Universal Inference
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.
Code (0)
등록된 구현이 없습니다.
Tasks
validSimilar Papers 제목 키워드 기반
Optimal Universal Quantum Encoding for Statistical Inference
Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statist…
Inference Compilation and Universal Probabilistic Programming
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the streng…
Probabilistic ProgrammingOn The Universality of Diagrams for Causal Inference and The Causal Reproducing Property
We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More fo…
Causal InferenceLEMMABuilding Efficient Universal Classifiers with Natural Language Inference
Generative Large Language Models (LLMs) have become the mainstream choice for fewshot and zeroshot learning thanks to the universality of text generation. Many users, however, do not need the broad capabilities of genera…
ClassificationNatural Language Inferencetext-classificationText Classification+1Distilling Morphology-Conditioned Hypernetworks for Efficient Universal Morphology Control
Learning a universal policy across different robot morphologies can significantly improve learning efficiency and enable zero-shot generalization to unseen morphologies. However, learning a highly performant universal po…
Zero-shot Generalization