Batch greedy maximization of non-submodular functions: Guarantees and applications to experimental design

by   Jayanth Jagalur-Mohan, et al.

We propose and analyze batch greedy heuristics for cardinality constrained maximization of non-submodular non-decreasing set functions. Our theoretical guarantees are characterized by the combination of submodularity and supermodularity ratios. We argue how these parameters define tight modular bounds based on incremental gains, and provide a novel reinterpretation of the classical greedy algorithm using the minorize-maximize (MM) principle. Based on that analogy, we propose a new class of methods exploiting any plausible modular bound. In the context of optimal experimental design for linear Bayesian inverse problems, we bound the submodularity and supermodularity ratios when the underlying objective is based on mutual information. We also develop novel modular bounds for the mutual information in this setting, and describe certain connections to polyhedral combinatorics. We discuss how algorithms using these modular bounds relate to established statistical notions such as leverage scores and to more recent efforts such as volume sampling. We demonstrate our theoretical findings on synthetic problems and on a real-world climate monitoring example.



There are no comments yet.


page 11

page 31


Unified greedy approximability beyond submodular maximization

We consider classes of objective functions of cardinality constrained ma...

Robust Maximization of Non-Submodular Objectives

We study the problem of maximizing a monotone set function subject to a ...

Concave Aspects of Submodular Functions

Submodular Functions are a special class of set functions, which general...

Approximate Submodular Functions and Performance Guarantees

We consider the problem of maximizing non-negative non-decreasing set fu...

On Approximation Guarantees for Greedy Low Rank Optimization

We provide new approximation guarantees for greedy low rank matrix estim...

Differentiable Greedy Submodular Maximization: Guarantees, Gradient Estimators, and Applications

We consider making outputs of the greedy algorithm for monotone submodul...

Probably Approximately Correct Greedy Maximization

Submodular function maximization finds application in a variety of real-...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.