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

Henry W J Reeve, Ata Kaban

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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.
Original languageEnglish
Pages (from-to)682-699
Number of pages18
JournalProceedings of Machine Learning Research
Volume98
Publication statusPublished - 24 Mar 2019
EventInternational Conference on Algorithmic Learning Theory - Chicago, United States
Duration: 22 Mar 201924 Mar 2019
Conference number: 30
http://algorithmiclearningtheory.org/alt2019/

Keywords

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

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