# Universal Inference

arXiv: https://arxiv.org/abs/1912.11436 · HTML: https://mlsanity.com/paper/1912.11436/

## Key facts

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

## Built on by (most cited first, 30 of 44)

- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference](https://mlsanity.com/paper/2107.03920/) (2021)
- [E-Valuating Classifier Two-Sample Tests](https://mlsanity.com/paper/2210.13027/) (2022)
- [Likelihood Ratio Confidence Sets for Sequential Decision Making](https://mlsanity.com/paper/2311.04402/) (2023)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [Conditional Data Synthesis Augmentation](https://mlsanity.com/paper/2504.07426/) (2025)
- [Boosting Data Analytics With Synthetic Volume Expansion](https://mlsanity.com/paper/2310.17848/) (2023)
- [Optimistic Interior Point Methods for Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2502.07774/) (2025)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [Universal Inference Meets Random Projections: A Scalable Test for Log-concavity](https://mlsanity.com/paper/2111.09254/) (2021)
- [Combining Evidence Across Filtrations](https://mlsanity.com/paper/2402.09698/) (2024)
- [Adaptive auditing of AI systems with anytime-valid guarantees](https://mlsanity.com/paper/2605.07002/) (2026)
- [On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models](https://mlsanity.com/paper/2606.22391/) (2026)
- [Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variance](https://mlsanity.com/paper/2310.03722/) (2023)
- [From Conformal Predictions to Confidence Regions](https://mlsanity.com/paper/2405.18601/) (2024)
- [Fundamental bounds on efficiency-confidence trade-off for transductive conformal prediction](https://mlsanity.com/paper/2509.04631/) (2025)
- [E-Scores for (In)Correctness Assessment of Generative Model Outputs](https://mlsanity.com/paper/2510.25770/) (2025)
- [Sequential Structure-Sensitive Residual Diagnostics for PDE Inverse Problems](https://mlsanity.com/paper/2607.02101/) (2026)
- [NetEffect: Discovery and Exploitation of Generalized Network Effects](https://mlsanity.com/paper/2301.00270/) (2022)
- [Valid Inference for Machine Learning Model Parameters](https://mlsanity.com/paper/2302.10840/) (2023)
- [Perturbation-Assisted Sample Synthesis: A Novel Approach for Uncertainty Quantification](https://mlsanity.com/paper/2305.18671/) (2023)
- [Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors](https://mlsanity.com/paper/2401.15254/) (2024)

## 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.