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# Compressed Maximum Likelihood

*Proceedings of the 38th International Conference on Machine Learning*, PMLR 139:4085-4095, 2021.

#### Abstract

Maximum likelihood (ML) is one of the most fundamental and general statistical estimation techniques. Inspired by recent advances in estimating distribution functionals, we propose $\textit{compressed maximum likelihood}$ (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.