TY - JOUR
T1 - Alternating estimation for structured high-dimensional multi-response models
AU - Chen, Sheng
AU - Banerjee, Arindam
N1 - Funding Information:
The research was supported by NSF grants IIS-1563950, IIS-1447566, IIS-1447574, IIS-1422557, CCF-1451986, CNS-1314560, IIS-0953274, IIS-1029711, NASA grant NNX12AQ39A, and gifts from Adobe, IBM, and Yahoo.
Publisher Copyright:
© 2017 Neural information processing systems foundation. All rights reserved.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - We consider the problem of learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among different responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters based on the generalized Dantzig selector (GDS). Under suitable sample size and resampling assumptions, we show that the error of the estimates generated by AltEst, with high probability, converges linearly to certain minimum achievable level, which can be tersely expressed by a few geometric measures, such as Gaussian width of sets related to the parameter structure. To the best of our knowledge, this is the first non-asymptotic statistical guarantee for such AltEst-type algorithm applied to estimation with general structures.
AB - We consider the problem of learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among different responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters based on the generalized Dantzig selector (GDS). Under suitable sample size and resampling assumptions, we show that the error of the estimates generated by AltEst, with high probability, converges linearly to certain minimum achievable level, which can be tersely expressed by a few geometric measures, such as Gaussian width of sets related to the parameter structure. To the best of our knowledge, this is the first non-asymptotic statistical guarantee for such AltEst-type algorithm applied to estimation with general structures.
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M3 - Conference article
AN - SCOPUS:85047001685
SN - 1049-5258
VL - 2017-December
SP - 2839
EP - 2849
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 31st Annual Conference on Neural Information Processing Systems, NIPS 2017
Y2 - 4 December 2017 through 9 December 2017
ER -