Oberwolfach Reports

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Volume 15, Issue 1, 2018, pp. 591–630
DOI: 10.4171/OWR/2018/12

Published online: 2019-01-04

Statistical Inference for Structured High-dimensional Models

Anatoli Juditsky[1], Alexandre B. Tsybakov[2] and Cun-Hui Zhang[3]

(1) Université Grenoble-Alpes, Saint-Martin-d’Hères, France
(2) CREST, Malakoff, France
(3) Rutgers University, Piscataway, USA

High-dimensional statistical inference is a newly emerged direction of statistical science in the 21 century. Its importance is due to the increasing dimensionality and complexity of models needed to process and understand the modern real world data. The main idea making possible meaningful inference about such models is to assume suitable lower dimensional underlying structure or low-dimensional approximations, for which the error can be reasonably controlled. Several types of such structures have been recently introduced including sparse high-dimensional regression, sparse and/or low rank matrix models, matrix completion models, dictionary learning, network models (stochastic block model, mixed membership models) and more. The workshop focused on recent developments in structured sequence and regression models, matrix and tensor estimation, robustness, statistical learning in complex settings, network data, and topic models.

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Juditsky Anatoli, Tsybakov Alexandre, Zhang Cun-Hui: Statistical Inference for Structured High-dimensional Models. Oberwolfach Rep. 15 (2018), 591-630. doi: 10.4171/OWR/2018/12