  This paper investigates the integration of gradient boosted decision trees
and varying coefficient models. We introduce the tree boosted varying
coefficient framework which justifies the implementation of decision tree
boosting as the nonparametric effect modifiers in varying coefficient models.
This framework requires no structural assumptions in the space containing the
varying coefficient covariates, is easy to implement, and keeps a balance
between model complexity and interpretability. To provide statistical
guarantees, we prove the asymptotic consistency of the proposed method under
the regression settings with $L^2$ loss. We further conduct a thorough
empirical study to show that the proposed method is capable of providing
accurate predictions as well as intelligible visual explanations.
