Genomic transcription regulatory element location analysis via poisson weighted lasso

The distances between DNA Transcription Regulatory Elements (TRE) provide important clues to their dependencies and function within the gene regulation process. However, the locations of those TREs as well as their cross distances between occurrences are stochastic, in part due to the inherent limitations of Next Generation Sequencing methods used to localize them, in part due to biology itself. This paper describes a novel approach to analyzing these locations and their cross distances even at long range via a Poisson random convolution. The resulting deconvolution problem is ill-posed, and sparsity regularization is used to offset this challenge. Unlike previous work on sparse Poisson inverse problems, this paper adopts a weighted LASSO estimator with data-dependent weights calculated using concentration inequalities that account for the Poisson noise. This method exhibits better squared error performance than the classical (unweighted) LASSO both in theoretical performance bounds and in simulation studies, and can easily be computed using off-the-shelf LASSO solvers.