Speeding up computations

Tree fitting algorithm

By default, pre uses the conditional inference tree algorithm Hothorn, Hornik, & Zeileis (2006) as implemented in function ctree of R package partykit Hothorn & Zeileis (2015) for rule induction. The main reason is that it does not present with a selection bias towards variables with a greater number of possible cut points. Yet, use of ctree brings a relatively heavy computational load:

airq <- airquality[complete.cases(airquality), ]
airq$Month <- factor(airq$Month)
library("pre")
set.seed(42)
system.time(airq.ens <- pre(Ozone ~ ., data = airq))

##    user  system elapsed 
##    2.74    0.01    2.75

summary(airq.ens)

## 
## Final ensemble with cv error within 1se of minimum: 
## 
##   lambda =  3.229132
##   number of terms = 13
##   mean cv error (se) = 336.2188 (95.24635)
## 
##   cv error type : Mean-Squared Error

Computational load can be substantially reduced by employing the CART algorithm of Breiman, Friedman, Olshen, & Stone (1984) as implemented in function rpart from the package of the same name of Therneau & Atkinson (2022). This can be specified through the tree.unbiased argument:

set.seed(42)
system.time(airq.ens.cart <- pre(Ozone ~ ., data = airq, tree.unbiased = FALSE))

##    user  system elapsed 
##    1.67    0.03    1.70

summary(airq.ens.cart)

## 
## Final ensemble with cv error within 1se of minimum: 
## 
##   lambda =  1.935814
##   number of terms = 23
##   mean cv error (se) = 287.7377 (86.43107)
## 
##   cv error type : Mean-Squared Error

Note, however, that the variable selection induced by fitting CART trees may also present in the final ensemble. Furthermore, use of CART trees will tend to result in more complex ensembles, because the default stopping criterion in rpart is considerably less conservative than that of ctree. As a result, many more rules may be created and retained.

Maximum rule depth

Reducing tree (and therby rule) depth will reduce computational load of both rule fitting and estimation of the final ensemble:

set.seed(42)
system.time(airq.ens.md <- pre(Ozone ~ ., data = airq, maxdepth = 1L))

##    user  system elapsed 
##    2.26    0.05    2.33

summary(airq.ens.md)

## 
## Final ensemble with cv error within 1se of minimum: 
## 
##   lambda =  1.676698
##   number of terms = 14
##   mean cv error (se) = 424.1761 (126.9922)
## 
##   cv error type : Mean-Squared Error

Likely, reducing the maximum depth will improve interpretability, but may decrease predictive accuracy for the final ensemble.

Number of trees

By default, 500 trees are generated. Computation time can be reduced substantially by reducing the number of trees. This may of course negatively impact predictive accuracy. When using a smaller number of trees, it is likely beneficial to increase the learning rate (learnrate = .01, by default) accordingly:

set.seed(42)
system.time(airq.ens.nt <- pre(Ozone ~ ., data = airq, ntrees = 100L, learnrate = .05))

##    user  system elapsed 
##    0.83    0.01    0.85

summary(airq.ens.nt)

## 
## Final ensemble with cv error within 1se of minimum: 
## 
##   lambda =  1.935814
##   number of terms = 11
##   mean cv error (se) = 276.9282 (69.1872)
## 
##   cv error type : Mean-Squared Error

Parallel computation

For example, parallel computation can be employed by specifying par.final = TRUE in the call to pre (and registering parallel beforehand, e.g., using doMC). Parallel computation will not affect performance of the final ensemble. Note that parallel computation will only reduce computation time for datasets with a (very) large number of observations. For smaller datasets, use of parallel computation may even be increased computation time.

Number of cross-validation folds

The number of cross-validation repetitions can be also be reduced, but this will likely affect predictive performance of the final ensemble.

set.seed(42)
system.time(airq.ens.nf <- pre(Ozone ~ ., data = airq, nfolds = 5L))

##    user  system elapsed 
##    2.67    0.00    2.68

summary(airq.ens.nf)

## 
## Final ensemble with cv error within 1se of minimum: 
## 
##   lambda =  2.559032
##   number of terms = 13
##   mean cv error (se) = 307.2755 (105.2568)
## 
##   cv error type : Mean-Squared Error