'SmoothGrad' was introduced by D. Smilkov et al. (2017) and is an extension
to the classical Vanilla Gradient method. It takes the mean of the
gradients for n perturbations of each data point, i.e. with
\(\epsilon \sim N(0,\sigma)\)
$$1/n \sum_n d f(x+ \epsilon)_j / d x_j.$$
References
D. Smilkov et al. (2017) SmoothGrad: removing noise by adding noise. CoRR, abs/1706.03825
Super classes
innsight::InterpretingMethod -> innsight::GradientBased -> SmoothGrad
Public fields
nNumber of perturbations of the input data (default: \(50\)).
noise_levelThe standard deviation of the Gaussian perturbation, i.e. \(\sigma = (max(x) - min(x)) *\)
noise_level.
Methods
Method new()
Create a new instance of the SmoothGrad method.
Usage
SmoothGrad$new(
converter,
data,
channels_first = TRUE,
output_idx = NULL,
ignore_last_act = TRUE,
times_input = FALSE,
n = 50,
noise_level = 0.1,
dtype = "float"
)Arguments
converterAn instance of the R6 class
Converter.dataThe data for which the smoothed gradients are to be calculated. It has to be an array or array-like format of size (batch_size, dim_in).
channels_firstThe format of the given data, i.e. channels on last dimension (
FALSE) or after the batch dimension (TRUE). If the data has no channels, use the default valueTRUE.output_idxThis vector determines for which outputs the method will be applied. By default (
NULL), all outputs (but limited to the first 10) are considered.ignore_last_actA boolean value to include the last activation into all the calculations, or not (default:
TRUE). In some cases, the last activation leads to a saturation problem.times_inputMultiplies the gradients with the input features. This method is called 'SmoothGrad x Input'. Default:
FALSE.nNumber of perturbations of the input data (default: \(50\)).
noise_levelDetermines the standard deviation of the gaussian perturbation, i.e. \(\sigma = (max(x) - min(x)) *\)
noise_level.dtypeThe data type for the calculations. Use either
'float'for torch::torch_float or'double'for torch::torch_double.
Examples
# ------------------------- Example 1: Torch -------------------------------
library(torch)
# Create nn_sequential model and data
model <- nn_sequential(
nn_linear(5, 10),
nn_relu(),
nn_linear(10, 2),
nn_sigmoid()
)
data <- torch_randn(25, 5)
# Create Converter
converter <- Converter$new(model, input_dim = c(5))
# Calculate the smoothed Gradients
smoothgrad <- SmoothGrad$new(converter, data)
#> Backward pass 'SmoothGrad':
#>
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# Print the result as a data.frame for first 5 rows
smoothgrad$get_result("data.frame")[1:5, ]
#> data feature class value
#> 1 data_1 X1 Y1 -0.1037277
#> 2 data_2 X1 Y1 -0.1112626
#> 3 data_3 X1 Y1 -0.1047125
#> 4 data_4 X1 Y1 -0.1354966
#> 5 data_5 X1 Y1 -0.1952363
# Plot the result for both classes
plot(smoothgrad, output_idx = 1:2)
# Plot the boxplot of all datapoints
boxplot(smoothgrad, output_idx = 1:2)
# ------------------------- Example 2: Neuralnet ---------------------------
library(neuralnet)
data(iris)
# Train a neural network
nn <- neuralnet(Species ~ ., iris,
linear.output = FALSE,
hidden = c(10, 5),
act.fct = "logistic",
rep = 1
)
# Convert the trained model
converter <- Converter$new(nn)
# Calculate the smoothed gradients
smoothgrad <- SmoothGrad$new(converter, iris[, -5], times_input = FALSE)
#> Backward pass 'SmoothGrad':
#>
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# Plot the result for the first and 60th data point and all classes
plot(smoothgrad, data_idx = c(1, 60), output_idx = 1:3)
# Calculate SmoothGrad x Input and do not ignore the last activation
smoothgrad <- SmoothGrad$new(converter, iris[, -5], ignore_last_act = FALSE)
#> Backward pass 'SmoothGrad':
#>
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# Plot the result again
plot(smoothgrad, data_idx = c(1, 60), output_idx = 1:3)
# ------------------------- Example 3: Keras -------------------------------
library(keras)
if (is_keras_available()) {
data <- array(rnorm(64 * 60 * 3), dim = c(64, 60, 3))
model <- keras_model_sequential()
model %>%
layer_conv_1d(
input_shape = c(60, 3), kernel_size = 8, filters = 8,
activation = "softplus", padding = "valid"
) %>%
layer_conv_1d(
kernel_size = 8, filters = 4, activation = "tanh",
padding = "same"
) %>%
layer_conv_1d(
kernel_size = 4, filters = 2, activation = "relu",
padding = "valid"
) %>%
layer_flatten() %>%
layer_dense(units = 64, activation = "relu") %>%
layer_dense(units = 16, activation = "relu") %>%
layer_dense(units = 3, activation = "softmax")
# Convert the model
converter <- Converter$new(model)
# Apply the SmoothGrad method
smoothgrad <- SmoothGrad$new(converter, data, channels_first = FALSE)
# Plot the result for the first datapoint and all classes
plot(smoothgrad, output_idx = 1:3)
# Plot the result as boxplots for first two classes
boxplot(smoothgrad, output_idx = 1:2)
# You can also create an interactive plot with plotly.
# This is a suggested package, so make sure that it is installed
library(plotly)
# Result as boxplots
boxplot(smoothgrad, as_plotly = TRUE)
# Result of the second data point
plot(smoothgrad, data_idx = 2, as_plotly = TRUE)
}
#> Backward pass 'SmoothGrad':
#>
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# ------------------------- Advanced: Plotly -------------------------------
# If you want to create an interactive plot of your results with custom
# changes, you can take use of the method plotly::ggplotly
library(ggplot2)
library(plotly)
library(neuralnet)
data(iris)
nn <- neuralnet(Species ~ .,
iris,
linear.output = FALSE,
hidden = c(10, 8), act.fct = "tanh", rep = 1, threshold = 0.5
)
# create an converter for this model
converter <- Converter$new(nn)
# create new instance of 'SmoothGrad'
smoothgrad <- SmoothGrad$new(converter, iris[, -5])
#> Backward pass 'SmoothGrad':
#>
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library(plotly)
# Get the ggplot and add your changes
p <- plot(smoothgrad, output_idx = 1, data_idx = 1:2) +
theme_bw() +
scale_fill_gradient2(low = "green", mid = "black", high = "blue")
#> Scale for 'fill' is already present. Adding another scale for 'fill', which
#> will replace the existing scale.
# Now apply the method plotly::ggplotly with argument tooltip = "text"
plotly::ggplotly(p, tooltip = "text")