Compressed Maximum Likelihood
Yi Hao,u00a0Alon Orlitsky
Maximum likelihood (ML) is one of the most fundamental and general statistical estimation techniques. Inspired by recent advances in estimating distribution functionals, we propose $ extit{compressed maximum likelihood}$ (CML) that applies ML to the compressed samples. We then show that CML is sample-efficient for several essential learning tasks over both discrete and continuous domains, including learning densities with structures, estimating probability multisets, and inferring symmetric distribution functionals.
