We introduce Resilient Multiple Choice Learning (rMCL), an extension of the MCL approach for conditional distribution estimation in regression settings where multiple targets may be sampled for each training input. Multiple Choice Learning is a simple framework to tackle multimodal density estimation, using the Winner-Takes-All (WTA) loss for a set of hypotheses. In regression settings, the existing MCL variants focus on merging the hypotheses, thereby eventually sacrificing the diversity of the predictions. In contrast, our method relies on a novel learned scoring scheme underpinned by a mathematical framework based on Voronoi tessellations of the output space, from which we can derive a probabilistic interpretation. After empirically validating rMCL with experiments on synthetic data, we further assess its merits on the sound source localization problem, demonstrating its practical usefulness and the relevance of its interpretation.

翻译：我们提出了弹性多选学习（rMCL），这是对多选学习（MCL）方法的扩展，用于回归场景中条件分布估计，其中每个训练输入可能对应多个采样目标。多选学习是一种处理多模态密度估计的简单框架，它使用一组假设的胜者全得（WTA）损失函数。在回归场景中，现有的MCL变体侧重于合并假设，从而最终牺牲了预测的多样性。相比之下，我们的方法依赖于一种新颖的基于学习的评分方案，该方案基于输出空间的沃罗诺伊镶嵌（Voronoi tessellations）的数学框架，并由此得出概率解释。通过在合成数据上进行实验验证rMCL后，我们进一步评估其在声源定位问题中的优点，展示了其实用价值及其解释的相关性。