  With the advancement of data science, the collection of increasingly complex
datasets has become commonplace. In such datasets, the data dimension can be
extremely high, and the underlying data generation process can be unknown and
highly nonlinear. As a result, the task of making causal inference with
high-dimensional complex data has become a fundamental problem in many
disciplines, such as medicine, econometrics, and social science. However, the
existing methods for causal inference are frequently developed under the
assumption that the data dimension is low or that the underlying data
generation process is linear or approximately linear. To address these
challenges, this paper proposes a novel causal inference approach for dealing
with high-dimensional complex data. The proposed approach is based on deep
learning techniques, including sparse deep learning theory and stochastic
neural networks, that have been developed in recent literature. By using these
techniques, the proposed approach can address both the high dimensionality and
unknown data generation process in a coherent way. Furthermore, the proposed
approach can also be used when missing values are present in the datasets.
Extensive numerical studies indicate that the proposed approach outperforms
existing ones.
