Data Summarization beyond Monotonicity: Non-monotone Two-Stage Submodular Maximization
This addresses data summarization challenges in domains like machine learning, but it is incremental as it generalizes existing monotone assumptions.
The paper tackles the problem of two-stage submodular maximization for data summarization by extending it to non-monotone functions, introducing the first constant-factor approximation algorithms.
The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set yields results comparable to those obtained over the original ground set. This problem has applications in various domains including data summarization. Existing studies often assume the monotonicity of the objective function, whereas our work pioneers the extension of this research to accommodate non-monotone submodular functions. We have introduced the first constant-factor approximation algorithms for this more general case.