Tree family plotting

[jemus42]

Resolves #51 if it works out ok, vibecoded example below

# pak::pak("PlantedML/randomPlantedForest@tree-plot")
library(randomPlantedForest)

A toy example

y has a main effect of x1 and an interaction of x2 and x3, x4 is noise. A single tree family with a few splits is small enough to read as a diagram.

set.seed(1)
n <- 500
toy <- data.frame(x1 = runif(n), x2 = runif(n), x3 = runif(n), x4 = runif(n))
toy$y <- 2 * toy$x1 + 4 * (toy$x2 > 0.5) * toy$x3 + rnorm(n, sd = 0.2)

fit_toy <- rpf(y ~ ., data = toy, ntrees = 1, splits = 12)
plot(fit_toy)

Each tree belongs to a set of variables and the prediction is the sum of the values of all leaves containing a point. The same leaves in variable space, before and after purification:

head(rpf_boxes(fit_toy), 3)
#>          tree order box      value    x1_lower  x1_upper x2_lower x2_upper
#> 1 (Intercept)     0   1  0.0000000          NA        NA       NA       NA
#> 2          x1     1   1 -0.4789080 0.001836858 0.4935413       NA       NA
#> 3          x1     1   2  0.7489024 0.754705622 1.0160774       NA       NA
#>   x3_lower x3_upper x4_lower x4_upper
#> 1       NA       NA       NA       NA
#> 2       NA       NA       NA       NA
#> 3       NA       NA       NA       NA
plot(fit_toy, type = "boxes")

purify(fit_toy)
plot(fit_toy, type = "boxes")

Bike sharing

data("Bikeshare", package = "ISLR2")
bike <- Bikeshare
bike$hr <- as.numeric(as.character(bike$hr))
bike$workingday <- factor(bike$workingday, levels = 0:1, labels = c("no", "yes"))
bike$season <- factor(bike$season, levels = 1:4, labels = c("Winter", "Spring", "Summer", "Fall"))
bike <- bike[setdiff(names(bike), c("atemp", "day", "registered", "casual", "mnth"))]

A small fit as a diagram, with the root split twice on the hour of day and two interaction trees:

set.seed(1)
fit_small <- rpf(bikers ~ hr + workingday + temp, data = bike, ntrees = 1, splits = 12)
plot(fit_small)

With tuned parameters,
one tree family is enough for plotting. At the tuned max_interaction = 7, most leaves are in trees on many variables, which
plot() summarizes as a remainder:

tuned <- list(
  splits = 1000, split_try = 3, t_try = 0.0116, split_decay_rate = 0.357,
  max_candidates = 73, delete_leaves = FALSE, split_structure = "leaves"
)
set.seed(1)
fit_tuned <- do.call(rpf, c(list(bikers ~ ., data = bike, ntrees = 1, max_interaction = 7), tuned))
table(order = rpf_boxes(fit_tuned)$order)
#> order
#>   0   1   2   3   4   5   6   7 
#>   1  10  64 298 634 524 382  88

Restricting the forest to pairwise interactions costs some accuracy (test RMSE, 80/20 split, ntrees = 200):

max_interaction	test RMSE
7 (tuned)	34.1
2	41.3
1	74.1
intercept only	131.7

In exchange, after purification, every tree is a component of the functional decomposition that can be read off directly:

set.seed(1)
fit_pairs <- do.call(rpf, c(list(bikers ~ ., data = bike, ntrees = 1, max_interaction = 2), tuned))
purify(fit_pairs)
plot(fit_pairs, type = "boxes", trees = c("hr", "temp", "season", "hr:workingday", "hr:temp", "hr:season"))