  Because of the widespread use of black box prediction methods such as random
forests and neural nets, there is renewed interest in developing methods for
quantifying variable importance as part of the broader goal of interpretable
prediction. A popular approach is to define a variable importance parameter -
known as LOCO (Leave Out COvariates) - based on dropping covariates from a
regression model. This is essentially a nonparametric version of R-squared.
This parameter is very general and can be estimated nonparametrically, but it
can be hard to interpret because it is affected by correlation between
covariates. We propose a method for mitigating the effect of correlation by
defining a modified version of LOCO. This new parameter is difficult to
estimate nonparametrically, but we show how to estimate it using semiparametric
models.
