  Matching is one of the simplest approaches for estimating causal effects from
observational data. Matching techniques compare the observed outcomes across
pairs of individuals with similar covariate values but different treatment
statuses in order to estimate causal effects. However, traditional matching
techniques are unreliable given high-dimensional covariates due to the infamous
curse of dimensionality. To overcome this challenge, we propose a simple, fast,
yet highly effective approach to matching using Random Hyperplane Tessellations
(RHPT). First, we prove that the RHPT representation is an approximate
balancing score -- thus maintaining the strong ignorability assumption -- and
provide empirical evidence for this claim. Second, we report results of
extensive experiments showing that matching using RHPT outperforms traditional
matching techniques and is competitive with state-of-the-art deep learning
methods for causal effect estimation. In addition, RHPT avoids the need for
computationally expensive training of deep neural networks.
