Submodular meets Structured: Finding Diverse Subsets in Exponentially-Large Structured Item Sets

TL;DR

This paper introduces a novel approach combining submodular functions and high-order potentials to efficiently find diverse solutions in large structured output spaces, improving proposal quality in complex prediction tasks.

Contribution

It establishes a connection between submodular diversity functions and high-order potentials, enabling efficient approximate maximization in structured prediction problems.

Findings

Efficient sub-linear time approximate maximization achieved

Structured representations of marginal gains enable better diversity

Proposed methods lead to significantly improved proposals

Abstract

To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured prediction problems, this becomes a daunting task, as the solution space (image labelings, sentence parses, etc.) is exponentially large. We study greedy algorithms for finding a diverse subset of solutions in structured-output spaces by drawing new connections between submodular functions over combinatorial item sets and High-Order Potentials (HOPs) studied for graphical models. Specifically, we show via examples that when marginal gains of submodular diversity functions allow structured representations, this enables efficient (sub-linear time) approximate maximization by reducing the greedy augmentation step to inference in a factor graph with appropriately constructed HOPs. We discuss benefits, tradeoffs, and show that our constructions lead to significantly better proposals.