论文标题
通过将数据通过少量锚点移动，使运输更加健壮和可解释
Making transport more robust and interpretable by moving data through a small number of anchor points
论文作者
论文摘要
最佳运输（OT）是一种广泛使用的技术，用于分配对齐，并在整个机器学习，图形和视力社区中进行了应用。但是，如果没有任何其他关于跨端口的结构假设，那么OT可能会对异常值或噪声脆弱，尤其是在高维度上。在这里，我们介绍了一种新形式的结构化ot，该形式同时学习数据中的低维结构，同时利用此结构来解决对齐任务。与OT相比，最终的运输计划具有更好的结构性解释性，突出了各个数据点与局部几何形状之间的连接，并且对噪声和采样更强大。我们将方法应用于合成和真实数据集，我们表明我们的方法可以促进在嘈杂的设置中对齐，并且可以用于纠正和解释域移动。
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can be fragile to outliers or noise, especially in high dimensions. Here, we introduce a new form of structured OT that simultaneously learns low-dimensional structure in data while leveraging this structure to solve the alignment task. Compared with OT, the resulting transport plan has better structural interpretability, highlighting the connections between individual data points and local geometry, and is more robust to noise and sampling. We apply the method to synthetic as well as real datasets, where we show that our method can facilitate alignment in noisy settings and can be used to both correct and interpret domain shift.
