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Motivation: Modeling genetics of gene expression had been effective at highlighting cis-eQTLs, variants that control nearby transcripts. Yet, incorporation of long-range effects has been hampered by unfavora- ble statistical considerations. On the other end, expression alone has been modeled across tissues by decomposition into contributing factors, without any connection to genetics. Results: We develop MIxed-Layer Analysis of Genetics and Expression (MILAGE), a model that combines direct effects of cis-SNPs on nearby transcripts with trans-effects that control global factors of expression in a tissue-specific pattern. We develop judicious initialization of the model, followed by gradient descent learning. We present GPU-based implementation of the learner to enable computational feasibility in this otherwise intractably-large parameter space. We show the model to explain > 59% of test-set variation in GTEx data. The inferred genetically-regulated factors are consistent with expected tissue similarity.