论文标题
基于正规化最佳运输的分布的高斯流程
Gaussian Processes on Distributions based on Regularized Optimal Transport
论文作者
论文摘要
我们根据最佳正则运输的双重公式在概率度量的空间上提出了一种新的内核。我们提出了希尔伯特人使用其凹痕电位嵌入概率空间的嵌入，这是双熵放松的最佳运输概率和参考度量$ \ Mathcal {u} $之间的解决方案。我们证明，这种构建能够使用Hilbert Norms获得有效的内核。我们证明，内核享有理论属性，例如普遍性和一些不变性，同时仍然在计算上可行。此外，我们为基于此内核的高斯过程的行为提供了理论保证。将经验性能与其他传统的内核选择进行了比较，以索引分布的过程。
We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are solutions of the dual entropic relaxed optimal transport between the probabilities and a reference measure $\mathcal{U}$. We prove that this construction enables to obtain a valid kernel, by using the Hilbert norms. We prove that the kernel enjoys theoretical properties such as universality and some invariances, while still being computationally feasible. Moreover we provide theoretical guarantees on the behaviour of a Gaussian process based on this kernel. The empirical performances are compared with other traditional choices of kernels for processes indexed on distributions.
