The high heritability of amyotrophic lateral sclerosis (ALS) contrasts with its low molecular diagnosis rate post-genetic testing, pointing to potential undiscovered genetic factors. To aid the exploration of these factors, we introduced EpiOut, an algorithm to identify chromatin accessibility outliers that are regions exhibiting divergent accessibility from the population baseline in a single or few samples. Annotation of accessible regions with histone chromatin immunoprecipitation sequencing and Hi-C indicates that outliers are concentrated in functional loci, especially among promoters interacting with active enhancers. Across different omics levels, outliers are robustly replicated, and chromatin accessibility outliers are reliable predictors of gene expression outliers and aberrant protein levels. When promoter accessibility does not align with gene expression, our results indicate that molecular aberrations are more likely to be linked to post-transcriptional regulation rather than transcriptional regulation. Our findings demonstrate that the outlier detection paradigm can uncover dysregulated regions in rare diseases. EpiOut is available at github.com/uci-cbcl/EpiOut.