Wiki Home
Likelihood-ratio test
Definition
A likelihood-ratio test decides between two hypotheses by computing the ratio of the observation’s probability under each and comparing it to a threshold. The Neyman-Pearson lemma gives the test its authority: among all tests with a given false-positive rate, thresholding the likelihood ratio achieves the highest true-positive rate (Neyman and Pearson, 1933). When a detection problem can be cast as distinguishing two known distributions, the likelihood-ratio test is optimal, and every other attack is an approximation to it.
The lemma’s premise is the catch: both distributions must be known. In practice they are estimated, either nonparametrically from samples or by fitting a parametric family such as a Gaussian. The quality of the test then rests on the quality of the estimate, and parametric assumptions matter most in the distribution tails, the regime that low false-positive operation depends on.
Papers that use this concept
- Membership Inference Attacks From First Principles — frames membership inference as a likelihood-ratio test between models trained with and without the target example; the attack is named for it.
- Extracting Training Data from Large Language Models — ranks candidate sequences by the target model’s perplexity relative to reference models, a likelihood-ratio style calibration of the membership signal.
See also
References
- Neyman, J. and Pearson, E. S. “On the Problem of the Most Efficient Tests of Statistical Hypotheses.” Philosophical Transactions of the Royal Society of London, 231(694-706), 1933.