imp = predictorImportance(ens)
[imp,ma]
= predictorImportance(ens)
computes
estimates of predictor importance for imp
= predictorImportance(ens
)ens
by summing
these estimates over all weak learners in the ensemble. imp
has
one element for each input predictor in the data used to train this
ensemble. A high value indicates that this predictor is important
for ens
.
[
returns
a imp
,ma
]
= predictorImportance(ens
)P
byP
matrix with predictive
measures of association for P
predictors.

A regression ensemble created by 

A row vector with the same number of elements as the number
of predictors (columns) in 

A 
predictorImportance
computes estimates of predictor
importance for tree
by summing changes in the
mean squared error (MSE) due to splits on every predictor and dividing
the sum by the number of branch nodes. If the tree is grown without
surrogate splits, this sum is taken over best splits found at each
branch node. If the tree is grown with surrogate splits, this sum
is taken over all splits at each branch node including surrogate splits. imp
has
one element for each input predictor in the data used to train this
tree. At each node, MSE is estimated as node error weighted by the
node probability. Variable importance associated with this split is
computed as the difference between MSE for the parent node and the
total MSE for the two children.
The predictive measure of association is a value that indicates the similarity between decision rules that split observations. Among all possible decision splits that are compared to the optimal split (found by growing the tree), the best surrogate decision split yields the maximum predictive measure of association. The secondbest surrogate split has the secondlargest predictive measure of association.
Suppose x_{j} and x_{k} are predictor variables j and k, respectively, and j ≠ k. At node t, the predictive measure of association between the optimal split x_{j} < u and a surrogate split x_{k} < v is
$${\lambda}_{jk}=\frac{\text{min}\left({P}_{L},{P}_{R}\right)\left(1{P}_{{L}_{j}{L}_{k}}{P}_{{R}_{j}{R}_{k}}\right)}{\text{min}\left({P}_{L},{P}_{R}\right)}.$$
P_{L} is the proportion of observations in node t, such that x_{j} < u. The subscript L stands for the left child of node t.
P_{R} is the proportion of observations in node t, such that x_{j} ≥ u. The subscript R stands for the right child of node t.
$${P}_{{L}_{j}{L}_{k}}$$ is the proportion of observations at node t, such that x_{j} < u and x_{k} < v.
$${P}_{{R}_{j}{R}_{k}}$$ is the proportion of observations at node t, such that x_{j} ≥ u and x_{k} ≥ v.
Observations with missing values for x_{j} or x_{k} do not contribute to the proportion calculations.
λ_{jk} is a value in (–∞,1]. If λ_{jk} > 0, then x_{k} < v is a worthwhile surrogate split for x_{j} < u.
Element ma(i,j)
is the predictive measure
of association averaged over surrogate splits on predictor j
for
which predictor i
is the optimal split predictor.
This average is computed by summing positive values of the predictive
measure of association over optimal splits on predictor i
and
surrogate splits on predictor j
and dividing by
the total number of optimal splits on predictor i
,
including splits for which the predictive measure of association between
predictors i
and j
is negative.