290 citations · 1.8k across the 59 of their papers we have counts for
Showing 2012 · math.STShow all
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math.ST2012★ 6 cited
Estimation of Covariance Matrices under Sparsity Constraints
Philippe Rigollet, Alexandre Tsybakov
We prove optimal sparsity oracle inequalities for the estimation of covariance matrix under the Frobenius norm. In particular we explore various sparsity structures on the underlyi…
math.ST2012★ 51 cited
Deviation optimal learning using greedy Q-aggregation
Dong Dai, Philippe Rigollet, Tong Zhang
Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown…
math.ST2012★ 261 cited
Optimal detection of sparse principal components in high dimension
Quentin Berthet, Philippe Rigollet
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse e…