Obtain importance of individual trees in a RandomForest
When training a randomForest model, the importance scores are computed for the entire forest and stored directly inside the object. Tree-specific scores are not kept and so cannot be directly retrieved from a randomForest object.
Unfortunately, you are correct about having to incrementally construct a forest. The good news is that a randomForest object is self-contained, and you don't need to implement your own run_rf. Instead, you can use stats::update to re-fit the random forest model with a single tree and randomForest::grow to add additional trees one at a time:
## Starting with a random forest having a single tree,
## grow it 9 times, one tree at a time
rfs <- purrr::accumulate( .init = update(rf_mod, ntree=1),
rep(1,9), randomForest::grow )
## Retrieve the importance scores from each random forest
imp <- purrr::map( rfs, ~importance(.x)[,"%IncMSE"] )
## Combine all results into a single data frame
dplyr::bind_rows( !!!imp )
# # A tibble: 10 x 10
# cyl disp hp drat wt qsec vs am gear carb
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 0 18.8 8.63 1.05 0 1.17 0 0 0 0.194
# 2 0 10.0 46.4 0.561 0 -0.299 0 0 0.543 2.05
# 3 0 22.4 31.2 0.955 0 -0.199 0 0 0.362 5.1
# 4 1.55 24.1 23.4 0.717 0 -0.150 0 0 0.272 5.28
# 5 1.24 22.8 23.6 0.573 0 -0.178 0 0 -0.0259 4.98
# 6 1.03 26.2 22.3 0.478 1.25 0.775 0 0 -0.0216 4.1
# 7 0.887 22.5 22.5 0.406 1.79 -0.101 0 0 -0.0185 3.56
# 8 0.776 19.7 21.3 0.944 1.70 0.105 0 0.0225 -0.0162 3.11
# 9 0.690 18.4 19.1 0.839 1.51 1.24 1.01 0.02 -0.0144 2.77
# 10 0.621 18.4 21.2 0.937 1.32 1.11 0.910 0.0725 -0.114 2.49
The data frame shows how feature importance changes with each additional tree. This is the right panel of your plot example. The trees themselves (for the left panel) can be retrieved from the final forest, which is given by dplyr::last( rfs ).
We can simplify it by
library(tidyverse)
out <- map(seq_len(nn), ~
run_rf(.x) %>%
importance) %>%
reduce(`+`) %>%
magrittr::divide_by(nn)
Disclaimer: This is not really an answer, but too long to post as a comment. Will remove if deemed not appropriate.
While I (think I) understand your question, to be honest I am unsure whether your question makes sense from a statistics/ML point-of-view. The following is based on my obviously limited understanding of RF and CART. Perhaps my comment-post will lead to some insights.
Let's start with some general random forest (RF) theory on variable importance from Hastie, Tibshirani, Friedman, The Elements of Statistical Learning, p. 593 (bold-face mine):
At each split in each tree, the improvement in the split-criterion is the importance measure attributed to the splitting variable, and is accumulated over all the trees in the forest separately for each variable. [...] Random forests also use the oob samples to construct a different variable-importance measure, apparently to measure the prediction strength of each variable.
So the variable importance measure in RF is defined as a measure accumulated over all trees.
In traditional single classification trees (CARTs), variable importance is characterised through the Gini index that measures node impurity (see e.g. How to measure/rank “variable importance” when using CART? (specifically using {rpart} from R) and Carolin Strobl's PhD thesis)
More complex measures to characterise variable importance in CART-like models exist; for example in rpart:
An overall measure of variable importance is the sum of the goodness of split measures for each split for which it was the primary variable, plus goodness * (adjusted agreement) for all splits in which it was a surrogate. In the printout these are scaled to sum to 100 and the rounded values are shown, omitting any variable whose proportion is less than 1%.
So the bottom line here is the following: At the very least it won't be easy (and in the worst case it won't make sense) to compare variable measures from single classifaction trees with variable importance measures applied to ensemble-based methods like RF.
Which leads me to ask: Why do you want to extract variable importance measures for individual trees from an RF model? Even if you came up with a method to calculate variable importances from individual trees, I believe they wouldn't be very meaningful, and they wouldn't have to "converge" to the ensemble-accumulated values.