  We introduce a powerful deep classifier two-sample test for high-dimensional
data based on E-values, called E-value Classifier Two-Sample Test (E-C2ST). Our
test combines ideas from existing work on split likelihood ratio tests and
predictive independence tests. The resulting E-values are suitable for
anytime-valid sequential two-sample tests. This feature allows for more
effective use of data in constructing test statistics. Through simulations and
real data applications, we empirically demonstrate that E-C2ST achieves
enhanced statistical power by partitioning datasets into multiple batches
beyond the conventional two-split (training and testing) approach of standard
classifier two-sample tests. This strategy increases the power of the test
while keeping the type I error well below the desired significance level.
