mlsanityData to 14 Oct 2026

Universal Inference

arXiv 1912.11436 ↗First posted 24 Dec 2019math.ST stat.ME stat.MLcited by 44

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Abstract (arXiv)

We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a modified version of the usual likelihood ratio statistic, that we call "the split likelihood ratio test" (split LRT). The method is especially appealing for irregular statistical models. Canonical examples include mixture models and models that arise in shape-constrained inference. Constructing tests and confidence sets for such models is notoriously difficult. Typical inference methods, like the likelihood ratio test, are not useful in these cases because they have intractable limiting distributions. In contrast, the method we suggest works for any parametric model and also for some nonparametric models. The split LRT can also be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid p-values and confidence sequences.

Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Dec 2019.

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Citing papers per year: 2021: 5; 2022: 4; 2023: 9; 2024: 5; 2025: 8; 2026: 13.

44 papers.

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  1. 2022E-detectors: a nonparametric framework for sequential change detectioncited by 32
  2. 2021Time-uniform central limit theory and asymptotic confidence sequencescited by 29
  3. 2024A Unified Confidence Sequence for Generalized Linear Models, with Applications to Banditscited by 29
  4. 2023Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversioncited by 24
  5. 2023Sequential Predictive Two-Sample and Independence Testingcited by 21
  6. 2025E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testingcited by 17
  7. 2025WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingalescited by 16
  8. 2021Significance tests of feature relevance for a black-box learnercited by 15
  9. 2023Online multiple testing with e-valuescited by 12
  10. 2021Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inferencecited by 11
  11. 2022E-Valuating Classifier Two-Sample Testscited by 10
  12. 2023Likelihood Ratio Confidence Sets for Sequential Decision Makingcited by 10
32 more
  1. 2022Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observationscited by 9
  2. 2025Conditional Data Synthesis Augmentationcited by 8
  3. 2023Boosting Data Analytics With Synthetic Volume Expansioncited by 7
  4. 2025Optimistic Interior Point Methods for Sequential Hypothesis Testing by Bettingcited by 4
  5. 2026Testing For Distribution Shifts with Conditional Conformal Test Martingalescited by 4
  6. 2021Universal Inference Meets Random Projections: A Scalable Test for Log-concavitycited by 3
  7. 2024Combining Evidence Across Filtrationscited by 3
  8. 2026Adaptive auditing of AI systems with anytime-valid guaranteescited by 3
  9. 2026On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Modelscited by 3
  10. 2023Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variancecited by 2
  11. 2024From Conformal Predictions to Confidence Regionscited by 2
  12. 2025Fundamental bounds on efficiency-confidence trade-off for transductive conformal predictioncited by 2
  13. 2025E-Scores for (In)Correctness Assessment of Generative Model Outputscited by 2
  14. 2026Sequential Structure-Sensitive Residual Diagnostics for PDE Inverse Problemscited by 2
  15. 2022NetEffect: Discovery and Exploitation of Generalized Network Effectscited by 1
  16. 2023Valid Inference for Machine Learning Model Parameterscited by 1
  17. 2023Perturbation-Assisted Sample Synthesis: A Novel Approach for Uncertainty Quantificationcited by 1
  18. 2024Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictorscited by 1
  19. 2024XNB: Explainable Class-Specific NaIve-Bayes Classifiercited by 1
  20. 2025Optimal Anytime-Valid Tests for Composite Nullscited by 1
  21. 2026Principled Confidence Estimation for Deep Computed Tomographycited by 1
  22. 2026Online monotone density estimation and log-optimal calibrationcited by 1
  23. 2026Multi-Armed Sequential Hypothesis Testing by Bettingcited by 1
  24. 2026Semi-Supervised Hypothesis Testing by Betting on Predictionscited by 1
  25. 2021Comments on Leo Breiman's paper 'Statistical Modeling: The Two Cultures' (Statistical Science, 2001, 16(3), 199-231)cited by 0
  26. 2023Model-free generalized fiducial inferencecited by 0
  27. 2025On the Precise Asymptotics of Universal Inferencecited by 0
  28. 2026Finite-Sample Inference for Sparsely Permuted Linear Regressioncited by 0
  29. 2026Optimal sequential tests yield log-optimal e-processescited by 0
  30. 2026Bentkus-type asymptotic e-valuescited by 0
  31. 2026Sharp Limits for Honest Uncertainty in Hard-Budget Repeated Evaluationcited by 0
  32. 2026SLICE: Sequential Likelihood-Free Inference via Conformal E-Valuescited by 0