Connection Weight method for neural network variable importance

The function computes the matrix multiplications of hidden weight matrices (Wx,...,Wy), i.e., the product of the raw input-hidden and hidden-output connection weights between each input and output neuron and sums the products across all hidden neurons, as proposed by Olden (2004).

getConnectionWeight(object, thr = NULL, verbose = FALSE, ...)

Arguments

object: A neural network object from SEMdnn() function.
thr: A numeric value [0-1] indicating the threshold to apply to the Olden's connection weights to color the graph. If thr = NULL (default), the threshold is set to thr = 0.5*max(abs(connection weights)).
verbose: A logical value. If FALSE (default), the processed graph will not be plotted to screen.
...: Currently ignored.

Value

A list of three object: (i) est: a data.frame including the connections together with their connection weights(W), (ii) gest: if the outcome vector is given, a data.frame of connection weights for outcome lavels, and (iii) dag: DAG with colored edges/nodes. If abs(W) > thr and W < 0, the edge W > 0, the edge is activated and it is highlighted in red. If the outcome vector is given, nodes with absolute connection weights summed over the outcome levels, i.e. sum(abs(W[outcome levels])) > thr, will be highlighted in pink.

Details

In a neural network, the connections between inputs and outputs are represented by the connection weights between the neurons. The importance values assigned to each input variable using the Olden method are in units that are based directly on the summed product of the connection weights. The amount and direction of the link weights largely determine the proportional contributions of the input variables to the neural network's prediction output. Input variables with larger connection weights indicate higher intensities of signal transfer and are therefore more important in the prediction process. Positive connection weights represent excitatory effects on neurons (raising the intensity of the incoming signal) and increase the value of the predicted response, while negative connection weights represent inhibitory effects on neurons (reducing the intensity of the incoming signal). The weights that change sign (e.g., positive to negative) between the input-hidden to hidden-output layers would have a cancelling effect, and vice versa weights with the same sign would have a synergistic effect. Note that in order to map the connection weights to the DAG edges, the element-wise product, W*A is performed between the Olden's weights entered in a matrix, W(pxp) and the binary (1,0) adjacency matrix, A(pxp) of the input DAG.

References

Olden, Julian & Jackson, Donald. (2002). Illuminating the "black box": A randomization approach for understanding variable contributions in artificial neural networks. Ecological Modelling. 154. 135-150. 10.1016/S0304-3800(02)00064-9.

Olden, Julian. (2004). An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. Ecological Modelling. 178. 10.1016/S0304-3800(04)00156-5.

Author

Mario Grassi mario.grassi@unipv.it

Examples


# \donttest{
if (torch::torch_is_installed()){

# load ALS data
ig<- alsData$graph
data<- alsData$exprs
data<- transformData(data)$data

#ncores<- parallel::detectCores(logical = FALSE)
dnn0<- SEMdnn(ig, data, outcome = NULL, thr = NULL,
      #hidden = 5*K, link = "selu", bias = TRUE,
      hidden = c(10,10,10), link = "selu", bias = TRUE,
      validation = 0,  epochs = 32, ncores = 2)

cw05<- getConnectionWeight(dnn0, thr = 0.5, verbose = TRUE)
table(E(cw05$dag)$color)
}
#> Conducting the nonparanormal transformation via shrunkun ECDF...done.
#> Running SEM model via DNN...
#>  done.
#> 
#> DNN solver ended normally after 736 iterations
#> 
#>  logL:-50.497857  srmr:0.211551

#> 
#>     gray50       red2 royalblue3 
#>         30         11          4 
# }