Workflow of HYFA. The model receives as input a variable number of gene expression samples ${{{{\mathbf{x}}}}}_{i}^{(k)}$ corresponding to the collected tissues $k\in {{{\mathcal{T}}}}(i)$ of a given individual i . The samples ${{{{\mathbf{x}}}}}_{i}^{(k)}$ are fed through an encoder that computes low-dimensional representations ${{{{\mathbf{e}}}}}_{ij}^{(k)}$ for each metagene j ∈ 1, ..., M . A metagene is a latent, low-dimensional representation that captures certain gene expression patterns of the high-dimensional input sample. These representations are then used as hyperedge features in a message-passing neural network that operates on a hypergraph. In the hypergraph representation, each hyperedge labelled with ${{{{\mathbf{e}}}}}_{ij}^{(k)}$ connects an individual i with metagene j and tissue k if tissue k was collected for individual i , that is $k\in {{{\mathcal{T}}}}(i)$ . Through message passing, HYFA learns factorized representations of individual, tissue and metagene nodes. To infer the gene expression of an uncollected tissue u of individual i , the corresponding factorized representations are fed through an MLP that predicts low-dimensional features ${{{{\mathbf{e}}}}}_{ij}^{(u)}$ for each metagene j ∈ 1, ..., M . HYFA finally processes these latent representations through a decoder that recovers the uncollected gene expression sample ${\hat{{{{\mathbf{x}}}}}}_{i}^{(u)}$.
