  Much of machine learning relies on comparing distributions with discrepancy
measures. Stein's method creates discrepancy measures between two distributions
that require only the unnormalized density of one and samples from the other.
Stein discrepancies can be combined with kernels to define kernelized Stein
discrepancies (KSDs). While kernels make Stein discrepancies tractable, they
pose several challenges in high dimensions. We introduce kernelized complete
conditional Stein discrepancies (KCC-SDs). Complete conditionals turn a
multivariate distribution into multiple univariate distributions. We show that
KCC-SDs distinguish distributions. To show the efficacy of KCC-SDs in
distinguishing distributions, we introduce a goodness-of-fit test using
KCC-SDs. We empirically show that KCC-SDs have higher power over baselines and
use KCC-SDs to assess sample quality in Markov chain Monte Carlo.
