  In many scientific fields such as biology, psychology and sociology, there is
an increasing interest in estimating the causal effect of a matrix exposure on
an outcome. Covariate balancing is crucial in causal inference and both exact
balancing and approximate balancing methods have been proposed in the past
decades. However, due to the large number of constraints, it is difficult to
achieve exact balance or to select the threshold parameters for approximate
balancing methods when the treatment is a matrix. To meet these challenges, we
propose the weighted Euclidean balancing method, which approximately balance
covariates from an overall perspective. This method is also applicable to
high-dimensional covariates scenario. Both parametric and nonparametric methods
are proposed to estimate the causal effect of matrix treatment and theoretical
properties of the two estimations are provided. Furthermore, the simulation
results show that the proposed method outperforms other methods in various
cases. Finally, the method is applied to investigating the causal relationship
between children's participation in various training courses and their IQ. The
results show that the duration of attending hands-on practice courses for
children at 6-9 years old has a siginificantly positive impact on children's
IQ.
