Guarantees for Greedy Maximization of Non-submodular Functions with Applications

A. Organization of the Appendix Appendix B presents the proofs for our approximation guarantees and its tightness for the GREEDY algorithm. Appendix C provides details on existing notions of curvature and submodularity ratio, and relates it to the notions in this paper. Appendix D presents detailed proofs for bounding the submodularity ratio and curvature for various applications. Appendix E gives details on the classical SDP formulation of the Bayesian A-optimality objective. Appendix F provides proofs omitted in Section 6. Appendix G provides information on more applications, including sparse modeling with strongly convex loss functions, subset selection using the R2 objective and optimal budget allocation with combinatorial constraints. Appendix H provides experimental results on subset selection with the R2 objective and additional results on experimental design.