Exploiting geometric structure in mixture proportion estimation with generalised Blanchard-Lee-Scott estimators

Henry Reeve, Ata Kabán
Proceedings of the 30th International Conference on Algorithmic Learning Theory, PMLR 98:682-699, 2019.

Abstract

Mixture proportion estimation is a building block in many weakly supervised classification tasks (missing labels, label noise, anomaly detection). Estimators with finite sample guarantees help analyse algorithms for such tasks, but so far only exist for Euclidean and Hilbert space data. We generalise the framework of Blanchard, Lee and Scott to allow extensions to other data types, and exemplify its use by deducing novel estimators for metric space data, and for randomly compressed Euclidean data – both of which make use of favourable geometry to tighten guarantees. Finally we demonstrate a theoretical link with the state of the art estimator specialised for Hilbert space data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v98-reeve19a, title = {Exploiting geometric structure in mixture proportion estimation with generalised Blanchard-Lee-Scott estimators}, author = {Reeve, Henry and Kab\'{a}n, Ata}, booktitle = {Proceedings of the 30th International Conference on Algorithmic Learning Theory}, pages = {682--699}, year = {2019}, editor = {Garivier, Aurélien and Kale, Satyen}, volume = {98}, series = {Proceedings of Machine Learning Research}, month = {22--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v98/reeve19a/reeve19a.pdf}, url = {https://proceedings.mlr.press/v98/reeve19a.html}, abstract = { Mixture proportion estimation is a building block in many weakly supervised classification tasks (missing labels, label noise, anomaly detection). Estimators with finite sample guarantees help analyse algorithms for such tasks, but so far only exist for Euclidean and Hilbert space data. We generalise the framework of Blanchard, Lee and Scott to allow extensions to other data types, and exemplify its use by deducing novel estimators for metric space data, and for randomly compressed Euclidean data – both of which make use of favourable geometry to tighten guarantees. Finally we demonstrate a theoretical link with the state of the art estimator specialised for Hilbert space data.} }
Endnote
%0 Conference Paper %T Exploiting geometric structure in mixture proportion estimation with generalised Blanchard-Lee-Scott estimators %A Henry Reeve %A Ata Kabán %B Proceedings of the 30th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Aurélien Garivier %E Satyen Kale %F pmlr-v98-reeve19a %I PMLR %P 682--699 %U https://proceedings.mlr.press/v98/reeve19a.html %V 98 %X Mixture proportion estimation is a building block in many weakly supervised classification tasks (missing labels, label noise, anomaly detection). Estimators with finite sample guarantees help analyse algorithms for such tasks, but so far only exist for Euclidean and Hilbert space data. We generalise the framework of Blanchard, Lee and Scott to allow extensions to other data types, and exemplify its use by deducing novel estimators for metric space data, and for randomly compressed Euclidean data – both of which make use of favourable geometry to tighten guarantees. Finally we demonstrate a theoretical link with the state of the art estimator specialised for Hilbert space data.
APA
Reeve, H. & Kabán, A.. (2019). Exploiting geometric structure in mixture proportion estimation with generalised Blanchard-Lee-Scott estimators. Proceedings of the 30th International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 98:682-699 Available from https://proceedings.mlr.press/v98/reeve19a.html.

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