Validating Conditional Density Models and Bayesian Inference Algorithms

Conditional density models f(y|x), where x represents a potentially high-dimensional feature vector, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, such models can be difficult to calibrate. While existing validation techniques can determine whether an approximated conditional density is compatible overall with a data sample, they lack practical procedures for identifying, localizing, and interpreting the nature of (statistically significant) discrepancies over the entire feature space. In this paper, we present more discerning diagnostics such as (i) the "Local Coverage Test" (LCT), which is able to distinguish 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 a realistic application to parameter inference for galaxy images.