无需预设样本量，可实时停止的密度检验新方法。
Sequential Kernelized Stein Discrepancy
- 基于核化Stein分歧构造可连续监测的检验过程
- 在非归一化密度下保持错误发现率控制
- 适用于需要动态决策的机器学习场景
我们提出一种序列化的核化Stein分歧拟合优度检验方法，可用于对未归一化密度进行持续监测并自适应停止。样本量无需预先固定，研究者可在任意时刻决定是否停止或继续收集证据，同时控制错误发现率。与现有工作不同，本文不假设Stein核一致有界，而是利用其在任意点评估下的潜在有界性，定义检验鞅，进而构建新型序列检验。证明了检验的有效性，并给出了备择假设下财富过程对数增长的渐近下界。通过多种分布（包括受限玻尔兹曼机）的实验验证了该方法的实证性能。
原文摘要 · Abstract (English)
We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.
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