Gene expression as an intermediate molecular phenotype has been a focus of research interest. In particular, studies of expression quantitative trait loci (eQTL) have offered promise for understanding gene regulation through the discovery of genetic variants that explain variation in gene expression levels. Existing eQTL methods are designed for assessing the effects of common variants, but not rare variants. Here, we address the problem by establishing a novel analytical framework for evaluating the effects of rare or private variants on gene expression. Our method starts from the identification of outlier individuals that show markedly different gene expression from the majority of a population, and then reveals the contributions of private SNPs to the aberrant gene expression in these outliers. Using population-scale mRNA sequencing data, we identify outlier individuals using a multivariate approach. We find that outlier individuals are more readily detected with respect to gene sets that include genes involved in cellular regulation and signal transduction, and less likely to be detected with respect to the gene sets with genes involved in metabolic pathways and other fundamental molecular functions. Analysis of polymorphic data suggests that private SNPs of outlier individuals are enriched in the enhancer and promoter regions of corresponding aberrantly-expressed genes, suggesting a specific regulatory role of private SNPs, while the commonly-occurring regulatory genetic variants (i.e., eQTL SNPs) show little evidence of involvement. Additional data suggest that non-genetic factors may also underlie aberrant gene expression. Taken together, our findings advance a novel viewpoint relevant to situations wherein common eQTLs fail to predict gene expression when heritable, rare inter-individual variation exists. The analytical framework we describe, taking into consideration the reality of differential phenotypic robustness, may be valuable for investigating complex traits and conditions.