Minimax rate of convergence and the performance of empirical risk minimization in phase retrieval

COUV_CAHIER_EGND_A30by Guillaume Lecué and Shahar Mendelson

We study the performance of Empirical Risk Minimization in both noisy and noiseless phase retrieval problems, indexed by subsets of Rn and relative to subgaussian sampling; that is, when the given data is yi = <ai, x0 >2 + wi for a subgaussian random vector a, independent subgaussian noise w and a fixed but unknown x0 that belongs to a given T⊂Rn

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