Fig. 1

Matrix factorization model to dissect eQTL effects across tissues. a Simplified examples of the relationship between eQTL effect sizes and factors. eQTL1: the effect of an eQTL in the spleen can be represented by a spleen-specific factor. eQTL2: the effect of an eQTL in all nine tissues can be summarized as a ubiquitous effect across all tissues. eQTL3: the effect of an eQTL in four brain tissues and three skin tissues can be summarized as the summation of brain-specific effect and skin-specific effect. b Learning factors underlying eQTL effects from GTEx. X matrix represents the effect size of eQTLs across tissues (see the “Methods” section). Patterns of tissue-sharing and tissue-specificity are observed in X. Matrix factorization is implemented to learn the factor matrix F, where each factor captures a pattern of eQTL effect sizes across tissues. c Matrix W represents the weights for each eQTL across tissues. Each weight is the reciprocal of the standard error. d The objective function in sn-spMF, where α and λ are sparsity penalty parameters, and D is the number of eQTLs