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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Colleges, School and Institutes

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.

Details

Original languageEnglish
Title of host publication30th International Conference on Algorithmic Learning Theory (ALT'19)
Publication statusPublished - 2019
Event30th International Conference on Algorithmic Learning Theory (ALT'19) - Chicago, United States
Duration: 22 Mar 201924 Mar 2019

Publication series

NameProceedings of Machine Learning Research
Volume98
ISSN (Electronic)2640-3498

Conference

Conference30th International Conference on Algorithmic Learning Theory (ALT'19)
CountryUnited States
CityChicago
Period22/03/1924/03/19

Keywords

  • Mixture proportion estimation, metric spaces, covering dimension, randonm projections, Gaussian width