Introduction to innsight

In the last decade, there has been a tremendous rush and growth in machine learning. Almost every year, new architectures break records on scientific test data sets, and the number of layers continues to grow through regularization methods making today’s neural networks far more complex than an original linear or logistic model. Nevertheless, the scientific focus is more on the predictive power than on the interpretability and the respective methods that already exist for the interpretation of single predictions or the whole neural networks are only sparsely or rarely implemented in the R programming language. The innsight package addresses this lack of interpretable machine learning methods in R (similar to iNNvestigate for Python) and provides the most popular methods for neural networks trained in R for analysis in one unified interface.

The steps for explaining individual predictions with the provided methods are unified in this package and follow a strict scheme. This will hopefully allow any user a smooth and easy introduction to the possibilities of this package. The steps are:

# Step 1: Model creation and converting
model = ...
converter <- Converter$new(model)

# Step 2: Apply selected method to your data
result <- Method$new(converter, data)

# Step 3: Plot the results

Step 1: Model Creation and Converting

The innsight package aims to be as flexible as possible and independent of any particular deep learning package in which the passed network was learned or defined. For this reason, there are several ways in this package to pass a neural network and then interpret their predictions.

Package torch

Currently, only models created by torch::nn_sequential are accepted. However, the most popular standard layers and activation functions are available:

If you want to create an instance of the class Converter with a torch model that meets the above conditions, you have to keep the following things in mind:

Example 1: Dense Network


# Create model
model <- nn_sequential(
  nn_linear(3, 10),
  nn_linear(10, 2, bias = FALSE),
# Convert the model
conv_dense <- Converter$new(model, input_dim = c(3))
# Convert model with input and output names
conv_dense_with_names <- 
  Converter$new(model, input_dim = c(3),
                input_names = list(c("Price", "Weight", "Height")),
                output_names = list(c("Buy it!", "Don't buy it!")))
# Show output names
#> [[1]]
#> [1] "Buy it!"       "Don't buy it!"

Example 2: CNN

Unfortunately, at the moment (torch = 0.6.0) it is not possible to use a flatten module in nn_sequential, because it is only implemented as a function (torch_flatten). For this reason we define our own module as described in torch issue #716. To ensure that our package recognizes this module as a flattening layer, classname = "nn_flatten" must be set.

nn_flatten <- nn_module(
    classname = "nn_flatten",
    initialize = function(start_dim = 2, end_dim = -1) {
      self$start_dim <- start_dim
      self$end_dim <- end_dim
    forward = function(x) {
      torch_flatten(x, start_dim = self$start_dim, end_dim = self$end_dim)
# Create CNN for images of size (3, 28, 28)
model <- nn_sequential(
  nn_conv2d(3, 5, c(2, 2)),
  nn_conv2d(5, 6, c(2, 3), stride = c(1, 2)),
  nn_conv2d(6, 2, c(2, 2), dilation = c(1, 2), padding = c(5,4)),
  nn_linear(48, 5),

# Convert the model
conv_cnn <- Converter$new(model, input_dim = c(3, 10, 10))

Package keras

Keras models created by keras_model_sequential or keras_model are accepted. Within these functions, the following layers are allowed to be used:

Analogous to a torch model, no names of inputs or outputs are stored in a keras model, i.e. if no further arguments are set for the Converter instance, default labels are generated for the input (e.g. 'X1', 'X2', …) and output names ('Y1', 'Y2', … ). In the converter, however, there is the possibility (argument input_names and output_names) to pass the names, which will then be used in all results and plots created by this object.

Example 1: Dense Network


# Create model
model <- keras_model_sequential()
model <- model %>%
  layer_dense(10, input_shape = c(5), activation = "softplus") %>%
  layer_dense(8, use_bias = FALSE, activation = "tanh") %>%
  layer_dropout(0.2) %>%
  layer_dense(4, activation = "softmax")

# Convert the model
conv_dense <- Converter$new(model)
#> Skipping Dropout ...

Example 2: CNN


# Create model
model <- keras_model_sequential()
model <- model %>%
  layer_conv_2d(4, c(5,4), input_shape = c(10,10,3), activation = "softplus") %>%
  layer_max_pooling_2d(c(2,2), strides = c(1,1)) %>%
  layer_conv_2d(6, c(3,3), activation = "relu", padding = "same") %>%
  layer_max_pooling_2d(c(2,2)) %>%
  layer_conv_2d(4, c(2,2), strides = c(2,1), activation = "relu") %>%
  layer_flatten() %>%
  layer_dense(5, activation = "softmax")

# Convert the model
conv_cnn <- Converter$new(model)

Package neuralnet

The usage with nets from the package neuralnet is very simple and straightforward, because the package offers much fewer options than torch or keras. The only thing to note is that no custom activation function can be used. However, the package saves the names of the inputs and outputs, which can of course be overwritten with the arguments input_names and output_names when creating the converter object.

Example 1: Dense Network


# Create model
model <- neuralnet(Species ~ Petal.Length + Petal.Width, iris, 
                   linear.output = FALSE)

# Convert model
conv_dense <- Converter$new(model)
# Show input names
#> [[1]]
#> [1] "Petal.Length" "Petal.Width"
# Show output names
#> [[1]]
#> [1] "setosa"     "versicolor" "virginica"

Step 2: Apply selected Method

The innsight package provides the following tools for analyzing black box neural networks based on dense or convolution layers:

\[ \begin{align} \text{Gradient}(x)_i^C &= \frac{\partial f(x)_C}{\partial x_i}\\ \text{Gradient x Input}(x)_i^C &= x_i \cdot \text{Gradient}(x)_i^C \end{align} \]


Example 1: Gradient and Gradient x Input

Make sure that Example 1 from the section on neuralnet and Example 2 from the section on keras were run last.

# Apply method 'Gradient' for the dense network
grad_dense <- Gradient$new(conv_dense, iris[-c(1,2,5)])

# Apply method 'Gradient x Input' for CNN
x <- torch_randn(c(10,3,10,10))
grad_cnn <- Gradient$new(conv_cnn, x, times_input = TRUE)

Example 2: SmoothGrad and SmoothGrad x Input

Make sure that Example 1 from the section on neuralnet and Example 2 from the section on keras were run last.

# Apply method 'SmoothGrad' for the dense network
smooth_dense <- SmoothGrad$new(conv_dense, iris[-c(1,2,5)])

# Apply method 'SmoothGrad x Input' for CNN
x <- torch_randn(c(10,3,10,10))
smooth_cnn <- SmoothGrad$new(conv_cnn, x, times_input = TRUE)

Example 3: LRP

Make sure that Example 1 from the section on neuralnet and Example 2 from the section on keras were run last.

# Apply method 'LRP' for the dense network
lrp_dense <- LRP$new(conv_dense, iris[-c(1,2,5)])

# Apply method 'LRP' for CNN with alpha-beta-rule
x <- torch_randn(c(10,10,10,3))
lrp_cnn <- LRP$new(conv_cnn, x, rule_name = "alpha_beta", rule_param = 1,
                   channels_first = FALSE)

Example 4: DeepLift

Make sure that Example 1 from the section on neuralnet and Example 2 from the section on keras were run last.

# Define reference value
x_ref <- array(colMeans(iris[-c(1,2,5)]), dim = c(1,2))
# Apply method 'DeepLift' for the dense network
deeplift_dense <- DeepLift$new(conv_dense, iris[-c(1,2,5)], x_ref = x_ref)

# Apply method 'DeepLift' for CNN
x <- torch_randn(c(10,3,10,10))
deeplift_cnn <- DeepLift$new(conv_cnn, x)

Step 3: Show and Plot the Results

Once a method object has been created, the results can be returned as an array, data.frame, or torch_tensor, and can be further processed as desired. In addition, for each of the three sizes of the inputs (1D, 2D, or 3D) suitable plot and boxplot functions based on ggplot2 are implemented. Due to the complexity of higher dimensional inputs, these plots and boxplots can also be displayed as an interactive plotly plots by using the argument as_plotly.

Get Results

Each instance of the interpretability methods have the class method get_result, which is used to return the results. You can choose between the data formats array, data.frame or torch_tensor by passing the name as an character for argument type.

Array (Default)

# Get result (make sure 'grad_dense' is defined!)
result_array <- grad_dense$get_result()

# Show for datapoint 1 and 71 the result
#> , , setosa
#>    Petal.Length Petal.Width
#> 1    -17.705021  -37.914467
#> 71    -1.752118   -3.752078
#> , , versicolor
#>    Petal.Length Petal.Width
#> 1    0.30512863  0.65341860
#> 71   0.03019602  0.06466337
#> , , virginica
#>    Petal.Length Petal.Width
#> 1     22.329956   47.818550
#> 71     2.209809    4.732201

Data Frame

# Get result as data.frame (make sure 'lrp_cnn' is defined!)
result_data.frame <- lrp_cnn$get_result("data.frame")

# Show the first 5 rows
head(result_data.frame, 5)
#>     data feature_h feature_w channel class        value
#> 1 data_1        H1        W1      C1    Y1 1.408816e-05
#> 2 data_2        H1        W1      C1    Y1 1.124055e-05
#> 3 data_3        H1        W1      C1    Y1 3.590281e-06
#> 4 data_4        H1        W1      C1    Y1 1.057909e-05
#> 5 data_5        H1        W1      C1    Y1 1.460757e-05

Torch Tensor

# Get result (make sure 'deeplift_dense' is defined!)
result_torch <- deeplift_dense$get_result("torch_tensor")

# Show for datapoint 1 and 71 the result
#> torch_tensor
#> (1,.,.) = 
#>   60.1352  -1.0364 -75.8438
#>   54.5763  -0.9406 -68.8328
#> (2,.,.) = 
#>  -5.5242  0.0952  6.9673
#>  -6.8194  0.1175  8.6008
#> [ CPUFloatType{2,2,3} ]

Plot Results

The package innsight also provides methods for visualizing the results. By default a ggplot2-plot is created, but it can also be rendered as an interactive plotly plot with the as_plotly argument. You can use the argument output_idx to select the indices of the output nodes for the plot. In addition, if the results have channels, the aggr_channels argument can be used to determine how the channels are aggregated.

Note: If you want to make a change to the results before plotting, you can get the results with Method$result (torch tensor!), change it accordingly, and then save it back to the attribute Method$result as a torch tensor.

Plot Function

Plot result for the first data point and all outputs: (make sure smooth_dense and lrp_cnn are defined!)

plot(smooth_dense, output_idx = 1:3)

# You can plot several data points at once
plot(smooth_dense, data_idx = c(1,71), output_idx = 1:3)

# Plot result for the first data point and first and fourth output
plot(lrp_cnn, aggr_channels = 'norm', output_idx = c(1,4))

# Create a plotly plot for the first output
plot(lrp_cnn, aggr_channels = 'norm', output_idx = c(1), as_plotly = TRUE)

Boxplot Function

Plot result for the first data point and first two outputs:
(make sure smooth_dense is defined!)

boxplot(smooth_dense, output_idx = 1:2)

# Use no preprocess function (default: abs) and plot reference data point
boxplot(smooth_dense, output_idx = 1:3, preprocess_FUN = identity,
        ref_data_idx = c(55))

Same as plotly.
In addition, you have a drop-down menu to select other data points you can define the indices for the drop-down menu with individual_data_idx.

boxplot(smooth_dense, output_idx = 1:3, preprocess_FUN = identity,
        ref_data_idx = c(55), as_plotly = TRUE, individual_data_idx = c(1))