Sequential Kernelized Stein Discrepancy
This provides a more flexible testing framework for practitioners in statistics and machine learning, though it is incremental as it builds on existing kernelized Stein discrepancy methods.
The paper tackles the problem of conducting goodness-of-fit tests for unnormalized densities with adaptive stopping, allowing continuous monitoring without a fixed sample size while controlling the false discovery rate. The result is a sequential test that avoids uniform boundedness constraints on the Stein kernel, with proven validity and asymptotic lower bounds for growth under alternatives, demonstrated empirically on distributions like restricted Boltzmann machines.
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.