Learning Mixtures of Linear Classifiers

Yuekai Sun, Stratis Ioannidis, Andrea Montanari
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):721-729, 2014.

Abstract

We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable guarantees. We develop a simple method based on spectral techniques and a ‘mirroring’ trick, that discovers the subspace spanned by the classifiers’ parameter vectors. Under a probabilistic assumption on the feature vector distribution, we prove that this approach has nearly optimal statistical efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-sunb14, title = {Learning Mixtures of Linear Classifiers}, author = {Sun, Yuekai and Ioannidis, Stratis and Montanari, Andrea}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {721--729}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/sunb14.pdf}, url = {https://proceedings.mlr.press/v32/sunb14.html}, abstract = {We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable guarantees. We develop a simple method based on spectral techniques and a ‘mirroring’ trick, that discovers the subspace spanned by the classifiers’ parameter vectors. Under a probabilistic assumption on the feature vector distribution, we prove that this approach has nearly optimal statistical efficiency.} }
Endnote
%0 Conference Paper %T Learning Mixtures of Linear Classifiers %A Yuekai Sun %A Stratis Ioannidis %A Andrea Montanari %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-sunb14 %I PMLR %P 721--729 %U https://proceedings.mlr.press/v32/sunb14.html %V 32 %N 2 %X We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable guarantees. We develop a simple method based on spectral techniques and a ‘mirroring’ trick, that discovers the subspace spanned by the classifiers’ parameter vectors. Under a probabilistic assumption on the feature vector distribution, we prove that this approach has nearly optimal statistical efficiency.
RIS
TY - CPAPER TI - Learning Mixtures of Linear Classifiers AU - Yuekai Sun AU - Stratis Ioannidis AU - Andrea Montanari BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-sunb14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 721 EP - 729 L1 - http://proceedings.mlr.press/v32/sunb14.pdf UR - https://proceedings.mlr.press/v32/sunb14.html AB - We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable guarantees. We develop a simple method based on spectral techniques and a ‘mirroring’ trick, that discovers the subspace spanned by the classifiers’ parameter vectors. Under a probabilistic assumption on the feature vector distribution, we prove that this approach has nearly optimal statistical efficiency. ER -
APA
Sun, Y., Ioannidis, S. & Montanari, A.. (2014). Learning Mixtures of Linear Classifiers. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):721-729 Available from https://proceedings.mlr.press/v32/sunb14.html.

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