Effects of Linear Kernel Approximation in High-Dimensional Kernel Balancing

Determine how using a linear kernel approximation in high-dimensional kernel balancing affects covariate balance, treatment-effect estimation, and the resulting performance gains.

Background

The paper applies kernel balancing within causal forests and X-learners to improve covariate balance and conditional average treatment effect estimation, particularly under limited overlap. However, the computational cost of kernel balancing makes it infeasible in high-dimensional settings, motivating the use of a linear kernel approximation to reduce runtime.

The unresolved issue is whether this approximation changes the quality of covariate balance, the accuracy of treatment-effect estimates, or the performance improvements attributed to kernel balancing. Resolving this question would clarify the reliability and computational trade-offs of approximate kernel balancing in high-dimensional applications.