Distance-based supervised method, the minimal learning machine, constructs a predictive model from data by learning a mapping between input and output distance matrices. In this paper, we propose methods and evaluate how this technique and its core component, the distance mapping, can be adapted to multi-label learning. The proposed approach is based on combining the distance mapping with an inverse distance weighting. Although the proposal is one of the simplest methods in the multi-label learning literature, it achieves state-of-the-art performance for small to moderate-sized multi-label learning problems. Besides its simplicity, the proposed method is fully deterministic and its hyper-parameter can be selected via ranking loss-based statistic which has a closed form, thus avoiding conventional cross-validation-based hyper-parameter tuning. In addition, due to its simple linear distance mapping-based construction, we demonstrate that the proposed method can assess predictions' uncertainty for multi-label classification, which is a valuable capability for data-centric machine learning pipelines.

翻译：基于距离的监督方法——最小学习机，通过学习输入与输出距离矩阵之间的映射关系，从数据中构建预测模型。本文提出相应方法并评估该技术及其核心组件——距离映射——如何适应多标签学习任务。所提方法将距离映射与反距离加权相结合。尽管该方法是多标签学习文献中最简单的技术之一，但在小规模至中等规模的多标签学习问题上达到了最先进性能。除简洁性外，该方法具有完全确定性，其超参数可通过具有封闭形式的基于排序损失的统计量进行选择，从而避免传统的基于交叉验证的超参数调优。此外，由于采用简单的线性距离映射结构，我们证明该方法能够评估多标签分类的预测不确定性，这对以数据为中心的机器学习流水线而言是一种有价值的特性。