论文标题
使用最大平均差异对概率度量的最佳定量
Optimal quantisation of probability measures using maximum mean discrepancy
论文作者
论文摘要
一些研究人员提出，最大化最大平均差异（MMD）是一种量化概率度量的方法，即通过代表点集近似目标分布。我们考虑在离散候选集合中贪婪地最大程度地减少MMD的顺序算法。我们提出了一种新型的非侧重算法，为了提高统计效率并降低计算成本，我们研究了一种将该技术应用于每次迭代中的小型候选者的变体。当从目标中取样候选点时，建立了这些新算法的一致性及其迷你批次变体。我们在一系列重要的计算问题上演示了算法，包括优化贝叶斯立方体中的节点和马尔可夫链输出的变化。
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that greedily minimise MMD over a discrete candidate set. We propose a novel non-myopic algorithm and, in order to both improve statistical efficiency and reduce computational cost, we investigate a variant that applies this technique to a mini-batch of the candidate set at each iteration. When the candidate points are sampled from the target, the consistency of these new algorithm - and their mini-batch variants - is established. We demonstrate the algorithms on a range of important computational problems, including optimisation of nodes in Bayesian cubature and the thinning of Markov chain output.
