The Cartesian Gaussian Additive Noise Model for Causal Inference with Dependent Samples

We study the task of causal structure discovery from observational data when both the features and samples of our observation have causal structure. An example application is single-cell RNA-sequencing data, in which both the genes (features) and the cells (samples) interact in meaningful ways. We introduce the Cartesian Linear Gaussian Additive Noise Model to account for sample interactions, and generalize it to tensor-variate datasets with arbitrary interactions along each axis. We prove identifiability conditions analogous to those for the standard Linear Gaussian Additive Model, and produce a fast algorithm to learn the causal structure. Our method performs well on real data.