Background <p>Access to omics datasets, such as single-cell RNA-sequencing, enables us to estimate the regulatory networks governing the differentiation, proliferation, and interaction of cells in our body. Knowledge of such networks can give us valuable insight on the structure and progression of diseases; the difficulty is in estimating them. Most methods that estimate these networks either make an independence assumption (‘the cells in your body do not interact’), or ignore the directional nature of gene regulation.</p> Methodology <p>In this paper, we introduce the Cartesian Linear Gaussian Additive Noise Model to learn both cell-cell and gene-gene interactions. Our method is a statistical method; it is fit with maximum likelihood estimation, and we prove that a unique optimum always exists (under certain assumptions) using tools from high-dimensional statistics.</p> Results <p>Our method differs from prior work in its lack of an independence assumption; we show that this leads to a real improvement in gene regulatory network and cell network reconstructions relative to analogous independence-assuming methods.</p> Conclusions <p>We have developed and proved viable a novel method that learns directed gene regulatory networks, without assuming independence of cells. Our method is also extensible to more complicated omics datasets, such as longitudinal bulk RNA-sequencing datasets, through its ability to handle ‘tensor-variate’ datasets.</p> Trial Registration <p>Clinical trial number: not applicable.</p>