Step-by-Step

• On the left we see the averaged model predictions that are generated by a specific combination of the 4 most important variables. You can find the combinations by tracing the coloured flows.
• The stratum label of the individual feature variables indicate the variable value and which fraction of the colored flows pass through it.
• On the right you see the feature importance of all variables and the proportion contributed by the plotted variables on the alluvial plot.
• On the top left you see how the distribution of the generated predictions compare to the distribution of the predicted variable (in this case disp) in the training data.
• The marginal histograms indicate the original distributions in the raining data and the lines indicate the location of the values picked for the data grid.

A more in-depth tutorial for this feature can be found on the project’s github page which will also be vailable on this blog in a few days.

If you are as enthusiastic about alluvial plots as me you will appreciate partial dependency alluvial plots because they can help us to get an immediate intuitive understanding how predictions of a certain range can be generated by the model. They can be understood by none-statistical stakeholders and invite the viewer to start exploring and question the decision making process of the model while also conveying an appreciation for the model complexity as flows branch out to the variables of lower feature importance. Ther are limitations though.

Limitations

• There is a loss of information when binning the numerical variables
• The combinations generated when making the grid might be outside the feature distribution space (generate combinations that are impossible)
• We only look at the combination of 4 features and disregard the others
• For a better interpretability of the feature importance it is adivable to remove strongly correlating variables and to scale, center and transform (Yeo-Johnson, Box-Cox) numerical variables, depending on the statistical model.

To alleviate this you can reduce the complexity of the model by reducing features (take out correlating variables) or use additional model exploration methods such as classical PDPs, ALE plots, Shapely values, etc, …

We do not have to use caret

Note: importance is calculated differently when using this implementation of random forest.

df = select(mtcars2, -ids)
m = randomForest::randomForest( disp ~ ., df)
imp = m$importance

dspace = get_data_space(df, imp, degree = 4)

pred = get_pdp_predictions(df, imp
                           , m
                           , degree = 4
                           , bins = 5)


p = alluvial_model_response(pred, dspace, imp, degree = 4, method = 'pdp')

p_grid = add_marginal_histograms(p, df, plot = F) %>%
  add_imp_plot(p, df)