论文标题
通过最佳运输的Riemannian度量学习
Riemannian Metric Learning via Optimal Transport
论文作者
论文摘要
我们引入了一个基于最佳运输模型，用于从常见的riemannian歧管上的概率度量的横截面样品中学习度量张量。我们将标准作为空间变化的矩阵字段进行神经参数，并使用简单的交替方案有效地优化了模型的目标。使用此学到的度量，我们可以在歧管上的概率度量和计算大地测量学之间进行非线性插值。我们表明，使用我们的方法学到的指标提高了SCRNA和鸟类迁移数据的轨迹推断的质量，而几乎没有其他横截面数据。
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using a simple alternating scheme. Using this learned metric, we can nonlinearly interpolate between probability measures and compute geodesics on the manifold. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sectional data.
