Thank you to the reviewers for their thorough evaluation of this submission. One reviewer stood out with a "reject" NeurIPS seemed to us to be this venue, and the quality of the reviews confirmed our impression. "other notions of diversity", "related sparse formulations", and "other sparse solvers". We will try to apply "significant This is actually some work in progress, with modifications (with a "group-lasso like formulation") required to the "figure 1, why random similarity performs better than the identify matrix? "Are there other applications beyond metagenomics?"

When analyzing communities of microorganisms from their sequenced DNA, an important task is taxonomic profiling: enumerating the presence and relative abundance of all organisms, or merely of all taxa, contained in the sample. This task can be tackled via compressive-sensing-based approaches, which favor communities featuring the fewest organisms among those consistent with the observed DNA data. Despite their successes, these parsimonious approaches sometimes conflict with biological realism by overlooking organism similarities. Here, we leverage a recently developed notion of biological diversity that simultaneously accounts for organism similarities and retains the optimization strategy underlying compressive-sensing-based approaches. We demonstrate that minimizing biological diversity still produces sparse taxonomic profiles and we experimentally validate superiority to existing compressive-sensing-based approaches.