Unobserved discrete data are ubiquitous in many scientific disciplines, and
how to learn the causal structure of these latent variables is crucial for
uncovering data patterns. Most studies focus on the linear latent variable
model or impose strict constraints on latent structures, which fail to address
cases in discrete data involving non-linear relationships or complex latent
structures. To achieve this, we explore a tensor rank condition on contingency
tables for an observed variable set $\mathbf{X}_p$, showing that the rank is
determined by the minimum support of a specific conditional set (not necessary
in $\mathbf{X}_p$) that d-separates all variables in $\mathbf{X}_p$. By this,
one can locate the latent variable through probing the rank on different
observed variables set, and further identify the latent causal structure under
some structure assumptions. We present the corresponding identification
algorithm and conduct simulated experiments to verify the effectiveness of our
method. In general, our results elegantly extend the identification boundary
for causal discovery with discrete latent variables and expand the application
scope of causal discovery with latent variables.

通过对观察变量集 $X_p$ 的条件集的最小支持率进行张量秩条件探测，我们可以确定潜在变量的秩，并在某些结构假设下识别出潜在因果结构。