In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important problem in several machine learning applications where human understanding of the learning models and underlying data distribution is essential for decision making. We model the prototype selection problem as learning a sparse (empirical) probability distribution having the minimum OT distance from the target distribution. The learned probability measure supported on the chosen prototypes directly corresponds to their importance in representing the target data. We show that our objective function enjoys a key property of submodularity and propose an efficient greedy method that is both computationally fast and possess deterministic approximation guarantees. Empirical results on several real world benchmarks illustrate the efficacy of our approach.

翻译：在这项工作中,我们开发了一个基于最佳运输(OT)框架,选择最能代表特定目标数据集的信息性原型样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样像样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样像样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样样