# Discovering Genetic Networks Using Compressive Sensing

Consider a particular quantitative trait, and suppose we want to discover a function that maps how n participating genes (or even environmental influences) interact to express the trait. Under plausible assumptions of how they evolved, certain traits can be viewed as “smooth” functions on the n-dimensional Boolean lattice of possible genomes. This allows approximation of their Fourier transforms, i.e., their gene networks, as sparse, dominated by “low-frequency” components.

In turn, we can use compressive sensing theory to record the trait values from relatively few genomes, yet achieve accurate recovery of the gene network. Work is currently underway to see if empirical data fit the proposed model. If so, it could offer a radical reduction in the number of measurements — from exponential to polynomial in some cases — necessary to quantify the relationship between genomes and certain traits.

In the talk, we will review the Fourier theory connecting quantitative traits and their network of gene interactions, with both concrete and theoretical examples to motivate the idea of “low-level concentration.” If time permits, we will present new results from a trait data set of mouse myopia.

Matthew Herman is Chief Research Scientist at Fourier Genetics in Austin, TX. From 2011 to 2018 he was Senior Algorithm Engineer at InView Technology Corporation, doing R&D on the “single-pixel camera.” He received a Ph.D. in Applied Mathematics in 2009 from the University of California, Davis, focusing on applications of compressive sensing, such as radar and mismatches in the model of the sensing/system matrix — his work on radar was recognized with the 2013 Best Paper Award from the IEEE Signal Processing Society. In his spare time Matt plays the drums in different bands in Austin.