'.outcome'

Details

In case of using an input of classfactor and a package whichneed to enter the input data as matrix, the dummies must be created beforetraining the neural network.

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

Value

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

Plots

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

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 100decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPNeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)# Try HessianMLP to calculate sensitivities with respect to output of hidden neuronesNeuralSens::HessianMLP(nnetmod, trData = nntrData,                             sens_origin_layer = 2,                             sens_end_layer = "last",                             sens_origin_input = FALSE,                             sens_end_input = FALSE)## Train caret NNET ------------------------------------------------------------# Create trainControlctrl_tune <- caret::trainControl(method = "boot",                                 savePredictions = FALSE,                                 summaryFunction = caret::defaultSummary)set.seed(150) #For replicationcaretmod <- 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 HessianMLPNeuralSens::HessianMLP(caretmod)## Train h2o NNET --------------------------------------------------------------# Create a cluster with 4 available coresh2o::h2o.init(ip = "localhost",              nthreads = 4)# Reset the clusterh2o::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 HessianMLPNeuralSens::HessianMLP(h2omod)# Turn off the clusterh2o::h2o.shutdown(prompt = FALSE)rm(fdata_h2o)## Train RSNNS NNET ------------------------------------------------------------# Normalize data using RSNNS algorithmstrData <- 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 HessianMLPNeuralSens::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$coefnames,                            actfun = c("linear","sigmoid","linear"),                            output_name = "DEM")#########################################################################################################  CLASSIFICATION NNET ################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.cl <- fdata[,2:ncol(fdata)]fdata.Reg.cl[,2:3] <- fdata.Reg.cl[,2:3]/10fdata.Reg.cl[,1] <- fdata.Reg.cl[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.cl)# Factorize the outputfdata.Reg.cl$DEM <- factor(round(fdata.Reg.cl$DEM, digits = 1))# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.cl)## Train caret NNET ------------------------------------------------------------# Create trainControlctrl_tune <- caret::trainControl(method = "boot",                                 savePredictions = FALSE,                                 summaryFunction = caret::defaultSummary)set.seed(150) #For replicationcaretmod <- 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 HessianMLPNeuralSens::HessianMLP(caretmod)## Train h2o NNET --------------------------------------------------------------# Create local cluster with 4 available coresh2o::h2o.init(ip = "localhost",              nthreads = 4)# Reset the clusterh2o::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 HessianMLPNeuralSens::HessianMLP(h2omod)# Apaga el clusterh2o::h2o.shutdown(prompt = FALSE)rm(fdata_h2o)## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPNeuralSens::HessianMLP(nnetmod, trData = nntrData)

Neural network structure sensitivity plot

Description

Plot a neural interpretation diagram colored by sensitivitiesof the model

Usage

PlotSensMLP(  MLP.fit,  metric = "mean",  sens_neg_col = "red",  sens_pos_col = "blue",  ...)

Arguments

MLP.fit

fitted neural network model

metric

metric to plot in the NID. It can be "mean" (default), "median or "sqmean".It can be any metric to combine the raw sensitivities

sens_neg_col

character string indicating color of negative sensitivitymeasure, default 'red'. The same is passed to argumentneg_col ofplotnet

sens_pos_col

character string indicating color of positive sensitivitymeasure, default 'blue'. The same is passed to argumentpos_col ofplotnet

...

additional arguments passed toplotnet and/orSensAnalysisMLP

Value

A graphics object

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 100decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPNeuralSens::PlotSensMLP(nnetmod, trData = nntrData)

Sensitivity of MLP models

Description

Function for evaluating the sensitivities of the inputsvariables in a mlp model

Usage

SensAnalysisMLP(  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:SensAnalysisMLP(  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,  preProc = NULL,  terms = NULL,  output_name = NULL,  ...)## S3 method for class 'train'SensAnalysisMLP(  MLP.fit,  .returnSens = TRUE,  plot = TRUE,  .rawSens = FALSE,  sens_origin_layer = 1,  sens_end_layer = "last",  sens_origin_input = TRUE,  sens_end_input = FALSE,  boot.R = NULL,  boot.seed = 1,  boot.alpha = 0.05,  ...)## S3 method for class 'H2OMultinomialModel'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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'SensAnalysisMLP(  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 isTRUE.

.rawSens

DEPRECATED

sens_origin_layer

numeric specifies the layer of neurons withrespect to which the derivative must be calculated. The input layer isspecified by 1 (default).

sens_end_layer

numeric specifies the layer of neurons of whichthe derivative is calculated. It may also be 'last' to specify the outputlayer (default).

sens_origin_input

logical specifies if the derivative must becalculated with respect to the inputs (TRUE) or output(FALSE) of thesens_origin_layer layer of the model. Bydefault isTRUE.

sens_end_input

logical specifies if the derivative calculatedis of the output (FALSE) or from the input (TRUE) of thesens_end_layer layer of the model. By default isFALSE.

...

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 eachneurons layer.

deractfunc

character vector indicating the derivative of the activationfunction of each neurons layer.

preProc

preProcess structure applied to the training data. See alsopreProcess

terms

function applied to the training data to create factors. Seealsotrain

output_name

character name of the output variable in order toavoid changing the name of the output variable intrData to'.outcome'

boot.R

int Number of bootstrap samples to calculate. Usedto detect significant inputs and significant non-linearities. Onlyavailable fortrain objects. Defaults toNULL.

boot.seed

int Seed of bootstrap evaluations.

boot.alpha

float Significance level of statistical test.

Details

In case of using an input of classfactor and a package whichneed to enter the input data as matrix, the dummies must be created beforetraining the neural network.

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

Value

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

Plots

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

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 100decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData)# Try SensAnalysisMLP to calculate sensitivities with respect to output of hidden neuronesNeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData,                             sens_origin_layer = 2,                             sens_end_layer = "last",                             sens_origin_input = FALSE,                             sens_end_input = FALSE)## Train caret NNET ------------------------------------------------------------# Create trainControlctrl_tune <- caret::trainControl(method = "boot",                                 savePredictions = FALSE,                                 summaryFunction = caret::defaultSummary)set.seed(150) #For replicationcaretmod <- 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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(caretmod)## Train h2o NNET --------------------------------------------------------------# Create a cluster with 4 available coresh2o::h2o.init(ip = "localhost",              nthreads = 4)# Reset the clusterh2o::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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(h2omod)# Turn off the clusterh2o::h2o.shutdown(prompt = FALSE)rm(fdata_h2o)## Train RSNNS NNET ------------------------------------------------------------# Normalize data using RSNNS algorithmstrData <- 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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(RSNNSmod, trData = trData, output_name = "DEM")## USE DEFAULT METHOD ----------------------------------------------------------NeuralSens::SensAnalysisMLP(caretmod$finalModel$wts,                            trData = fdata.Reg.tr,                            mlpstr = caretmod$finalModel$n,                            coefnames = caretmod$coefnames,                            actfun = c("linear","sigmoid","linear"),                            output_name = "DEM")#########################################################################################################  CLASSIFICATION NNET ################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.cl <- fdata[,2:ncol(fdata)]fdata.Reg.cl[,2:3] <- fdata.Reg.cl[,2:3]/10fdata.Reg.cl[,1] <- fdata.Reg.cl[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.cl)# Factorize the outputfdata.Reg.cl$DEM <- factor(round(fdata.Reg.cl$DEM, digits = 1))# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.cl, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.cl)## Train caret NNET ------------------------------------------------------------# Create trainControlctrl_tune <- caret::trainControl(method = "boot",                                 savePredictions = FALSE,                                 summaryFunction = caret::defaultSummary)set.seed(150) #For replicationcaretmod <- 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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(caretmod)## Train h2o NNET --------------------------------------------------------------# Create local cluster with 4 available coresh2o::h2o.init(ip = "localhost",              nthreads = 4)# Reset the clusterh2o::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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(h2omod)# Apaga el clusterh2o::h2o.shutdown(prompt = FALSE)rm(fdata_h2o)## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPNeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData)

Sensitivity scatter plot against input values

Description

Plot of sensitivities of the neural network output respectto the inputs

Usage

SensDotPlot(  object,  fdata = NULL,  input_vars = "all",  output_vars = "all",  smooth = FALSE,  nspline = NULL,  color = NULL,  grid = FALSE,  ...)

Arguments

object

fitted neural network model orarray containing the rawsensitivities from the functionSensAnalysisMLP

fdata

data.frame containing the data to evaluate the sensitivity of the model.

input_vars

character vector with the variables to create the scatter plot. If"all",then scatter plots are created for all the input variables infdata.

output_vars

character vector with the variables to create the scatter plot. If"all",then scatter plots are created for all the output variables infdata.

smooth

logical ifTRUE,geom_smooth plots are added to each variable plot

nspline

integer ifsmooth is TRUE, this determine the degree of the spline usedto performgeom_smooth. Ifnspline is NULL, the square root of the length of the datais used as degrees of the spline.

color

character specifying the name of anumeric variable offdata to color the scatter plot.

grid

logical. IfTRUE, plots created are show together usingarrangeGrob

...

further arguments that should be passed toSensAnalysisMLP function

Value

list ofgeom_point plots for the inputs variables representing thesensitivity of each output respect to the inputs

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensDotPlotNeuralSens::SensDotPlot(nnetmod, fdata = nntrData)

Feature sensitivity plot

Description

Show the distribution of the sensitivities of the outputingeom_sina() plot which color depends on the input values

Usage

SensFeaturePlot(object, fdata = NULL, ...)

Arguments

object

fitted neural network model orarray containing the rawsensitivities from the functionSensAnalysisMLP

fdata

data.frame containing the data to evaluate the sensitivity of the model.Not needed if the raw sensitivities has been passed asobject

...

further arguments that should be passed toSensAnalysisMLP function

Value

list of Feature sensitivity plot as described inhttps://www.r-bloggers.com/2019/03/a-gentle-introduction-to-shap-values-in-r/

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)NeuralSens::SensFeaturePlot(sens)

Constructor of the SensMLP Class

Description

Create an object of SensMLP class

Usage

SensMLP(  sens = list(),  raw_sens = list(),  mlp_struct = numeric(),  trData = data.frame(),  coefnames = character(),  output_name = character(),  cv = NULL,  boot = NULL,  boot.alpha = NULL)

Arguments

sens

list of sensitivity measures, onedata.frame per output neuron

raw_sens

list of sensitivities, onematrix per output neuron

mlp_struct

numeric vector describing the structur of the MLP model

trData

data.frame with the data used to calculate the sensitivities

coefnames

character vector with the name of the predictor(s)

output_name

character vector with the name of the output(s)

cv

list list with critical values of significance for std and mean square.

boot

array bootstrapped sensitivity measures.

boot.alpha

array significance level.Defaults toNULL. Only available for analyzedcaret::train models.

Value

SensMLP object

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Plot sensitivities of a neural network model

Description

Function to plot the sensitivities created byHessianMLP.

Usage

SensMatPlot(  hess,  sens = NULL,  output = 1,  metric = c("mean", "std", "meanSensSQ"),  senstype = c("matrix", "interactions"),  ...)

Arguments

hess

HessMLP object created byHessianMLP.

sens

SensMLP object created bySensAnalysisMLP.

output

numeric orcharacter specifying the output neuron or output name to be plotted.By default is the first output (output = 1).

metric

character specifying the metric to be plotted. It can be "mean","std" or "meanSensSQ".

senstype

character specifying the type of plot to be plotted. It can be "matrix" or"interactions". If type = "matrix", only the second derivatives are plotted. If type = "interactions"the main diagonal are the first derivatives respect each input variable.

...

further argument passed similar toggcorrplot arguments.

Details

Most of the code of this function is based onggcorrplot() function from packageggcorrplot. However, due to theinhability of changing the limits of the color scale, it keeps giving a warningif that function is used and the color scale overwritten.

Value

a list ofggplots, one for each output neuron.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 100decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPH <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)NeuralSens::SensMatPlot(H)S <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)NeuralSens::SensMatPlot(H, S, senstype = "interactions")

Sensitivity analysis plot over time of the data

Description

Plot of sensitivity of the neural network output respectto the inputs over the time variable from the data provided

Usage

SensTimePlot(  object,  fdata = NULL,  date.var = NULL,  facet = FALSE,  smooth = FALSE,  nspline = NULL,  ...)

Arguments

object

fitted neural network model orarray containing the rawsensitivities from the functionSensAnalysisMLP

fdata

data.frame containing the data to evaluate the sensitivity of the model.Not needed if the raw sensitivities has been passed asobject

date.var

Posixct vector with the date of each sample offdataIfNULL, the first variable with Posixct format offdata is used as dates

facet

logical ifTRUE, functionfacet_grid fromggplot2 is used

smooth

logical ifTRUE,geom_smooth plots are added to each variable plot

nspline

integer ifsmooth is TRUE, this determine the degree of the spline usedto performgeom_smooth. Ifnspline is NULL, the square root of the length of the timeseriesis used as degrees of the spline.

...

further arguments that should be passed toSensAnalysisMLP function

Value

list ofgeom_line plots for the inputs variables representing thesensitivity of each output respect to the inputs over time

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TRfdata[,3] <- ifelse(as.data.frame(fdata)[,3] %in% c("SUN","SAT"), 0, 1)## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensTimePlotNeuralSens::SensTimePlot(nnetmod, fdata = nntrData, date.var = NULL)

Plot sensitivities of a neural network model

Description

Function to plot the sensitivities created bySensAnalysisMLP.

Usage

SensitivityPlots(  sens = NULL,  der = TRUE,  zoom = TRUE,  quit.legend = FALSE,  output = 1,  plot_type = NULL,  inp_var = NULL,  title = "Sensitivity Plots",  dodge_var = FALSE)

Arguments

sens

SensAnalysisMLP object created bySensAnalysisMLP orHessMLP objectcreated byHessianMLP.

der

logical indicating if density plots should be created. By default isTRUE

zoom

logical indicating if the distributions should be zoomed when there is any of them which is too tiny to be appreciated in the third plot.facet_zoom function fromggforce package is required.

quit.legend

logical indicating if legend of the third plot should be removed. By default isFALSE

output

numeric orcharacter specifying the output neuron or output name to be plotted.By default is the first output (output = 1).

plot_type

character indicating which of the 3 plots to show. Useful when several variables are analyzed.Acceptable values are 'mean_sd', 'square', 'raw' corresponding to first, second and third plot respectively. IfNULL,all plots are shown at the same time. By default isNULL.

inp_var

title

character title of the sensitivity plots

dodge_var

bool Flag to indicate that x ticks in meanSensSQ plot must dodge between them. Useful withtoo long input names.

Value

List with the following plot for each output:

Plot 1: colorful plot with theclassification of the classes in a 2D map
Plot 2: b/w plot withprobability of the chosen class in a 2D map
Plot 3: plot with thestats::predictions of the data provided if paramder isFALSE

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)NeuralSens::SensitivityPlots(sens)

Define function to create a 'diagonal' array or get the diagonal of an array

Description

Define function to create a 'diagonal' array or get the diagonal of an array

Usage

diag3Darray(x = 1, dim = length(x), out = "vector")

Arguments

x

number orvector defining the value of the diagonal of3D array

dim

integer defining the length of the diagonal. Default islength(x).Iflength(x) != 1,dim must be equal tolength(x).

out

character specifying which type of diagonal to return ("vector"or"matrix"). SeeDetails

Details

The diagonal of a 3D array has been defined as those elements in positions c(int,int,int),i.e., the three digits are the same.

If the diagonal should be returned,out specifies if it should return a"vector" withthe elements of position c(int,int,int), or"matrix" with the elements of position c(int,dim,int),i.e.,dim = 2 -> elements (1,1,1),(2,1,2),(3,1,3),(1,2,1),(2,2,2),(3,2,3),(3,1,3),(3,2,3),(3,3,3).

Value

array with all elements zero except the diagonal, with dimensions c(dim,dim,dim)

Examples

x <- diag3Darray(c(1,4,6), dim = 3)x# , , 1## [,1] [,2] [,3]# [1,]    1    0    0# [2,]    0    0    0# [3,]    0    0    0## , , 2## [,1] [,2] [,3]# [1,]    0    0    0# [2,]    0    4    0# [3,]    0    0    0## , , 3## [,1] [,2] [,3]# [1,]    0    0    0# [2,]    0    0    0# [3,]    0    0    6diag3Darray(x)# 1, 4, 6

Define function to change the diagonal of array

Description

Define function to change the diagonal of array

Usage

diag3Darray(x) <- value

Arguments

x

3D array whose diagonal must be c hanged

value

vector defining the new values of diagonal.

Details

The diagonal of a 3D array has been defined as those elements in positions c(int,int,int),i.e., the three digits are the same.

Value

array with all elements zero except the diagonal, with dimensions c(dim,dim,dim)

Examples

x <- array(1, dim = c(3,3,3))diag3Darray(x) <- c(2,2,2)x#  , , 1##  [,1] [,2] [,3]#  [1,]    2    1    1#  [2,]    1    1    1#  [3,]    1    1    1##  , , 2##  [,1] [,2] [,3]#  [1,]    1    1    1#  [2,]    1    2    1#  [3,]    1    1    1##  , , 3##  [,1] [,2] [,3]#  [1,]    1    1    1#  [2,]    1    1    1#  [3,]    1    1    2

Define function to create a 'diagonal' array or get the diagonal of an array

Description

Define function to create a 'diagonal' array or get the diagonal of an array

Usage

diag4Darray(x = 1, dim = length(x))

Arguments

x

number orvector defining the value of the diagonal of4D array

dim

integer defining the length of the diagonal. Default islength(x).Iflength(x) != 1,dim must be equal tolength(x).

Details

The diagonal of a 4D array has been defined as those elements in positions c(int,int,int,int),i.e., the four digits are the same.

Value

array with all elements zero except the diagonal, with dimensions c(dim,dim,dim)

Examples

x <- diag4Darray(c(1,3,6,2), dim = 4)x# , , 1, 1##      [,1] [,2] [,3] [,4]# [1,]    1    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 2, 1##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 3, 1##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 4, 1##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 1, 2##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 2, 2##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    3    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 3, 2##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 4, 2##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 1, 3##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 2, 3##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 3, 3##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    6    0# [4,]    0    0    0    0## , , 4, 3##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 1, 4##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 2, 4##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 3, 4##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    0## , , 4, 4##      [,1] [,2] [,3] [,4]# [1,]    0    0    0    0# [2,]    0    0    0    0# [3,]    0    0    0    0# [4,]    0    0    0    2diag4Darray(x)# 1, 3, 6, 2

Define function to change the diagonal of array

Description

Define function to change the diagonal of array

Usage

diag4Darray(x) <- value

Arguments

x

3D array whose diagonal must be c hanged

value

vector defining the new values of diagonal.

Details

The diagonal of a 3D array has been defined as those elements in positions c(int,int,int),i.e., the three digits are the same.

Value

array with all elements zero except the diagonal, with dimensions c(dim,dim,dim)

Examples

x <- array(1, dim = c(4,4,4,4))diag4Darray(x) <- c(2,2,2,2)x# , , 1, 1##      [,1] [,2] [,3] [,4]# [1,]    2    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 2, 1##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 3, 1##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 4, 1##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 1, 2##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 2, 2##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    2    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 3, 2##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 4, 2##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 1, 3##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 2, 3##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 3, 3##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    2    1# [4,]    1    1    1    1## , , 4, 3##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 1, 4##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 2, 4##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 3, 4##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    1## , , 4, 4##      [,1] [,2] [,3] [,4]# [1,]    1    1    1    1# [2,]    1    1    1    1# [3,]    1    1    1    1# [4,]    1    1    1    2

Find Critical Value

Description

This function finds the smallest x such that the probability of a random variablebeing less than or equal to x is greater than or equal to 1 - alpha.It uses the uniroot function to find where the empirical cumulative distribution function (ECDF)crosses 1 - alpha.

Usage

find_critical_value(ecdf_func, alpha)

Arguments

ecdf_func

An ECDF function representing the distribution of a random variable.

alpha

A numeric value specifying the significance level.

Value

The smallest x such that P(X <= x) >= 1 - alpha.

Examples

data <- rnorm(100)ecdf_data <- ecdf(data)critical_val <- find_critical_value(ecdf_data, 0.05)

Check if object is of class`HessMLP`

Description

Check if object is of classHessMLP

Usage

is.HessMLP(object)

Arguments

object

HessMLP object

Value

TRUE ifobject is aHessMLP object

Check if object is of class`SensMLP`

Description

Check if object is of classSensMLP

Usage

is.SensMLP(object)

Arguments

object

SensMLP object

Value

TRUE ifobject is aSensMLP object

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

k-StepM Algorithm for Hypothesis Testing

Description

This function implements the k-stepM algorithm for multiple hypothesis testing.It tests each hypothesis using the critical value calculated from the ECDFof the k-max differences, updating the critical value, and iterating until all hypothesesare tested.

Usage

kStepMAlgorithm(original_stats, bootstrap_stats, num_hypotheses, alpha, k)

Arguments

original_stats

A numeric vector of original test statistics for each hypothesis.

bootstrap_stats

A numeric matrix of bootstrap test statistics, with rows representingbootstrap samples and columns representing hypotheses.

num_hypotheses

An integer specifying the total number of hypotheses.

alpha

A numeric value specifying the significance level.

k

An integer specifying the threshold number for controlling the k-familywise error rate.

Value

A list containing two elements: 'signif', a logical vector indicating which hypothesesare rejected, and 'cv', a numeric vector of critical values used for each hypothesis.

References

Romano, Joseph P., Azeem M. Shaikh, and Michael Wolf. "Formalized data snoopingbased on generalized error rates." Econometric Theory 24.2 (2008): 404-447.

Examples

original_stats <- rnorm(10)bootstrap_stats <- matrix(rnorm(1000), ncol = 10)result <- kStepMAlgorithm(original_stats, bootstrap_stats, 10, 0.05, 1)

Plot method for the HessMLP Class

Description

Plot the sensitivities and sensitivity metrics of aHessMLP object.

Usage

## S3 method for class 'HessMLP'plot(  x,  plotType = c("sensitivities", "time", "features", "matrix", "interactions"),  ...)

Arguments

x

HessMLP object created byHessianMLP

plotType

character specifying which type of plot should be created. It can be:

"sensitivities" (default): useHessianMLP function
"time": useSensTimePlot function
"features": useHessFeaturePlot function
"matrix": useSensMatPlot function to show the valuesof second partial derivatives
"interactions": useSensMatPlot function to show thevalues of second partial derivatives and the first partial derivatives in the diagonal

...

additional parameters passed to plot function of theNeuralSens package

Value

list of graphic objects created byggplot

Examples

#' ## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPsens <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)plot(sens)plot(sens,"time")

Plot method for the SensMLP Class

Description

Plot the sensitivities and sensitivity metrics of aSensMLP object.

Usage

## S3 method for class 'SensMLP'plot(x, plotType = c("sensitivities", "time", "features"), ...)

Arguments

x

SensMLP object created bySensAnalysisMLP

plotType

character specifying which type of plot should be created. It can be:

"sensitivities" (default): useSensAnalysisMLP function
"time": useSensTimePlot function
"features": useSensFeaturePlot function

...

additional parameters passed to plot function of theNeuralSens package

Value

list of graphic objects created byggplot

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

#' ## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)plot(sens)plot(sens,"time")plot(sens,"features")

Print method for the HessMLP Class

Description

Print the sensitivities of aHessMLP object.

Usage

## S3 method for class 'HessMLP'print(x, n = 5, round_digits = NULL, ...)

Arguments

x

HessMLP object created byHessianMLP

n

integer specifying number of sensitivities to print per each output

round_digits

integer number of decimal places, defaultNULL

...

additional parameters

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPsens <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)sens

Print method for the SensMLP Class

Description

Print the sensitivities of aSensMLP object.

Usage

## S3 method for class 'SensMLP'print(x, n = 5, round_digits = NULL, ...)

Arguments

x

SensMLP object created bySensAnalysisMLP

n

integer specifying number of sensitivities to print per each output

round_digits

integer number of decimal places, defaultNULL

...

additional parameters

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)sens

Print method of the summary HessMLP Class

Description

Print the sensitivity metrics of aHessMLP object.This metrics are the mean sensitivity, the standard deviationof sensitivities and the mean of sensitivities square

Usage

## S3 method for class 'summary.HessMLP'print(x, round_digits = NULL, ...)

Arguments

x

summary.HessMLP object created by summary method ofHessMLP object

round_digits

integer number of decimal places, defaultNULL

...

additional parameters

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPsens <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)print(summary(sens))

Print method of the summary SensMLP Class

Description

Print the sensitivity metrics of aSensMLP object.This metrics are the mean sensitivity, the standard deviationof sensitivities and the mean of sensitivities square

Usage

## S3 method for class 'summary.SensMLP'print(x, round_digits = NULL, boot.alpha = NULL, ...)

Arguments

x

summary.SensMLP object created by summary method ofSensMLP object

round_digits

integer number of decimal places, defaultNULL

boot.alpha

float significance level to show statistical metrics. IfNULL,boot.alpha inherits fromx is used. Defaults toNULL.

...

additional parameters

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)print(summary(sens))

Simulated data to test the package functionalities

Description

data.frame with 2000 rows of 4 columns with 3input variablesX1, X2, X3 and one output variableY.The data is already scaled, and has been generated using the following code:

set.seed(150)

simdata <- data.frame( "X1" = rnorm(2000, 0, 1), "X2" = rnorm(2000, 0, 1), "X3" = rnorm(2000, 0, 1) )

simdata$Y <- simdata$X1^2 + 0.5*simdata$X2 + 0.1*rnorm(2000, 0, 1)

Format

A data frame with 2000 rows and 4 variables:

X1: Random input 1
X2: Random input 2
X3: Random input 3
Y: Output

Author(s)

Jaime Pizarroso Gonzalo

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Summary Method for the HessMLP Class

Description

Print the sensitivity metrics of aHessMLP object.This metrics are the mean sensitivity, the standard deviationof sensitivities and the mean of sensitivities square

Usage

## S3 method for class 'HessMLP'summary(object, ...)

Arguments

object

HessMLP object created byHessianMLP

...

additional parameters

Value

summary object of theHessMLP object passed

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 HessianMLPsens <- NeuralSens::HessianMLP(nnetmod, trData = nntrData, plot = FALSE)summary(sens)

Summary Method for the SensMLP Class

Description

Print the sensitivity metrics of aSensMLP object.This metrics are the mean sensitivity, the standard deviationof sensitivities and the mean of sensitivities square

Usage

## S3 method for class 'SensMLP'summary(object, ...)

Arguments

object

SensMLP object created bySensAnalysisMLP

...

additional parameters

Value

summary object of theSensMLP object passed

References

Pizarroso J, Portela J, Muñoz A (2022). NeuralSens: Sensitivity Analysis ofNeural Networks. Journal of Statistical Software, 102(7), 1-36.

Examples

## Load data -------------------------------------------------------------------data("DAILY_DEMAND_TR")fdata <- DAILY_DEMAND_TR## Parameters of the NNET ------------------------------------------------------hidden_neurons <- 5iters <- 250decay <- 0.1#########################################################################################################  REGRESSION NNET ####################################################################################################################### Regression dataframe --------------------------------------------------------# Scale the datafdata.Reg.tr <- fdata[,2:ncol(fdata)]fdata.Reg.tr[,3] <- fdata.Reg.tr[,3]/10fdata.Reg.tr[,1] <- fdata.Reg.tr[,1]/1000# Normalize the data for some modelspreProc <- caret::preProcess(fdata.Reg.tr, method = c("center","scale"))nntrData <- predict(preProc, fdata.Reg.tr)#' ## TRAIN nnet NNET --------------------------------------------------------# Create a formula to train NNETform <- 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 SensAnalysisMLPsens <- NeuralSens::SensAnalysisMLP(nnetmod, trData = nntrData, plot = FALSE)summary(sens)

Movatterモバイル変換

NeuralSens: Sensitivity Analysis of Neural Networks

Description

Author(s)

See Also

Activation function of neuron

Description

Usage

Arguments

Value

References

Examples

Sensitivity alpha-curve associated to MLP function

Description

Usage

Arguments

Value

Examples

Sensitivity alpha-curve associated to MLP function of an input variable

Description

Usage

Arguments

Value

Examples

Change significance of boot SensMLP Class

Description

Usage

Arguments

Value

Examples

Sensitivity analysis plot over time of the data

Description

Usage

Arguments

Value

Examples

Plot sensitivities of a neural network model

Description

Usage

Arguments

Value

Examples

Plot sensitivities of a neural network model

Description

Usage

Arguments

Value

References

Examples

Data frame with 4 variables

Description

Format

Author(s)

References

Data frame with 3 variables

Description

Format

Author(s)

References

Second derivative of activation function of neuron

Description

Usage

Arguments

Value

Examples

Third derivative of activation function of neuron

Description

Usage

Arguments

Value

Examples

Derivative of activation function of neuron

Description

Usage

Arguments

Value

References

Examples

Second derivatives 3D scatter or surface plot against input values

Description