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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.
Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly. In this paper, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estim
In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust nonlinear iterat
Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation o
High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We
Modern microbiome compositional data are often high-dimensional and exhibit complex dependency among microbial taxa. However, existing approaches to analyzing microbiome compositional data either do not adequately account for the complex dependency o