Conditional independence provides a way to understand causal relationships
among the variables of interest. An underlying system may exhibit more
fine-grained causal relationships especially between a variable and its
parents, which will be called the local independence relationships. One of the
most widely studied local relationships is Context-Specific Independence (CSI),
which holds in a specific assignment of conditioned variables. However, its
applicability is often limited since it does not allow continuous variables:
data conditioned to the specific value of a continuous variable contains few
instances, if not none, making it infeasible to test independence. In this
work, we define and characterize the local independence relationship that holds
in a specific set of joint assignments of parental variables, which we call
context-set specific independence (CSSI). We then provide a canonical
representation of CSSI and prove its fundamental properties. Based on our
theoretical findings, we cast the problem of discovering multiple CSSI
relationships in a system as finding a partition of the joint outcome space.
Finally, we propose a novel method, coined neural contextual decomposition
(NCD), which learns such partition by imposing each set to induce CSSI via
modeling a conditional distribution. We empirically demonstrate that the
proposed method successfully discovers the ground truth local independence
relationships in both synthetic dataset and complex system reflecting the
real-world physical dynamics.

通过建模条件分布，本文提出了一种名为神经上下文分解（NCD）的方法，用于发现系统中多个上下文集特定独立性关系，并通过在合成数据集和反映现实世界物理动力学的复杂系统中的实证演示，成功地发现了真实的局部独立性关系。