  Kernel two-sample testing is a useful statistical tool in determining whether
data samples arise from different distributions without imposing any parametric
assumptions on those distributions. However, raw data samples can expose
sensitive information about individuals who participate in scientific studies,
which makes the current tests vulnerable to privacy breaches. Hence, we design
a new framework for kernel two-sample testing conforming to differential
privacy constraints, in order to guarantee the privacy of subjects in the data.
Unlike existing differentially private parametric tests that simply add noise
to data, kernel-based testing imposes a challenge due to a complex dependence
of test statistics on the raw data, as these statistics correspond to
estimators of distances between representations of probability measures in
Hilbert spaces. Our approach considers finite dimensional approximations to
those representations. As a result, a simple chi-squared test is obtained,
where a test statistic depends on a mean and covariance of empirical
differences between the samples, which we perturb for a privacy guarantee. We
investigate the utility of our framework in two realistic settings and conclude
that our method requires only a relatively modest increase in sample size to
achieve a similar level of power to the non-private tests in both settings.
