  Most work on supervised learning research has focused on marginal
predictions. In decision problems, joint predictive distributions are essential
for good performance. Previous work has developed methods for assessing
low-order predictive distributions with inputs sampled i.i.d. from the testing
distribution. With low-dimensional inputs, these methods distinguish agents
that effectively estimate uncertainty from those that do not. We establish that
the predictive distribution order required for such differentiation increases
greatly with input dimension, rendering these methods impractical. To
accommodate high-dimensional inputs, we introduce \textit{dyadic sampling},
which focuses on predictive distributions associated with random \textit{pairs}
of inputs. We demonstrate that this approach efficiently distinguishes agents
in high-dimensional examples involving simple logistic regression as well as
complex synthetic and empirical data.
