Compute partial dependence for an oblique random forest. Partial dependence (PD) shows the expected prediction from a model as a function of a single predictor or multiple predictors. The expectation is marginalized over the values of all other predictors, giving something like a multivariable adjusted estimate of the model's prediction. You can compute partial dependence three ways using a random forest:
using in-bag predictions for the training data
using out-of-bag predictions for the training data
using predictions for a new set of data
See examples for more details
Usage
orsf_pd_oob(
object,
pred_spec,
pred_horizon = NULL,
pred_type = NULL,
expand_grid = TRUE,
prob_values = c(0.025, 0.5, 0.975),
prob_labels = c("lwr", "medn", "upr"),
boundary_checks = TRUE,
n_thread = NULL,
verbose_progress = NULL,
...
)
orsf_pd_inb(
object,
pred_spec,
pred_horizon = NULL,
pred_type = NULL,
expand_grid = TRUE,
prob_values = c(0.025, 0.5, 0.975),
prob_labels = c("lwr", "medn", "upr"),
boundary_checks = TRUE,
n_thread = NULL,
verbose_progress = NULL,
...
)
orsf_pd_new(
object,
pred_spec,
new_data,
pred_horizon = NULL,
pred_type = NULL,
na_action = "fail",
expand_grid = TRUE,
prob_values = c(0.025, 0.5, 0.975),
prob_labels = c("lwr", "medn", "upr"),
boundary_checks = TRUE,
n_thread = NULL,
verbose_progress = NULL,
...
)Arguments
- object
(ObliqueForest) a trained oblique random forest object (see orsf).
- pred_spec
(named list, pspec_auto, or data.frame).
If
pred_specis a named list, Each item in the list should be a vector of values that will be used as points in the partial dependence function. The name of each item in the list should indicate which variable will be modified to take the corresponding values.If
pred_specis created usingpred_spec_auto(), all that is needed is the names of variables to use (see pred_spec_auto).If
pred_specis adata.frame, columns will indicate variable names, values will indicate variable values, and partial dependence will be computed using the inputs on each row.
- pred_horizon
(double) Only relevent for survival forests. A value or vector indicating the time(s) that predictions will be calibrated to. E.g., if you were predicting risk of incident heart failure within the next 10 years, then
pred_horizon = 10.pred_horizoncan beNULLifpred_typeis'mort', since mortality predictions are aggregated over all event times- pred_type
(character) the type of predictions to compute. Valid Valid options for survival are:
'risk' : probability of having an event at or before
pred_horizon.'surv' : 1 - risk.
'chf': cumulative hazard function
'mort': mortality prediction
'time': survival time prediction
For classification:
'prob': probability for each class
For regression:
'mean': predicted mean, i.e., the expected value
- expand_grid
(logical) if
TRUE, partial dependence will be computed at all possible combinations of inputs inpred_spec. IfFALSE, partial dependence will be computed for each variable inpred_spec, separately.- prob_values
(numeric) a vector of values between 0 and 1, indicating what quantiles will be used to summarize the partial dependence values at each set of inputs.
prob_valuesshould have the same length asprob_labels. The quantiles are calculated based on predictions fromobjectat each set of values indicated bypred_spec.- prob_labels
(character) a vector of labels with the same length as
prob_values, with each label indicating what the corresponding value inprob_valuesshould be labelled as in summarized outputs.prob_labelsshould have the same length asprob_values.- boundary_checks
(logical) if
TRUE,pred_specwill be checked to make sure the requested values are between the 10th and 90th percentile in the object's training data. IfFALSE, these checks are skipped.- 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 will be printed to console. IfFALSE(the default), nothing will be printed.- ...
Further arguments passed to or from other methods (not currently used).
- new_data
a data.frame, tibble, or data.table to compute predictions in.
- na_action
(character) what should happen when
new_datacontains missing values (i.e.,NAvalues). Valid options are:'fail' : an error is thrown if
new_datacontainsNAvalues'omit' : rows in
new_datawith incomplete data will be dropped
Value
a data.table containing partial dependence values for the specified variable(s) and, if relevant, at the specified prediction horizon(s).
Details
Partial dependence has a number of known limitations and assumptions that users should be aware of (see Hooker, 2021). In particular, partial dependence is less intuitive when >2 predictors are examined jointly, and it is assumed that the feature(s) for which the partial dependence is computed are not correlated with other features (this is likely not true in many cases). Accumulated local effect plots can be used (see here) in the case where feature independence is not a valid assumption.
Examples
You can compute partial dependence and individual conditional expectations in three ways:
using in-bag predictions for the training data. In-bag partial dependence indicates relationships that the model has learned during training. This is helpful if your goal is to interpret the model.
using out-of-bag predictions for the training data. Out-of-bag partial dependence indicates relationships that the model has learned during training but using the out-of-bag data simulates application of the model to new data. This is helpful if you want to test your model’s reliability or fairness in new data but you don’t have access to a large testing set.
using predictions for a new set of data. New data partial dependence shows how the model predicts outcomes for observations it has not seen. This is helpful if you want to test your model’s reliability or fairness.
Classification
Begin by fitting an oblique classification random forest:
set.seed(329)
index_train <- sample(nrow(penguins_orsf), 150)
penguins_orsf_train <- penguins_orsf[index_train, ]
penguins_orsf_test <- penguins_orsf[-index_train, ]
fit_clsf <- orsf(data = penguins_orsf_train,
formula = species ~ .)Compute partial dependence using out-of-bag data for
flipper_length_mm = c(190, 210).
pred_spec <- list(flipper_length_mm = c(190, 210))
pd_oob <- orsf_pd_oob(fit_clsf, pred_spec = pred_spec)
pd_oob
#> Key: <class>
#> class flipper_length_mm mean lwr medn upr
#> <fctr> <num> <num> <num> <num> <num>
#> 1: Adelie 190 0.6176908 0.202278109 0.75856417 0.9810614
#> 2: Adelie 210 0.4338528 0.019173811 0.56489202 0.8648110
#> 3: Chinstrap 190 0.2114979 0.017643385 0.15211271 0.7215181
#> 4: Chinstrap 210 0.1803019 0.020108201 0.09679464 0.7035053
#> 5: Gentoo 190 0.1708113 0.001334861 0.02769695 0.5750201
#> 6: Gentoo 210 0.3858453 0.068685035 0.20717073 0.9532853Note that predicted probabilities are returned for each class and
probabilities in the mean column sum to 1 if you take the sum over
each class at a specific value of the pred_spec variables. For
example,
sum(pd_oob[flipper_length_mm == 190, mean])
#> [1] 1But this isn’t the case for the median predicted probability!
sum(pd_oob[flipper_length_mm == 190, medn])
#> [1] 0.9383738Regression
Begin by fitting an oblique regression random forest:
set.seed(329)
index_train <- sample(nrow(penguins_orsf), 150)
penguins_orsf_train <- penguins_orsf[index_train, ]
penguins_orsf_test <- penguins_orsf[-index_train, ]
fit_regr <- orsf(data = penguins_orsf_train,
formula = bill_length_mm ~ .)Compute partial dependence using new data for
flipper_length_mm = c(190, 210).
pred_spec <- list(flipper_length_mm = c(190, 210))
pd_new <- orsf_pd_new(fit_regr,
pred_spec = pred_spec,
new_data = penguins_orsf_test)
pd_new
#> flipper_length_mm mean lwr medn upr
#> <num> <num> <num> <num> <num>
#> 1: 190 42.96571 37.09805 43.69769 48.72301
#> 2: 210 45.66012 40.50693 46.31577 51.65163You can also let pred_spec_auto pick reasonable values like so:
pred_spec = pred_spec_auto(species, island, body_mass_g)
pd_new <- orsf_pd_new(fit_regr,
pred_spec = pred_spec,
new_data = penguins_orsf_test)
pd_new
#> species island body_mass_g mean lwr medn upr
#> <fctr> <fctr> <num> <num> <num> <num> <num>
#> 1: Adelie Biscoe 3200 40.31374 37.24373 40.31967 44.22824
#> 2: Chinstrap Biscoe 3200 45.10582 42.63342 45.10859 47.60119
#> 3: Gentoo Biscoe 3200 42.81649 40.19221 42.55664 46.84035
#> 4: Adelie Dream 3200 40.16219 36.95895 40.34633 43.90681
#> 5: Chinstrap Dream 3200 46.21778 43.53954 45.90929 49.19173
#> ---
#> 41: Chinstrap Dream 5300 48.48139 46.36282 48.25679 51.02996
#> 42: Gentoo Dream 5300 45.91819 43.62832 45.54110 49.91622
#> 43: Adelie Torgersen 5300 42.92879 40.66576 42.31072 46.76406
#> 44: Chinstrap Torgersen 5300 46.59576 44.80400 46.49196 49.03906
#> 45: Gentoo Torgersen 5300 45.11384 42.95190 44.51289 49.27629By default, all combinations of all variables are used. However, you can also look at the variables one by one, separately, like so:
pd_new <- orsf_pd_new(fit_regr,
expand_grid = FALSE,
pred_spec = pred_spec,
new_data = penguins_orsf_test)
pd_new
#> variable value level mean lwr medn upr
#> <char> <num> <char> <num> <num> <num> <num>
#> 1: species NA Adelie 41.90271 37.10417 41.51723 48.51478
#> 2: species NA Chinstrap 47.11314 42.40419 46.96478 51.51392
#> 3: species NA Gentoo 44.37038 39.87306 43.89889 51.21635
#> 4: island NA Biscoe 44.21332 37.22711 45.27862 51.21635
#> 5: island NA Dream 44.43354 37.01471 45.57261 51.51392
#> 6: island NA Torgersen 43.29539 37.01513 44.26924 49.84391
#> 7: body_mass_g 3200 <NA> 42.84625 37.03978 43.95991 49.19173
#> 8: body_mass_g 3550 <NA> 43.53326 37.56730 44.43756 50.47092
#> 9: body_mass_g 3975 <NA> 44.30431 38.31567 45.22089 51.50683
#> 10: body_mass_g 4700 <NA> 45.22559 39.88199 46.34680 51.18955
#> 11: body_mass_g 5300 <NA> 45.91412 40.84742 46.95327 51.48851And you can also bypass all the bells and whistles by using your own
data.frame for a pred_spec. (Just make sure you request values that
exist in the training data.)
custom_pred_spec <- data.frame(species = 'Adelie',
island = 'Biscoe')
pd_new <- orsf_pd_new(fit_regr,
pred_spec = custom_pred_spec,
new_data = penguins_orsf_test)
pd_new
#> species island mean lwr medn upr
#> <fctr> <fctr> <num> <num> <num> <num>
#> 1: Adelie Biscoe 41.98024 37.22711 41.65252 48.51478Survival
Begin by fitting an oblique survival random forest:
set.seed(329)
index_train <- sample(nrow(pbc_orsf), 150)
pbc_orsf_train <- pbc_orsf[index_train, ]
pbc_orsf_test <- pbc_orsf[-index_train, ]
fit_surv <- orsf(data = pbc_orsf_train,
formula = Surv(time, status) ~ . - id,
oobag_pred_horizon = 365.25 * 5)Compute partial dependence using in-bag data for bili = c(1,2,3,4,5):
pd_train <- orsf_pd_inb(fit_surv, pred_spec = list(bili = 1:5))
pd_train
#> pred_horizon bili mean lwr medn upr
#> <num> <num> <num> <num> <num> <num>
#> 1: 1826.25 1 0.2566200 0.02234786 0.1334170 0.8918909
#> 2: 1826.25 2 0.3121392 0.06853733 0.1896849 0.9204338
#> 3: 1826.25 3 0.3703242 0.11409793 0.2578505 0.9416791
#> 4: 1826.25 4 0.4240692 0.15645214 0.3331057 0.9591581
#> 5: 1826.25 5 0.4663670 0.20123406 0.3841700 0.9655296If you don’t have specific values of a variable in mind, let
pred_spec_auto pick for you:
pd_train <- orsf_pd_inb(fit_surv, pred_spec_auto(bili))
pd_train
#> pred_horizon bili mean lwr medn upr
#> <num> <num> <num> <num> <num> <num>
#> 1: 1826.25 0.55 0.2481444 0.02035041 0.1242215 0.8801444
#> 2: 1826.25 0.70 0.2502831 0.02045039 0.1271039 0.8836536
#> 3: 1826.25 1.50 0.2797763 0.03964900 0.1601715 0.9041584
#> 4: 1826.25 3.50 0.3959349 0.13431288 0.2920400 0.9501230
#> 5: 1826.25 7.25 0.5351935 0.28064629 0.4652185 0.9783000Specify pred_horizon to get partial dependence at each value:
pd_train <- orsf_pd_inb(fit_surv, pred_spec_auto(bili),
pred_horizon = seq(500, 3000, by = 500))
pd_train
#> pred_horizon bili mean lwr medn upr
#> <num> <num> <num> <num> <num> <num>
#> 1: 500 0.55 0.0617199 0.000443399 0.00865419 0.5907104
#> 2: 1000 0.55 0.1418501 0.005793742 0.05572853 0.7360749
#> 3: 1500 0.55 0.2082505 0.013609478 0.09174558 0.8556319
#> 4: 2000 0.55 0.2679017 0.023047689 0.14574169 0.8910549
#> 5: 2500 0.55 0.3179617 0.063797305 0.20254500 0.9017710
#> ---
#> 26: 1000 7.25 0.3264627 0.135343689 0.25956791 0.8884333
#> 27: 1500 7.25 0.4641265 0.218208755 0.38787435 0.9702903
#> 28: 2000 7.25 0.5511761 0.293367409 0.48427730 0.9812413
#> 29: 2500 7.25 0.6200238 0.371965247 0.56954399 0.9845058
#> 30: 3000 7.25 0.6803482 0.425128031 0.64642318 0.9888637vector-valued pred_horizon input comes with minimal extra
computational cost. Use a fine grid of time values and assess whether
predictors have time-varying effects. (see partial dependence vignette
for example)