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.
|Original language||English (US)|
|Number of pages||11|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2017|
|Event||31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States|
Duration: Dec 4 2017 → Dec 9 2017
Bibliographical noteFunding 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.
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