  Causal inference plays an important role in under standing the underlying
mechanisation of the data generation process across various domains. It is
challenging to estimate the average causal effect and individual causal effects
from observational data with high-dimensional covariates due to the curse of
dimension and the problem of data sufficiency. The existing matching methods
can not effectively estimate individual causal effect or solve the problem of
dimension curse in causal inference. To address this challenge, in this work,
we prove that the reduced set by sufficient dimension reduction (SDR) is a
balance score for confounding adjustment. Under the theorem, we propose to use
an SDR method to obtain a reduced representation set of the original covariates
and then the reduced set is used for the matching method. In detail, a
non-parametric model is used to learn such a reduced set and to avoid model
specification errors. The experimental results on real-world datasets show that
the proposed method outperforms the compared matching methods. Moreover, we
conduct an experiment analysis and the results demonstrate that the reduced
representation is enough to balance the imbalance between the treatment group
and control group individuals.
