Stein Points
Stein Points
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发表时间：
2018-03
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通讯作者：
W. Chen;Lester W. Mackey;Jackson Gorham;François‐Xavier Briol;C. Oates
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作者：
W. Chen;Lester W. Mackey;Jackson Gorham;François‐Xavier Briol;C. Oates
计算统计和机器学习中的一项重要任务是通过一组代表点 $\{x_i\}_{i=1}^n$ 支持的经验测量来近似后验分布 $p(x)$。本文重点关注点的选择本质上是确定性的方法，重点是当 $n$ 很小时实现准确的近似。为此，我们提出“斯坦因点”。这个想法是利用贪婪或条件梯度方法来迭代最小化经验测量和 $p(x)$ 之间的核 Stein 差异。我们的实证结果表明，斯坦因点能够以适度的计算成本精确逼近后验。此外，还提供了理论结果来确定该方法的收敛性。
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when $n$ is small. To this end, we present `Stein Points'. The idea is to exploit either a greedy or a conditional gradient method to iteratively minimise a kernel Stein discrepancy between the empirical measure and $p(x)$. Our empirical results demonstrate that Stein Points enable accurate approximation of the posterior at modest computational cost. In addition, theoretical results are provided to establish convergence of the method.