Multi-Trek Separation in Linear Structural Equation Models

Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give correspondence structure higher-order cumulants and combinatorial graph. It has previously been shown that low rank covariance matrix corresponds to trek separation Generalizing this criterion sets vertices, characterize when determinants subtensors cumulant tensors vanish. This applies hidden are present as well. For instance, it allows us identify presence common cause $k$ observed variables.