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Mohamed NDAOUD (CREST) – "Interplay of minimax estimation and minimax support recovery under sparsity"
Time: 2:00 pm – 3:15 pm
Date: 28 th of January 2019
Place: Room 1003. ⚠ salle 1003 !
Mohamed NDAOUD (CREST) – “Interplay of minimax estimation and minimax support recovery under sparsity”
Abstract: We introduce the notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. Fixing the scale of the signal-to-noise ratio, we prove that the estimation error can be much smaller than the global minimax error. Taking advantage of the interplay between estimation and support recovery we achieve optimal performance for both problems simultaneously under orthogonal designs. We also construct a new optimal estimator for scaled minimax sparse estimation. Sharp results for the classical minimax risk are recovered as a consequence of our study. For general designs, we introduce a new framework based on algorithmic regularization where previous sharp results hold. Our analysis bridges the gap between optimization and statistical accuracy. The procedure we present achieves optimal statistical error faster than, for instance, classical algorithms for the Lasso. As a consequence, we present a new iterative algorithm for high-dimensional linear regression that is scaled minimax optimal, fast and adaptive.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM