论文标题
用内核Stein差异测量运输
Measure Transport with Kernel Stein Discrepancy
论文作者
论文摘要
在贝叶斯环境中，测量运输是最近几种后近似算法的，其中试图将传输图从后近似到近似值最小化。 KLD是一种强大的收敛方式，需要允许措施的绝对连续性和放置可以在哪些允许的传输地图上进行限制。在这里，我们建议将内核Stein差异（KSD）最小化，仅要求以$ l^2 $感知的运输地图集合并证明如何验证这种情况。建立了相关后近似的一致性，并且经验结果表明，KSD具有竞争性和更灵活的KLD替代方法，可用于测量运输。
Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback--Leibler divergence (KLD) from the posterior to the approximation. The KLD is a strong mode of convergence, requiring absolute continuity of measures and placing restrictions on which transport maps can be permitted. Here we propose to minimise a kernel Stein discrepancy (KSD) instead, requiring only that the set of transport maps is dense in an $L^2$ sense and demonstrating how this condition can be validated. The consistency of the associated posterior approximation is established and empirical results suggest that KSD is competitive and more flexible alternative to KLD for measure transport.
