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 backpropagation. 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.
翻译:我们引入了一种最佳的运输模型,从一个通用的里曼多元体上不断演化的概率测量的跨部门样本中学习一公吨分母。我们将该测量仪作为空间变化矩阵字段进行神经平衡,并有效地利用反向分析优化我们模型的目标。我们利用这一所学的测量仪,可以在概率测量仪和对多元体的大地测量计算之间进行非线性内插。我们显示,使用我们的方法所学的测量仪提高了ScRNA和鸟类迁移数据的轨迹推断质量,而花费了很少额外的跨部门数据。