Regularized Maximum Likelihood for Intrinsic Dimension Estimation

Mithun Das Gupta, Thomas Huang
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:228-235, 2010.

Abstract

We propose a new method for estimating the in- trinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We pro- pose a regularization scheme which is motivated by divergence minimization principles. We de- rive the estimator by a Poisson process approx- imation, argue about its convergence properties and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-gupta10a, title = {Regularized Maximum Likelihood for Intrinsic Dimension Estimation}, author = {Gupta, Mithun Das and Huang, Thomas}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {228--235}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/gupta10a/gupta10a.pdf}, url = {https://proceedings.mlr.press/r8/gupta10a.html}, abstract = {We propose a new method for estimating the in- trinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We pro- pose a regularization scheme which is motivated by divergence minimization principles. We de- rive the estimator by a Poisson process approx- imation, argue about its convergence properties and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Regularized Maximum Likelihood for Intrinsic Dimension Estimation %A Mithun Das Gupta %A Thomas Huang %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-gupta10a %I PMLR %P 228--235 %U https://proceedings.mlr.press/r8/gupta10a.html %V R8 %X We propose a new method for estimating the in- trinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We pro- pose a regularization scheme which is motivated by divergence minimization principles. We de- rive the estimator by a Poisson process approx- imation, argue about its convergence properties and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators. %Z Reissued by PMLR on 04 October 2026.
APA
Gupta, M.D. & Huang, T.. (2010). Regularized Maximum Likelihood for Intrinsic Dimension Estimation. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:228-235 Available from https://proceedings.mlr.press/r8/gupta10a.html. Reissued by PMLR on 04 October 2026.

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