Robust Structured Estimation with Single-Index Models

Sheng Chen, Arindam Banerjee
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:712-721, 2017.

Abstract

In this paper, we investigate general single-index models (SIMs) in high dimensions. Based on U-statistics, we propose two types of robust estimators for the recovery of model parameters, which can be viewed as generalizations of several existing algorithms for one-bit compressed sensing (1-bit CS). With minimal assumption on noise, the statistical guarantees are established for the generalized estimators under suitable conditions, which allow general structures of underlying parameter. Moreover, the proposed estimator is novelly instantiated for SIMs with monotone transfer function, and the obtained estimator can better leverage the monotonicity. Experimental results are provided to support our theoretical analyses.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-chen17a, title = {Robust Structured Estimation with Single-Index Models}, author = {Sheng Chen and Arindam Banerjee}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {712--721}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/chen17a/chen17a.pdf}, url = {https://proceedings.mlr.press/v70/chen17a.html}, abstract = {In this paper, we investigate general single-index models (SIMs) in high dimensions. Based on U-statistics, we propose two types of robust estimators for the recovery of model parameters, which can be viewed as generalizations of several existing algorithms for one-bit compressed sensing (1-bit CS). With minimal assumption on noise, the statistical guarantees are established for the generalized estimators under suitable conditions, which allow general structures of underlying parameter. Moreover, the proposed estimator is novelly instantiated for SIMs with monotone transfer function, and the obtained estimator can better leverage the monotonicity. Experimental results are provided to support our theoretical analyses.} }
Endnote
%0 Conference Paper %T Robust Structured Estimation with Single-Index Models %A Sheng Chen %A Arindam Banerjee %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-chen17a %I PMLR %P 712--721 %U https://proceedings.mlr.press/v70/chen17a.html %V 70 %X In this paper, we investigate general single-index models (SIMs) in high dimensions. Based on U-statistics, we propose two types of robust estimators for the recovery of model parameters, which can be viewed as generalizations of several existing algorithms for one-bit compressed sensing (1-bit CS). With minimal assumption on noise, the statistical guarantees are established for the generalized estimators under suitable conditions, which allow general structures of underlying parameter. Moreover, the proposed estimator is novelly instantiated for SIMs with monotone transfer function, and the obtained estimator can better leverage the monotonicity. Experimental results are provided to support our theoretical analyses.
APA
Chen, S. & Banerjee, A.. (2017). Robust Structured Estimation with Single-Index Models. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:712-721 Available from https://proceedings.mlr.press/v70/chen17a.html.

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