cpi {cpi}  R Documentation 
A general test for conditional independence in supervised learning algorithms. Implements a conditional variable importance measure which can be applied to any supervised learning algorithm and loss function. Provides statistical inference procedures without parametric assumptions and applies equally well to continuous and categorical predictors and outcomes.
cpi(
task,
learner,
resampling = NULL,
test_data = NULL,
measure = NULL,
test = "t",
log = FALSE,
B = 1999,
alpha = 0.05,
x_tilde = NULL,
knockoff_fun = function(x) knockoff::create.second_order(as.matrix(x)),
groups = NULL,
verbose = FALSE
)
task 
The prediction 
learner 
The 
resampling 
Resampling strategy, 
test_data 
External validation data, use instead of resampling. 
measure 
Performance measure (loss). Per default, use MSE
( 
test 
Statistical test to perform, one of 
log 
Set to 
B 
Number of permutations for Fisher permutation test. 
alpha 
Significance level for confidence intervals. 
x_tilde 
Knockoff matrix or data.frame. If not given (the default), it will be
created with the function given in 
knockoff_fun 
Function to generate knockoffs. Default:

groups 
(Named) list with groups. Set to 
verbose 
Verbose output of resampling procedure. 
This function computes the conditional predictive impact (CPI) of one or several features on a given supervised learning task. This represents the mean error inflation when replacing a true variable with its knockoff. Large CPI values are evidence that the feature(s) in question have high conditional variable importance – i.e., the fitted model relies on the feature(s) to predict the outcome, even after accounting for the signal from all remaining covariates.
We build on the mlr3
framework, which provides a unified interface for
training models, specifying loss functions, and estimating generalization
error. See the package documentation for more info.
Methods are implemented for frequentist and Bayesian inference. The default
is test = "t"
, which is fast and powerful for most sample sizes. The
Wilcoxon signedrank test (test = "wilcox"
) may be more appropriate if
the CPI distribution is skewed, while the binomial test (test = "binom"
)
requires basically no assumptions but may have less power. For small sample
sizes, we recommend permutation tests (test = "fisher"
) or Bayesian
methods (test = "bayes"
). In the latter case, default priors are
assumed. See the BEST
package for more info.
For parallel execution, register a backend, e.g. with
doParallel::registerDoParallel()
.
For test = "bayes"
a list of BEST
objects. In any other
case, a data.frame
with a row for each feature and columns:
Variable/Group 
Variable/group name 
CPI 
CPI value 
SE 
Standard error 
test 
Testing method 
statistic 
Test statistic (only for ttest, Wilcoxon and binomial test) 
estimate 
Estimated mean (for ttest), median (for Wilcoxon test),
or proportion of 
p.value 
pvalue 
ci.lo 
Lower limit of (1  
Note that NA values are no error but a result of a CPI value of 0, i.e. no difference in model performance after replacing a feature with its knockoff.
Watson, D. & Wright, M. (2020). Testing conditional independence in supervised learning algorithms. Machine Learning, 110(8): 21072129. doi: 10.1007/s10994021060306
Candès, E., Fan, Y., Janson, L, & Lv, J. (2018). Panning for gold: 'modelX' knockoffs for high dimensional controlled variable selection. J. R. Statistc. Soc. B, 80(3): 551577. doi: 10.1111/rssb.12265
library(mlr3)
library(mlr3learners)
# Regression with linear model and holdout validation
cpi(task = tsk("mtcars"), learner = lrn("regr.lm"),
resampling = rsmp("holdout"))
# Classification with logistic regression, logloss and ttest
cpi(task = tsk("wine"),
learner = lrn("classif.glmnet", predict_type = "prob", lambda = 0.1),
resampling = rsmp("holdout"),
measure = "classif.logloss", test = "t")
# Use your own data (and outofbag loss with random forest)
mytask < as_task_classif(iris, target = "Species")
mylearner < lrn("classif.ranger", predict_type = "prob", keep.inbag = TRUE)
cpi(task = mytask, learner = mylearner,
resampling = "oob", measure = "classif.logloss")
# Group CPI
cpi(task = tsk("iris"),
learner = lrn("classif.ranger", predict_type = "prob", num.trees = 10),
resampling = rsmp("cv", folds = 3),
groups = list(Sepal = 1:2, Petal = 3:4))
## Not run:
# Bayesian testing
res < cpi(task = tsk("iris"),
learner = lrn("classif.glmnet", predict_type = "prob", lambda = 0.1),
resampling = rsmp("holdout"),
measure = "classif.logloss", test = "bayes")
plot(res$Petal.Length)
# Parallel execution
doParallel::registerDoParallel()
cpi(task = tsk("wine"),
learner = lrn("classif.glmnet", predict_type = "prob", lambda = 0.1),
resampling = rsmp("cv", folds = 5))
# Use sequential knockoffs for categorical features
# package available here: https://github.com/kormama1/seqknockoff
mytask < as_task_regr(iris, target = "Petal.Length")
cpi(task = mytask, learner = lrn("regr.ranger"),
resampling = rsmp("holdout"),
knockoff_fun = seqknockoff::knockoffs_seq)
## End(Not run)