Estimate the importance of individual predictor variables using oblique random forests.
Usage
orsf_vi(
object,
group_factors = TRUE,
importance = NULL,
oobag_fun = NULL,
n_thread = NULL,
verbose_progress = NULL,
...
)
orsf_vi_negate(
object,
group_factors = TRUE,
oobag_fun = NULL,
n_thread = NULL,
verbose_progress = NULL,
...
)
orsf_vi_permute(
object,
group_factors = TRUE,
oobag_fun = NULL,
n_thread = NULL,
verbose_progress = NULL,
...
)
orsf_vi_anova(object, group_factors = TRUE, verbose_progress = NULL, ...)Arguments
- object
(ObliqueForest) a trained oblique random forest object (see orsf).
- group_factors
(logical) if
TRUE, the importance of factor variables will be reported overall by aggregating the importance of individual levels of the factor. IfFALSE, the importance of individual factor levels will be returned.- importance
(character) Indicate method for variable importance:
'anova': compute analysis of variance (ANOVA) importance
'negate': compute negation importance
'permute': compute permutation importance
- oobag_fun
(function) to be used for evaluating out-of-bag prediction accuracy after negating coefficients (if importance = 'negate') or permuting the values of a predictor (if importance = 'permute')
When
oobag_fun = NULL(the default), the evaluation statistic is selected based on tree typesurvival: Harrell's C-statistic (1982)
classification: Area underneath the ROC curve (AUC-ROC)
regression: Traditional prediction R-squared
if you use your own
oobag_funnote the following:oobag_funshould have three inputs:y_mat,w_vec, ands_vecFor survival trees,
y_matshould be a two column matrix with first column named 'time' and second named 'status'. For classification trees,y_matshould be a matrix with number of columns = number of distinct classes in the outcome. For regression,y_matshould be a matrix with one column.s_vecis a numeric vector containing predictionsoobag_funshould return a numeric output of length 1the same
oobag_funshould have been used when you createdobjectso that the initial value of out-of-bag prediction accuracy is consistent with the values that will be computed while variable importance is estimated.
For more details, see the out-of-bag vignette.
- n_thread
(integer) number of threads to use while computing predictions. Default is 0, which allows a suitable number of threads to be used based on availability.
- verbose_progress
(logical) if
TRUE, progress messages are printed in the console. IfFALSE(the default), nothing is printed.- ...
Further arguments passed to or from other methods (not currently used).
Value
orsf_vi functions return a named numeric vector.
Names of the vector are the predictor variables used by
objectValues of the vector are the estimated importance of the given predictor.
The returned vector is sorted from highest to lowest value, with higher values indicating higher importance.
Details
When an ObliqueForest object is grown with importance = 'anova',
'negate', or 'permute', the output will have a vector of importance
values based on the requested type of importance. However, orsf_vi()
can be used to compute variable importance after growing a forest
or to compute a different type of importance.
orsf_vi() is a general purpose function to extract or compute variable
importance estimates from an ObliqueForest object (see orsf).
orsf_vi_negate(), orsf_vi_permute(), and orsf_vi_anova() are wrappers
for orsf_vi(). The way these functions work depends on whether the
object they are given already has variable importance estimates in it
or not (see examples).
Variable importance methods
negation importance: Each variable is assessed separately by multiplying the variable's coefficients by -1 and then determining how much the model's performance changes. The worse the model's performance after negating coefficients for a given variable, the more important the variable. This technique is promising b/c it does not require permutation and it emphasizes variables with larger coefficients in linear combinations, but it is also relatively new and hasn't been studied as much as permutation importance. See Jaeger, (2023) for more details on this technique.
permutation importance: Each variable is assessed separately by randomly permuting the variable's values and then determining how much the model's performance changes. The worse the model's performance after permuting the values of a given variable, the more important the variable. This technique is flexible, intuitive, and frequently used. It also has several known limitations
analysis of variance (ANOVA) importance: A p-value is computed for each coefficient in each linear combination of variables in each decision tree. Importance for an individual predictor variable is the proportion of times a p-value for its coefficient is < 0.01. This technique is very efficient computationally, but may not be as effective as permutation or negation in terms of selecting signal over noise variables. See Menze, 2011 for more details on this technique.
Examples
ANOVA importance
The default variable importance technique, ANOVA, is calculated while you fit an oblique random forest ensemble.
fit <- orsf(pbc_orsf, Surv(time, status) ~ . - id)
fit
#> ---------- Oblique random survival forest
#>
#> Linear combinations: Accelerated Cox regression
#> N observations: 276
#> N events: 111
#> N trees: 500
#> N predictors total: 17
#> N predictors per node: 5
#> Average leaves per tree: 21.022
#> Min observations in leaf: 5
#> Min events in leaf: 1
#> OOB stat value: 0.84
#> OOB stat type: Harrell's C-index
#> Variable importance: anova
#>
#> -----------------------------------------ANOVA is the default because it is fast, but it may not be as decisive as the permutation and negation techniques for variable selection.
Raw VI values
the ‘raw’ variable importance values can be accessed from the fit object
fit$get_importance_raw()
#> [,1]
#> trt_placebo 0.06355042
#> age 0.23259259
#> sex_f 0.14700432
#> ascites_1 0.46791708
#> hepato_1 0.14349776
#> spiders_1 0.17371938
#> edema_0.5 0.17459191
#> edema_1 0.51197605
#> bili 0.40590758
#> chol 0.17666667
#> albumin 0.25972156
#> copper 0.28840580
#> alk.phos 0.10614251
#> ast 0.18327491
#> trig 0.12815626
#> platelet 0.09265648
#> protime 0.22656250
#> stage 0.20264766these are ‘raw’ because values for factors have not been aggregated into a single value. Currently there is one value for k-1 levels of a k level factor. For example, you can see edema_1 and edema_0.5 in the importance values above because edema is a factor variable with levels of 0, 0.5, and 1.
Collapse VI across factor levels
To get aggregated values across all levels of each factor,
access the
importanceelement from theorsffit:# this assumes you used group_factors = TRUE in orsf() fit$importance #> ascites bili edema copper albumin age protime #> 0.46791708 0.40590758 0.31115216 0.28840580 0.25972156 0.23259259 0.22656250 #> stage ast chol spiders sex hepato trig #> 0.20264766 0.18327491 0.17666667 0.17371938 0.14700432 0.14349776 0.12815626 #> alk.phos platelet trt #> 0.10614251 0.09265648 0.06355042use
orsf_vi()with group_factors set toTRUE(the default)orsf_vi(fit) #> ascites bili edema copper albumin age protime #> 0.46791708 0.40590758 0.31115216 0.28840580 0.25972156 0.23259259 0.22656250 #> stage ast chol spiders sex hepato trig #> 0.20264766 0.18327491 0.17666667 0.17371938 0.14700432 0.14349776 0.12815626 #> alk.phos platelet trt #> 0.10614251 0.09265648 0.06355042
Note that you can make the default returned importance values ungrouped
by setting group_factors to FALSE in the orsf_vi functions or the
orsf function.
Add VI to an oblique random forest
You can fit an oblique random forest without VI, then add VI later
fit_no_vi <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
importance = 'none')
# Note: you can't call orsf_vi_anova() on fit_no_vi because anova
# VI can only be computed while the forest is being grown.
orsf_vi_negate(fit_no_vi)
#> bili copper sex protime age stage
#> 0.130439814 0.051880867 0.038308025 0.025115249 0.023826061 0.020354822
#> albumin ascites chol ast spiders hepato
#> 0.019997729 0.015918292 0.013320469 0.010086726 0.007409116 0.007326714
#> edema trt alk.phos trig platelet
#> 0.006844435 0.003214544 0.002517057 0.002469545 0.001056829
orsf_vi_permute(fit_no_vi)
#> bili copper age ascites protime
#> 0.0592069141 0.0237362075 0.0136479213 0.0130805894 0.0123091354
#> stage albumin chol hepato ast
#> 0.0117177661 0.0106414724 0.0064501213 0.0058813969 0.0057753740
#> edema spiders sex trig platelet
#> 0.0052171180 0.0048427005 0.0023386947 0.0017883700 0.0013533691
#> alk.phos trt
#> 0.0006492029 -0.0009921507Oblique random forest and VI all at once
fit an oblique random forest and compute vi at the same time
fit_permute_vi <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
importance = 'permute')
# get the vi instantly (i.e., it doesn't need to be computed again)
orsf_vi_permute(fit_permute_vi)
#> bili copper ascites protime albumin
#> 0.0571305446 0.0243657146 0.0138318057 0.0133401675 0.0130746154
#> age stage chol ast spiders
#> 0.0123610374 0.0102963203 0.0077895394 0.0075250059 0.0048628813
#> edema hepato sex platelet trig
#> 0.0046003168 0.0039818730 0.0016891584 0.0012767063 0.0007324402
#> alk.phos trt
#> 0.0005128897 -0.0014443967You can still get negation VI from this fit, but it needs to be computed
orsf_vi_negate(fit_permute_vi)
#> bili copper sex protime stage age
#> 0.123331760 0.052544318 0.037291358 0.024977898 0.023239189 0.021934511
#> albumin ascites chol ast spiders edema
#> 0.020586632 0.014229536 0.014053040 0.012227048 0.007643156 0.006832766
#> hepato trt alk.phos trig platelet
#> 0.006301693 0.004348705 0.002371797 0.002309396 0.001347035Custom functions for VI
The default prediction accuracy functions work well most of the time:
fit_standard <- orsf(penguins_orsf, bill_length_mm ~ ., tree_seeds = 1)
# Default method for prediction accuracy with VI is R-squared
orsf_vi_permute(fit_standard)
#> species flipper_length_mm body_mass_g bill_depth_mm
#> 0.3725898166 0.3261834607 0.2225730676 0.1026569498
#> island sex year
#> 0.0876071687 0.0844807334 0.0006978493But sometimes you want to do something specific and the defaults just
won’t work. For these cases, you can compute VI with any function you’d
like to measure prediction accuracy by supplying a valid function to the
oobag_fun input. For example, we use mean absolute error below. Higher
values are considered good when aorsf computes prediction accuracy, so
we make our function return a pseudo R-squared based on mean absolute
error:
rsq_mae <- function(y_mat, w_vec, s_vec){
mae_standard <- mean(abs((y_mat - mean(y_mat)) * w_vec))
mae_fit <- mean(abs((y_mat - s_vec) * w_vec))
1 - mae_fit / mae_standard
}
fit_custom <- orsf_update(fit_standard, oobag_fun = rsq_mae)
# not much changes, but the difference between variables shrinks
# and the ordering of sex and island has swapped
orsf_vi_permute(fit_custom)
#> species flipper_length_mm body_mass_g bill_depth_mm
#> 0.206951751 0.193248912 0.140899603 0.076759148
#> sex island year
#> 0.073042331 0.050851073 0.003633365References
Harrell, E F, Califf, M R, Pryor, B D, Lee, L K, Rosati, A R (1982). "Evaluating the yield of medical tests." Jama, 247(18), 2543-2546.
Breiman, Leo (2001). "Random Forests." Machine Learning, 45(1), 5-32. ISSN 1573-0565.
Menze, H B, Kelm, Michael B, Splitthoff, N D, Koethe, Ullrich, Hamprecht, A F (2011). "On oblique random forests." In Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2011, Athens, Greece, September 5-9, 2011, Proceedings, Part II 22, 453-469. Springer.
Jaeger BC, Welden S, Lenoir K, Speiser JL, Segar MW, Pandey A, Pajewski NM (2023). "Accelerated and interpretable oblique random survival forests." Journal of Computational and Graphical Statistics, 1-16.