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：我们提出弹性多选择学习（rMCL），这是对多选择学习（MCL）方法的扩展，用于回归设置中的条件分布估计，其中每个训练输入可能对应多个目标样本。多选择学习是一种处理多模态密度估计的简单框架，采用赢家通吃（WTA）损失函数对一组假设进行训练。在回归场景中，现有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机制，该机制以输出空间的Voronoi剖分数学框架为基础，进而我们可以从中推导出概率解释。通过合成数据实验对rMCL进行实证验证后，我们进一步在声源定位问题上评估其优势，展示了其实用价值及其解释的相关性。