A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions

Jayadev Acharya, Hirakendu Das, Alon Orlitsky, Ananda Theertha Suresh
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:11-21, 2017.

Abstract

Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sample-optimal for all the above properties.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-acharya17a, title = {A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions}, author = {Jayadev Acharya and Hirakendu Das and Alon Orlitsky and Ananda Theertha Suresh}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {11--21}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/acharya17a/acharya17a.pdf}, url = {https://proceedings.mlr.press/v70/acharya17a.html}, abstract = {Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sample-optimal for all the above properties.} }
Endnote
%0 Conference Paper %T A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions %A Jayadev Acharya %A Hirakendu Das %A Alon Orlitsky %A Ananda Theertha Suresh %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-acharya17a %I PMLR %P 11--21 %U https://proceedings.mlr.press/v70/acharya17a.html %V 70 %X Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sample-optimal for all the above properties.
APA
Acharya, J., Das, H., Orlitsky, A. & Suresh, A.T.. (2017). A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:11-21 Available from https://proceedings.mlr.press/v70/acharya17a.html.

Related Material