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Robust Structured Estimation with Single-Index Models
Sheng Chen · Arindam Banerjee

Tue Aug 08 06:42 PM -- 07:00 PM (PDT) @ C4.4

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.

Author Information

Sheng Chen (University of Minnesota)
Arindam Banerjee (University of Minnesota)
Arindam Banerjee

Arindam Banerjee is a Founder Professor at the Department of Computer Science, University of Illinois Urbana-Champaign. His research interests are in machine learning. His current research focuses on computational and statistical aspects of over-parameterized models including deep learning, spatial and temporal data analysis, generative models, and sequential decision making problems. His work also focuses on applications of machine learning in complex real-world and scientific domains including problems in climate science and ecology. He has won several awards, including the NSF CAREER award, the IBM Faculty Award, and six best paper awards in top-tier venues.

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