Submodular Maximization via Gradient Ascent: The Case of Deep Submodular Functions.

We study the problem of maximizing deep submodular functions (DSFs) [13, 3] subject to a matroid constraint. DSFs are an expressive class of submodular functions that include, as strict subfamilies, the facility location, weighted coverage, and sums of concave composed with modular functions. We use a strategy similar to the continuous greedy approach [6], but we show that the multilinear extension of any DSF has a natural and computationally attainable concave relaxation that we can optimize using gradient ascent.

Submodular Generalized Matching for Peptide Identification in Tandem Mass Spectrometry.

Identification of spectra produced by a shotgun proteomics mass spectrometry experiment is commonly performed by searching the observed spectra against a peptide database. The heart of this search procedure is a score function that evaluates the quality of a hypothesized match between an observed spectrum and a theoretical spectrum corresponding to a particular peptide sequence. Accordingly, the success of a spectrum analysis pipeline depends critically upon this peptide-spectrum score function.