mlsanityData to 7 Oct 2026

Are you using test log-likelihood correctly?

arXiv 2212.00219 ↗First posted 1 Dec 2022stat.ML cs.LG stat.OTcited by 8

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Abstract (arXiv)

Test log-likelihood is commonly used to compare different models of the same data or different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test log-likelihood can contradict comparisons according to other objectives. Specifically, our examples show that (i) approximate Bayesian inference algorithms that attain higher test log-likelihoods need not also yield more accurate posterior approximations and (ii) conclusions about forecast accuracy based on test log-likelihood comparisons may not agree with conclusions based on root mean squared error.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 23 of its 43 references that are in the map. First posted on arXiv 1 Dec 2022.

Builds on

23 of 43 references.

References · 23

  1. 2019A Simple Baseline for Bayesian Uncertainty in Deep Learningcited by 555
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  3. 2013Black Box Variational Inferencecited by 317
  4. 2021What Are Bayesian Neural Network Posteriors Really Like?cited by 307
  5. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
  6. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
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  10. 2019Subspace Inference for Bayesian Deep Learningcited by 94
  11. 2016Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriorscited by 82
  12. 2019Quality of Uncertainty Quantification for Bayesian Neural Network Inferencecited by 58
11 more
  1. 2022Bayesian Model Selection, the Marginal Likelihood, and Generalizationcited by 56
  2. 2013Understanding predictive information criteria for Bayesian modelscited by 51
  3. 2020Global inducing point variational posteriors for Bayesian neural networks and deep Gaussian processescited by 43
  4. 2018Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priorscited by 35
  5. 2018SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradientcited by 34
  6. 2019Validated Variational Inference via Practical Posterior Error Boundscited by 26
  7. 2017Visualization in Bayesian workflowcited by 25
  8. 2021Neural Variational Gradient Descentcited by 19
  9. 2016Scalable Bayesian Learning of Recurrent Neural Networks for Language Modelingcited by 9
  10. 2020Reproducible Model Selection Using Bagged Posteriorscited by 7
  11. 2015High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Modelscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 2; 2026: 1.

8 papers.

  1. 2024Thermometer: Towards Universal Calibration for Large Language Modelscited by 38
  2. 2026Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?cited by 6
  3. 2024Practical multi-fidelity machine learning: fusion of deterministic and Bayesian modelscited by 4
  4. 2023Variational Bayesian Neural Networks via Resolution of Singularitiescited by 1
  5. 2024Temperature Optimization for Bayesian Deep Learningcited by 1
  6. 2024Pathwise Gradient Variance Reduction with Control Variates in Variational Inferencecited by 0
  7. 2025Understanding the Trade-offs in Accuracy and Uncertainty Quantification: Architecture and Inference Choices in Bayesian Neural Networkscited by 0
  8. 2025Adaptive Bayesian Data-Driven Design of Reliable Solder Joints for Micro-electronic Devicescited by 0