Rates of estimation for determinantal point processes

Victor-Emmanuel Brunel, Ankur Moitra, Philippe Rigollet, John Urschel
Proceedings of the 2017 Conference on Learning Theory, PMLR 65:343-345, 2017.

Abstract

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of the maximum likelihood estimator (MLE) have received little attention. In this paper, we study the local geometry of the expected log-likelihood function to prove several rates of convergence for the MLE. We also give a complete characterization of the case where the MLE converges at a parametric rate. Even in the latter case, we also exhibit a potential curse of dimensionality where the asymptotic variance of the MLE is exponentially large in the dimension of the problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v65-brunel17a, title = {Rates of estimation for determinantal point processes}, author = {Brunel, Victor-Emmanuel and Moitra, Ankur and Rigollet, Philippe and Urschel, John}, booktitle = {Proceedings of the 2017 Conference on Learning Theory}, pages = {343--345}, year = {2017}, editor = {Kale, Satyen and Shamir, Ohad}, volume = {65}, series = {Proceedings of Machine Learning Research}, month = {07--10 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v65/brunel17a/brunel17a.pdf}, url = {https://proceedings.mlr.press/v65/brunel17a.html}, abstract = {Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of the maximum likelihood estimator (MLE) have received little attention. In this paper, we study the local geometry of the expected log-likelihood function to prove several rates of convergence for the MLE. We also give a complete characterization of the case where the MLE converges at a parametric rate. Even in the latter case, we also exhibit a potential curse of dimensionality where the asymptotic variance of the MLE is exponentially large in the dimension of the problem.} }
Endnote
%0 Conference Paper %T Rates of estimation for determinantal point processes %A Victor-Emmanuel Brunel %A Ankur Moitra %A Philippe Rigollet %A John Urschel %B Proceedings of the 2017 Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2017 %E Satyen Kale %E Ohad Shamir %F pmlr-v65-brunel17a %I PMLR %P 343--345 %U https://proceedings.mlr.press/v65/brunel17a.html %V 65 %X Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of the maximum likelihood estimator (MLE) have received little attention. In this paper, we study the local geometry of the expected log-likelihood function to prove several rates of convergence for the MLE. We also give a complete characterization of the case where the MLE converges at a parametric rate. Even in the latter case, we also exhibit a potential curse of dimensionality where the asymptotic variance of the MLE is exponentially large in the dimension of the problem.
APA
Brunel, V., Moitra, A., Rigollet, P. & Urschel, J.. (2017). Rates of estimation for determinantal point processes. Proceedings of the 2017 Conference on Learning Theory, in Proceedings of Machine Learning Research 65:343-345 Available from https://proceedings.mlr.press/v65/brunel17a.html.

Related Material