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

Diagnostics for Conditional Density Models and Bayesian Inference Algorithms