# Diagnostics for Conditional Density Models and Bayesian Inference Algorithms

arXiv: https://arxiv.org/abs/2102.10473 · HTML: https://mlsanity.com/paper/2102.10473/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2021.

## Built on by (most cited first, 28 of 28)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference](https://mlsanity.com/paper/2306.03580/) (2023)
- [Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference](https://mlsanity.com/paper/2107.03920/) (2021)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [Balancing Simulation-based Inference for Conservative Posteriors](https://mlsanity.com/paper/2304.10978/) (2023)
- [Interpretable Uncertainty Quantification in AI for HEP](https://mlsanity.com/paper/2208.03284/) (2022)
- [Validation Diagnostics for SBI algorithms based on Normalizing Flows](https://mlsanity.com/paper/2211.09602/) (2022)
- [Simultaneous identification of models and parameters of scientific simulators](https://mlsanity.com/paper/2305.15174/) (2023)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)
- [MD-split+: Practical Local Conformal Inference in High Dimensions](https://mlsanity.com/paper/2107.03280/) (2021)
- [Efficient identification of informative features in simulation-based inference](https://mlsanity.com/paper/2210.11915/) (2022)
- [A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models](https://mlsanity.com/paper/2410.02025/) (2024)
- [Re-calibrating Photometric Redshift Probability Distributions Using Feature-space Regression](https://mlsanity.com/paper/2110.15209/) (2021)
- [Simulation-based Inference with the Generalized Kullback-Leibler Divergence](https://mlsanity.com/paper/2310.01808/) (2023)
- [Conformal Calibration of Statistical Confidence Sets](https://mlsanity.com/paper/2411.19368/) (2024)
- [Improving Generalization and Uncertainty Quantification of Photometric Redshift Models](https://mlsanity.com/paper/2601.17222/) (2026)
- [Classification under Nuisance Parameters and Generalized Label Shift in Likelihood-Free Inference](https://mlsanity.com/paper/2402.05330/) (2024)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [PICZL: Image-based Photometric Redshifts for AGN](https://mlsanity.com/paper/2411.07305/) (2024)
- [LOCUS: A Distribution-Free Loss-Quantile Score for Risk-Aware Predictions](https://mlsanity.com/paper/2603.01971/) (2026)
- [Trustworthy Predictive Distributions for Tail Events with Semiparametric Diagnostic Transport Maps](https://mlsanity.com/paper/2603.11229/) (2026)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [How corner is a corner case? Percentile control for highway scenario generation](https://mlsanity.com/paper/2610.05003/) (2026)
- [Testing Conditional Distribution Equality Using Generative Models](https://mlsanity.com/paper/2610.20447/) (2026)

## Abstract (arXiv)

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.