Deep Submodular Peripteral Networks
This addresses a specific bottleneck in machine learning for applications like experimental design, but it is incremental as it builds on existing submodular and preference learning concepts.
The paper tackles the problem of learning submodular functions, which lack practical methods, by introducing deep submodular peripteral networks (DSPNs) and a training strategy using graded pairwise comparisons, showing efficacy in learning from costly target functions and superiority in experimental design and online streaming applications.
Submodular functions, crucial for various applications, often lack practical learning methods for their acquisition. Seemingly unrelated, learning a scaling from oracles offering graded pairwise preferences (GPC) is underexplored, despite a rich history in psychometrics. In this paper, we introduce deep submodular peripteral networks (DSPNs), a novel parametric family of submodular functions, and methods for their training using a GPC-based strategy to connect and then tackle both of the above challenges. We introduce newly devised GPC-style ``peripteral'' loss which leverages numerically graded relationships between pairs of objects (sets in our case). Unlike traditional contrastive learning, or RHLF preference ranking, our method utilizes graded comparisons, extracting more nuanced information than just binary-outcome comparisons, and contrasts sets of any size (not just two). We also define a novel suite of automatic sampling strategies for training, including active-learning inspired submodular feedback. We demonstrate DSPNs' efficacy in learning submodularity from a costly target submodular function and demonstrate its superiority both for experimental design and online streaming applications.