  We propose two nonparametric statistical tests of goodness of fit for
conditional distributions: given a conditional probability density function
$p(y|x)$ and a joint sample, decide whether the sample is drawn from
$p(y|x)r_x(x)$ for some density $r_x$. Our tests, formulated with a Stein
operator, can be applied to any differentiable conditional density model, and
require no knowledge of the normalizing constant. We show that 1) our tests are
consistent against any fixed alternative conditional model; 2) the statistics
can be estimated easily, requiring no density estimation as an intermediate
step; and 3) our second test offers an interpretable test result providing
insight on where the conditional model does not fit well in the domain of the
covariate. We demonstrate the interpretability of our test on a task of
modeling the distribution of New York City's taxi drop-off location given a
pick-up point. To our knowledge, our work is the first to propose such
conditional goodness-of-fit tests that simultaneously have all these desirable
properties.
