论文标题
最大平均差异的弱收敛量
Metrizing Weak Convergence with Maximum Mean Discrepancies
论文作者
论文摘要
本文表征了最大的平均差异（MMD），该差异将宽类核的概率度量的弱收敛性。更确切地说，我们证明，在局部紧凑的，非压缩的，Hausdorff空间，一个有界连续的Borel可测量内核K的MMD，其重现的内核Hilbert Space（RKHS）在Infinity上的功能在无穷大的效果上消失了有限的，常规的Borel措施。我们还纠正了Simon-Gabriel＆Schölkopf（JMLR，2018，THM.12）的先前结果，证明两者都存在有限的连续I.S.P.D.不会降低弱收敛性和有限的连续非i.s.p.d的内核。确实对其进行了Metrrize的内核。
This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD of a bounded continuous Borel measurable kernel k, whose reproducing kernel Hilbert space (RKHS) functions vanish at infinity, metrizes the weak convergence of probability measures if and only if k is continuous and integrally strictly positive definite (i.s.p.d.) over all signed, finite, regular Borel measures. We also correct a prior result of Simon-Gabriel & Schölkopf (JMLR, 2018, Thm.12) by showing that there exist both bounded continuous i.s.p.d. kernels that do not metrize weak convergence and bounded continuous non-i.s.p.d. kernels that do metrize it.
