  There has been growing interest in the AI community for precise uncertainty
quantification. Conditional density models f(y|x), where x represents
potentially high-dimensional features, are an integral part of uncertainty
quantification in prediction and Bayesian inference. However, it is challenging
to assess conditional density estimates and gain insight into modes of failure.
While existing diagnostic tools can determine whether an approximated
conditional density is compatible overall with a data sample, they lack a
principled framework for identifying, locating, and interpreting the nature of
statistically significant discrepancies over the entire feature space. In this
paper, we present rigorous and easy-to-interpret diagnostics such as (i) the
"Local Coverage Test" (LCT), which distinguishes an arbitrarily misspecified
model from the true conditional density of the sample, and (ii) "Amortized
Local P-P plots" (ALP) which can quickly provide interpretable graphical
summaries of distributional differences at any location x in the feature space.
Our validation procedures scale to high dimensions and can potentially adapt to
any type of data at hand. We demonstrate the effectiveness of LCT and ALP
through a simulated experiment and applications to prediction and parameter
inference for image data.
