# Yes, but Did It Work?: Evaluating Variational Inference

arXiv: https://arxiv.org/abs/1802.02538 · HTML: https://mlsanity.com/paper/1802.02538/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2018.

## Built on by (most cited first, 30 of 53)

- [Challenges and Opportunities in High-dimensional Variational Inference](https://mlsanity.com/paper/2103.01085/) (2021)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [Provable convergence guarantees for black-box variational inference](https://mlsanity.com/paper/2306.03638/) (2023)
- [Pathfinder: Parallel quasi-Newton variational inference](https://mlsanity.com/paper/2108.03782/) (2021)
- [On the Convergence of Black-Box Variational Inference](https://mlsanity.com/paper/2305.15349/) (2023)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [q-Paths: Generalizing the Geometric Annealing Path using Power Means](https://mlsanity.com/paper/2107.00745/) (2021)
- [ProbNeRF: Uncertainty-Aware Inference of 3D Shapes from 2D Images](https://mlsanity.com/paper/2210.17415/) (2022)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [STiL: Semi-supervised Tabular-Image Learning for Comprehensive Task-Relevant Information Exploration in Multimodal Classification](https://mlsanity.com/paper/2503.06277/) (2025)
- [PriorVAE: Encoding spatial priors with VAEs for small-area estimation](https://mlsanity.com/paper/2110.10422/) (2021)
- [Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs](https://mlsanity.com/paper/2403.13748/) (2024)
- [Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrix](https://mlsanity.com/paper/2410.11067/) (2024)
- [Toward a Taxonomy of Trust for Probabilistic Machine Learning](https://mlsanity.com/paper/2112.03270/) (2021)
- [Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport](https://mlsanity.com/paper/2202.01841/) (2022)
- [Variational Latent Branching Model for Off-Policy Evaluation](https://mlsanity.com/paper/2301.12056/) (2023)
- [Practical and Matching Gradient Variance Bounds for Black-Box Variational Bayesian Inference](https://mlsanity.com/paper/2303.10472/) (2023)
- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [Monotonic Alpha-divergence Minimisation for Variational Inference](https://mlsanity.com/paper/2103.05684/) (2021)
- [A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms](https://mlsanity.com/paper/2204.06043/) (2022)
- [Variational Inference with Coverage Guarantees in Simulation-Based Inference](https://mlsanity.com/paper/2305.14275/) (2023)
- [Forward chi2 Divergence Based Variational Importance Sampling](https://mlsanity.com/paper/2311.02516/) (2023)
- [An Easy to Interpret Diagnostic for Approximate Inference: Symmetric Divergence Over Simulations](https://mlsanity.com/paper/2103.01030/) (2021)
- [Bernstein Flows for Flexible Posteriors in Variational Bayes](https://mlsanity.com/paper/2202.05650/) (2022)
- [Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature](https://mlsanity.com/paper/2303.05263/) (2023)
- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)
- [Posterior SBC: Simulation-Based Calibration Checking Conditional on Data](https://mlsanity.com/paper/2502.03279/) (2025)
- [Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetry](https://mlsanity.com/paper/2511.01064/) (2025)
- [Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference](https://mlsanity.com/paper/2203.03353/) (2022)
- [Scalable Semi-Modular Inference with Variational Meta-Posteriors](https://mlsanity.com/paper/2204.00296/) (2022)

## Abstract (arXiv)

While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement for joint distributions, while simultaneously improving the error in the estimate. The variational simulation-based calibration (VSBC) assesses the average performance of point estimates.