Year: 2026
Type: preprint
Abstract: For Gaussian location mixtures with identity covariance, we prove that the nonparametric maximum likelihood estimator of the mixing distribution is unique for Lebesgue-almost every dataset, for every sample size and dimension. In particular, uniqueness holds almost surely whenever the joint distribution of the observations is absolutely continuous. The proof uses the finite-support theorem for Gaussian location NPMLEs and almost-everywhere differentiability of the optimal log-likelihood. Wherever this optimal value is differentiable, all NPMLEs have the same density derivatives at the observations. A minimal linear dependence among Gaussian evaluation vectors then rules out distinct solutions. An appendix extends the result to arbitrary fixed, known, observation-specific positive-definite covariances.
Source: arXiv (Cornell University)
Author: Wang, Haiyang
Institution: Yale University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214030217