Graduate School and Research Center in Digital Sciences

Submodularity in action: From machine learning to signal processing applications

Tohidi, Ehsan; Amiri, Rouhollah; Coutino, Mario; Gesbert, David; Leus, Geert; Karbasi, Amin

IEEE Signal Processing Magazine, June 2020

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the wellknown convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: (i) relaxation into the continuous domain to obtain an approximate solution, or (ii) development of a tailored algorithm that applies directly in the discrete domain. In both approaches, worst-case performance guarantees are often hard to establish. Furthermore, they are often complex, thus not practical for large-scale problems. In this paper, we show how certain scenarios lend themselves to exploiting submodularity so as to construct scalable solutions with provable worst-case performance guarantees. We introduce a variety of submodularfriendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization. With a mixture of theory and practice, we present different flavors of submodularity accompanying illustrative real-world case studies from modern SP and ML. In all cases, optimization algorithms are presented, along with hints on how optimality guarantees can be established.

Document Arxiv Bibtex

Title:Submodularity in action: From machine learning to signal processing applications
Type:Journal
Language:English
City:
Date:
Department:Communication systems
Eurecom ref:6296
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Bibtex: @article{EURECOM+6296, year = {2020}, month = {06}, title = {{S}ubmodularity in action: {F}rom machine learning to signal processing applications}, author = {{T}ohidi, {E}hsan and {A}miri, {R}ouhollah and {C}outino, {M}ario and {G}esbert, {D}avid and {L}eus, {G}eert and {K}arbasi, {A}min}, journal = {{IEEE} {S}ignal {P}rocessing {M}agazine, {J}une 2020}, url = {http://www.eurecom.fr/publication/6296} }
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