Partial Wasserstein Covering

TL;DR

This paper introduces a novel partial Wasserstein covering approach to identify dataset gaps by modeling it as a discrete optimization problem, and proposes efficient algorithms with theoretical guarantees.

Contribution

It formulates the partial Wasserstein covering as a submodular optimization problem and develops quasi-greedy algorithms with acceleration techniques for practical efficiency.

Findings

Successfully identifies missing patterns in real driving datasets.

Achieves efficient approximation with theoretical guarantees.

Demonstrates practical effectiveness in dataset gap filling.

Abstract

We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g., dataset obtained from actual applications). We model this task as a discrete optimization problem with partial Wasserstein divergence as an objective function. Although this problem is NP-hard, we prove that it satisfies the submodular property, allowing us to use a greedy algorithm with a 0.63 approximation. However, the greedy algorithm is still inefficient because it requires solving linear programming for each objective function evaluation. To overcome this inefficiency, we propose quasi-greedy algorithms that consist of a series of acceleration techniques, such as sensitivity analysis based on strong duality and the so-called C-transform in the optimal transport field. Experimentally, we demonstrate that we can efficiently fill in the gaps between the two datasets and find missing scene in real driving scenes datasets.